glucat  0.8.2
PyClical.cpp
Go to the documentation of this file.
1 /* Generated by Cython 0.23.4 */
2 
3 /* BEGIN: Cython Metadata
4 {
5  "distutils": {
6  "depends": [
7  "PyClical.h"
8  ],
9  "extra_compile_args": [
10  "-I.",
11  "-I..",
12  "-fno-strict-aliasing",
13  "-Wno-unused",
14  "-Wall",
15  "-std=c++11",
16  "-g",
17  "-O3",
18  "-fmessage-length=0",
19  "-grecord-gcc-switches",
20  "-O2",
21  "-Wall",
22  "-D_FORTIFY_SOURCE=2",
23  "-fstack-protector",
24  "-funwind-tables",
25  "-fasynchronous-unwind-tables",
26  "-march=native",
27  "-finline-limit=4000",
28  "--param",
29  "inline-unit-growth=200",
30  "-funroll-loops",
31  "-fvariable-expansion-in-unroller",
32  "-DNDEBUG",
33  "-DHAVE_BITS_WORDSIZE_H",
34  "-D_GLUCAT_USE_STD_UNORDERED_MAP",
35  "-D_GLUCAT_USE_DENSE_MATRICES",
36  "-D_GLUCAT_CHECK_ISNAN",
37  "-Wno-unused-local-typedefs",
38  "-Wno-misleading-indentation",
39  "-fno-check-new",
40  "-fexceptions"
41  ],
42  "include_dirs": [
43  ".",
44  ".."
45  ],
46  "language": "c++"
47  }
48 }
49 END: Cython Metadata */
50 
51 #define PY_SSIZE_T_CLEAN
52 #include "Python.h"
53 #ifndef Py_PYTHON_H
54  #error Python headers needed to compile C extensions, please install development version of Python.
55 #elif PY_VERSION_HEX < 0x02060000 || (0x03000000 <= PY_VERSION_HEX && PY_VERSION_HEX < 0x03020000)
56  #error Cython requires Python 2.6+ or Python 3.2+.
57 #else
58 #define CYTHON_ABI "0_23_4"
59 #include <stddef.h>
60 #ifndef offsetof
61 #define offsetof(type, member) ( (size_t) & ((type*)0) -> member )
62 #endif
63 #if !defined(WIN32) && !defined(MS_WINDOWS)
64  #ifndef __stdcall
65  #define __stdcall
66  #endif
67  #ifndef __cdecl
68  #define __cdecl
69  #endif
70  #ifndef __fastcall
71  #define __fastcall
72  #endif
73 #endif
74 #ifndef DL_IMPORT
75  #define DL_IMPORT(t) t
76 #endif
77 #ifndef DL_EXPORT
78  #define DL_EXPORT(t) t
79 #endif
80 #ifndef PY_LONG_LONG
81  #define PY_LONG_LONG LONG_LONG
82 #endif
83 #ifndef Py_HUGE_VAL
84  #define Py_HUGE_VAL HUGE_VAL
85 #endif
86 #ifdef PYPY_VERSION
87 #define CYTHON_COMPILING_IN_PYPY 1
88 #define CYTHON_COMPILING_IN_CPYTHON 0
89 #else
90 #define CYTHON_COMPILING_IN_PYPY 0
91 #define CYTHON_COMPILING_IN_CPYTHON 1
92 #endif
93 #if !defined(CYTHON_USE_PYLONG_INTERNALS) && CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x02070000
94 #define CYTHON_USE_PYLONG_INTERNALS 1
95 #endif
96 #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x02070600 && !defined(Py_OptimizeFlag)
97 #define Py_OptimizeFlag 0
98 #endif
99 #define __PYX_BUILD_PY_SSIZE_T "n"
100 #define CYTHON_FORMAT_SSIZE_T "z"
101 #if PY_MAJOR_VERSION < 3
102  #define __Pyx_BUILTIN_MODULE_NAME "__builtin__"
103  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
104  PyCode_New(a+k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
105  #define __Pyx_DefaultClassType PyClass_Type
106 #else
107  #define __Pyx_BUILTIN_MODULE_NAME "builtins"
108  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
109  PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
110  #define __Pyx_DefaultClassType PyType_Type
111 #endif
112 #ifndef Py_TPFLAGS_CHECKTYPES
113  #define Py_TPFLAGS_CHECKTYPES 0
114 #endif
115 #ifndef Py_TPFLAGS_HAVE_INDEX
116  #define Py_TPFLAGS_HAVE_INDEX 0
117 #endif
118 #ifndef Py_TPFLAGS_HAVE_NEWBUFFER
119  #define Py_TPFLAGS_HAVE_NEWBUFFER 0
120 #endif
121 #ifndef Py_TPFLAGS_HAVE_FINALIZE
122  #define Py_TPFLAGS_HAVE_FINALIZE 0
123 #endif
124 #if PY_VERSION_HEX > 0x03030000 && defined(PyUnicode_KIND)
125  #define CYTHON_PEP393_ENABLED 1
126  #define __Pyx_PyUnicode_READY(op) (likely(PyUnicode_IS_READY(op)) ?\
127  0 : _PyUnicode_Ready((PyObject *)(op)))
128  #define __Pyx_PyUnicode_GET_LENGTH(u) PyUnicode_GET_LENGTH(u)
129  #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_READ_CHAR(u, i)
130  #define __Pyx_PyUnicode_KIND(u) PyUnicode_KIND(u)
131  #define __Pyx_PyUnicode_DATA(u) PyUnicode_DATA(u)
132  #define __Pyx_PyUnicode_READ(k, d, i) PyUnicode_READ(k, d, i)
133 #else
134  #define CYTHON_PEP393_ENABLED 0
135  #define __Pyx_PyUnicode_READY(op) (0)
136  #define __Pyx_PyUnicode_GET_LENGTH(u) PyUnicode_GET_SIZE(u)
137  #define __Pyx_PyUnicode_READ_CHAR(u, i) ((Py_UCS4)(PyUnicode_AS_UNICODE(u)[i]))
138  #define __Pyx_PyUnicode_KIND(u) (sizeof(Py_UNICODE))
139  #define __Pyx_PyUnicode_DATA(u) ((void*)PyUnicode_AS_UNICODE(u))
140  #define __Pyx_PyUnicode_READ(k, d, i) ((void)(k), (Py_UCS4)(((Py_UNICODE*)d)[i]))
141 #endif
142 #if CYTHON_COMPILING_IN_PYPY
143  #define __Pyx_PyUnicode_Concat(a, b) PyNumber_Add(a, b)
144  #define __Pyx_PyUnicode_ConcatSafe(a, b) PyNumber_Add(a, b)
145 #else
146  #define __Pyx_PyUnicode_Concat(a, b) PyUnicode_Concat(a, b)
147  #define __Pyx_PyUnicode_ConcatSafe(a, b) ((unlikely((a) == Py_None) || unlikely((b) == Py_None)) ?\
148  PyNumber_Add(a, b) : __Pyx_PyUnicode_Concat(a, b))
149 #endif
150 #if CYTHON_COMPILING_IN_PYPY && !defined(PyUnicode_Contains)
151  #define PyUnicode_Contains(u, s) PySequence_Contains(u, s)
152 #endif
153 #define __Pyx_PyString_FormatSafe(a, b) ((unlikely((a) == Py_None)) ? PyNumber_Remainder(a, b) : __Pyx_PyString_Format(a, b))
154 #define __Pyx_PyUnicode_FormatSafe(a, b) ((unlikely((a) == Py_None)) ? PyNumber_Remainder(a, b) : PyUnicode_Format(a, b))
155 #if PY_MAJOR_VERSION >= 3
156  #define __Pyx_PyString_Format(a, b) PyUnicode_Format(a, b)
157 #else
158  #define __Pyx_PyString_Format(a, b) PyString_Format(a, b)
159 #endif
160 #if PY_MAJOR_VERSION >= 3
161  #define PyBaseString_Type PyUnicode_Type
162  #define PyStringObject PyUnicodeObject
163  #define PyString_Type PyUnicode_Type
164  #define PyString_Check PyUnicode_Check
165  #define PyString_CheckExact PyUnicode_CheckExact
166 #endif
167 #if PY_MAJOR_VERSION >= 3
168  #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj)
169  #define __Pyx_PyBaseString_CheckExact(obj) PyUnicode_CheckExact(obj)
170 #else
171  #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj))
172  #define __Pyx_PyBaseString_CheckExact(obj) (PyString_CheckExact(obj) || PyUnicode_CheckExact(obj))
173 #endif
174 #ifndef PySet_CheckExact
175  #define PySet_CheckExact(obj) (Py_TYPE(obj) == &PySet_Type)
176 #endif
177 #define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
178 #if PY_MAJOR_VERSION >= 3
179  #define PyIntObject PyLongObject
180  #define PyInt_Type PyLong_Type
181  #define PyInt_Check(op) PyLong_Check(op)
182  #define PyInt_CheckExact(op) PyLong_CheckExact(op)
183  #define PyInt_FromString PyLong_FromString
184  #define PyInt_FromUnicode PyLong_FromUnicode
185  #define PyInt_FromLong PyLong_FromLong
186  #define PyInt_FromSize_t PyLong_FromSize_t
187  #define PyInt_FromSsize_t PyLong_FromSsize_t
188  #define PyInt_AsLong PyLong_AsLong
189  #define PyInt_AS_LONG PyLong_AS_LONG
190  #define PyInt_AsSsize_t PyLong_AsSsize_t
191  #define PyInt_AsUnsignedLongMask PyLong_AsUnsignedLongMask
192  #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask
193  #define PyNumber_Int PyNumber_Long
194 #endif
195 #if PY_MAJOR_VERSION >= 3
196  #define PyBoolObject PyLongObject
197 #endif
198 #if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY
199  #ifndef PyUnicode_InternFromString
200  #define PyUnicode_InternFromString(s) PyUnicode_FromString(s)
201  #endif
202 #endif
203 #if PY_VERSION_HEX < 0x030200A4
204  typedef long Py_hash_t;
205  #define __Pyx_PyInt_FromHash_t PyInt_FromLong
206  #define __Pyx_PyInt_AsHash_t PyInt_AsLong
207 #else
208  #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t
209  #define __Pyx_PyInt_AsHash_t PyInt_AsSsize_t
210 #endif
211 #if PY_MAJOR_VERSION >= 3
212  #define __Pyx_PyMethod_New(func, self, klass) ((self) ? PyMethod_New(func, self) : PyInstanceMethod_New(func))
213 #else
214  #define __Pyx_PyMethod_New(func, self, klass) PyMethod_New(func, self, klass)
215 #endif
216 #if PY_VERSION_HEX >= 0x030500B1
217 #define __Pyx_PyAsyncMethodsStruct PyAsyncMethods
218 #define __Pyx_PyType_AsAsync(obj) (Py_TYPE(obj)->tp_as_async)
219 #elif CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
220 typedef struct {
221  unaryfunc am_await;
222  unaryfunc am_aiter;
223  unaryfunc am_anext;
224 } __Pyx_PyAsyncMethodsStruct;
225 #define __Pyx_PyType_AsAsync(obj) ((__Pyx_PyAsyncMethodsStruct*) (Py_TYPE(obj)->tp_reserved))
226 #else
227 #define __Pyx_PyType_AsAsync(obj) NULL
228 #endif
229 #ifndef CYTHON_RESTRICT
230  #if defined(__GNUC__)
231  #define CYTHON_RESTRICT __restrict__
232  #elif defined(_MSC_VER) && _MSC_VER >= 1400
233  #define CYTHON_RESTRICT __restrict
234  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
235  #define CYTHON_RESTRICT restrict
236  #else
237  #define CYTHON_RESTRICT
238  #endif
239 #endif
240 #define __Pyx_void_to_None(void_result) ((void)(void_result), Py_INCREF(Py_None), Py_None)
241 
242 #ifndef __cplusplus
243  #error "Cython files generated with the C++ option must be compiled with a C++ compiler."
244 #endif
245 #ifndef CYTHON_INLINE
246  #define CYTHON_INLINE inline
247 #endif
248 template<typename T>
249 void __Pyx_call_destructor(T& x) {
250  x.~T();
251 }
252 template<typename T>
253 class __Pyx_FakeReference {
254  public:
255  __Pyx_FakeReference() : ptr(NULL) { }
256  __Pyx_FakeReference(const T& ref) : ptr(const_cast<T*>(&ref)) { }
257  T *operator->() { return ptr; }
258  operator T&() { return *ptr; }
259  private:
260  T *ptr;
261 };
262 
263 #if defined(WIN32) || defined(MS_WINDOWS)
264  #define _USE_MATH_DEFINES
265 #endif
266 #include <math.h>
267 #ifdef NAN
268 #define __PYX_NAN() ((float) NAN)
269 #else
270 static CYTHON_INLINE float __PYX_NAN() {
271  float value;
272  memset(&value, 0xFF, sizeof(value));
273  return value;
274 }
275 #endif
276 
277 
278 #if PY_MAJOR_VERSION >= 3
279  #define __Pyx_PyNumber_Divide(x,y) PyNumber_TrueDivide(x,y)
280  #define __Pyx_PyNumber_InPlaceDivide(x,y) PyNumber_InPlaceTrueDivide(x,y)
281 #else
282  #define __Pyx_PyNumber_Divide(x,y) PyNumber_Divide(x,y)
283  #define __Pyx_PyNumber_InPlaceDivide(x,y) PyNumber_InPlaceDivide(x,y)
284 #endif
285 
286 #ifndef __PYX_EXTERN_C
287  #ifdef __cplusplus
288  #define __PYX_EXTERN_C extern "C"
289  #else
290  #define __PYX_EXTERN_C extern
291  #endif
292 #endif
293 
294 #define __PYX_HAVE__PyClical
295 #define __PYX_HAVE_API__PyClical
296 #include <vector>
297 #include "ios"
298 #include "new"
299 #include "stdexcept"
300 #include "typeinfo"
301 #include "PyClical.h"
302 #ifdef _OPENMP
303 #include <omp.h>
304 #endif /* _OPENMP */
305 
306 #ifdef PYREX_WITHOUT_ASSERTIONS
307 #define CYTHON_WITHOUT_ASSERTIONS
308 #endif
309 
310 #ifndef CYTHON_UNUSED
311 # if defined(__GNUC__)
312 # if !(defined(__cplusplus)) || (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4))
313 # define CYTHON_UNUSED __attribute__ ((__unused__))
314 # else
315 # define CYTHON_UNUSED
316 # endif
317 # elif defined(__ICC) || (defined(__INTEL_COMPILER) && !defined(_MSC_VER))
318 # define CYTHON_UNUSED __attribute__ ((__unused__))
319 # else
320 # define CYTHON_UNUSED
321 # endif
322 #endif
323 #ifndef CYTHON_NCP_UNUSED
324 # if CYTHON_COMPILING_IN_CPYTHON
325 # define CYTHON_NCP_UNUSED
326 # else
327 # define CYTHON_NCP_UNUSED CYTHON_UNUSED
328 # endif
329 #endif
330 typedef struct {PyObject **p; char *s; const Py_ssize_t n; const char* encoding;
331  const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry;
332 
333 #define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0
334 #define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT 0
335 #define __PYX_DEFAULT_STRING_ENCODING ""
336 #define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
337 #define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
338 #define __Pyx_uchar_cast(c) ((unsigned char)c)
339 #define __Pyx_long_cast(x) ((long)x)
340 #define __Pyx_fits_Py_ssize_t(v, type, is_signed) (\
341  (sizeof(type) < sizeof(Py_ssize_t)) ||\
342  (sizeof(type) > sizeof(Py_ssize_t) &&\
343  likely(v < (type)PY_SSIZE_T_MAX ||\
344  v == (type)PY_SSIZE_T_MAX) &&\
345  (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||\
346  v == (type)PY_SSIZE_T_MIN))) ||\
347  (sizeof(type) == sizeof(Py_ssize_t) &&\
348  (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||\
349  v == (type)PY_SSIZE_T_MAX))) )
350 #if defined (__cplusplus) && __cplusplus >= 201103L
351  #include <cstdlib>
352  #define __Pyx_sst_abs(value) std::abs(value)
353 #elif SIZEOF_INT >= SIZEOF_SIZE_T
354  #define __Pyx_sst_abs(value) abs(value)
355 #elif SIZEOF_LONG >= SIZEOF_SIZE_T
356  #define __Pyx_sst_abs(value) labs(value)
357 #elif defined (_MSC_VER) && defined (_M_X64)
358  #define __Pyx_sst_abs(value) _abs64(value)
359 #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
360  #define __Pyx_sst_abs(value) llabs(value)
361 #elif defined (__GNUC__)
362  #define __Pyx_sst_abs(value) __builtin_llabs(value)
363 #else
364  #define __Pyx_sst_abs(value) ((value<0) ? -value : value)
365 #endif
366 static CYTHON_INLINE char* __Pyx_PyObject_AsString(PyObject*);
367 static CYTHON_INLINE char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);
368 #define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s))
369 #define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)
370 #define __Pyx_PyBytes_FromString PyBytes_FromString
371 #define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize
372 static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*);
373 #if PY_MAJOR_VERSION < 3
374  #define __Pyx_PyStr_FromString __Pyx_PyBytes_FromString
375  #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
376 #else
377  #define __Pyx_PyStr_FromString __Pyx_PyUnicode_FromString
378  #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize
379 #endif
380 #define __Pyx_PyObject_AsSString(s) ((signed char*) __Pyx_PyObject_AsString(s))
381 #define __Pyx_PyObject_AsUString(s) ((unsigned char*) __Pyx_PyObject_AsString(s))
382 #define __Pyx_PyObject_FromCString(s) __Pyx_PyObject_FromString((const char*)s)
383 #define __Pyx_PyBytes_FromCString(s) __Pyx_PyBytes_FromString((const char*)s)
384 #define __Pyx_PyByteArray_FromCString(s) __Pyx_PyByteArray_FromString((const char*)s)
385 #define __Pyx_PyStr_FromCString(s) __Pyx_PyStr_FromString((const char*)s)
386 #define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s)
387 #if PY_MAJOR_VERSION < 3
388 static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u)
389 {
390  const Py_UNICODE *u_end = u;
391  while (*u_end++) ;
392  return (size_t)(u_end - u - 1);
393 }
394 #else
395 #define __Pyx_Py_UNICODE_strlen Py_UNICODE_strlen
396 #endif
397 #define __Pyx_PyUnicode_FromUnicode(u) PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u))
398 #define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode
399 #define __Pyx_PyUnicode_AsUnicode PyUnicode_AsUnicode
400 #define __Pyx_NewRef(obj) (Py_INCREF(obj), obj)
401 #define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None)
402 #define __Pyx_PyBool_FromLong(b) ((b) ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False))
403 static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
404 static CYTHON_INLINE PyObject* __Pyx_PyNumber_Int(PyObject* x);
405 static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
406 static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);
407 #if CYTHON_COMPILING_IN_CPYTHON
408 #define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))
409 #else
410 #define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)
411 #endif
412 #define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x))
413 #if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
414 static int __Pyx_sys_getdefaultencoding_not_ascii;
415 static int __Pyx_init_sys_getdefaultencoding_params(void) {
416  PyObject* sys;
417  PyObject* default_encoding = NULL;
418  PyObject* ascii_chars_u = NULL;
419  PyObject* ascii_chars_b = NULL;
420  const char* default_encoding_c;
421  sys = PyImport_ImportModule("sys");
422  if (!sys) goto bad;
423  default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL);
424  Py_DECREF(sys);
425  if (!default_encoding) goto bad;
426  default_encoding_c = PyBytes_AsString(default_encoding);
427  if (!default_encoding_c) goto bad;
428  if (strcmp(default_encoding_c, "ascii") == 0) {
429  __Pyx_sys_getdefaultencoding_not_ascii = 0;
430  } else {
431  char ascii_chars[128];
432  int c;
433  for (c = 0; c < 128; c++) {
434  ascii_chars[c] = c;
435  }
436  __Pyx_sys_getdefaultencoding_not_ascii = 1;
437  ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL);
438  if (!ascii_chars_u) goto bad;
439  ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL);
440  if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) {
441  PyErr_Format(
442  PyExc_ValueError,
443  "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.",
444  default_encoding_c);
445  goto bad;
446  }
447  Py_DECREF(ascii_chars_u);
448  Py_DECREF(ascii_chars_b);
449  }
450  Py_DECREF(default_encoding);
451  return 0;
452 bad:
453  Py_XDECREF(default_encoding);
454  Py_XDECREF(ascii_chars_u);
455  Py_XDECREF(ascii_chars_b);
456  return -1;
457 }
458 #endif
459 #if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3
460 #define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL)
461 #else
462 #define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL)
463 #if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
464 static char* __PYX_DEFAULT_STRING_ENCODING;
465 static int __Pyx_init_sys_getdefaultencoding_params(void) {
466  PyObject* sys;
467  PyObject* default_encoding = NULL;
468  char* default_encoding_c;
469  sys = PyImport_ImportModule("sys");
470  if (!sys) goto bad;
471  default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL);
472  Py_DECREF(sys);
473  if (!default_encoding) goto bad;
474  default_encoding_c = PyBytes_AsString(default_encoding);
475  if (!default_encoding_c) goto bad;
476  __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c));
477  if (!__PYX_DEFAULT_STRING_ENCODING) goto bad;
478  strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c);
479  Py_DECREF(default_encoding);
480  return 0;
481 bad:
482  Py_XDECREF(default_encoding);
483  return -1;
484 }
485 #endif
486 #endif
487 
488 
489 /* Test for GCC > 2.95 */
490 #if defined(__GNUC__) && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95)))
491  #define likely(x) __builtin_expect(!!(x), 1)
492  #define unlikely(x) __builtin_expect(!!(x), 0)
493 #else /* !__GNUC__ or GCC < 2.95 */
494  #define likely(x) (x)
495  #define unlikely(x) (x)
496 #endif /* __GNUC__ */
497 
498 static PyObject *__pyx_m;
499 static PyObject *__pyx_d;
500 static PyObject *__pyx_b;
501 static PyObject *__pyx_empty_tuple;
502 static PyObject *__pyx_empty_bytes;
503 static int __pyx_lineno;
504 static int __pyx_clineno = 0;
505 static const char * __pyx_cfilenm= __FILE__;
506 static const char *__pyx_filename;
507 
508 
509 static const char *__pyx_f[] = {
510  "PyClical.pyx",
511 };
512 
513 /*--- Type declarations ---*/
514 struct __pyx_obj_8PyClical_index_set;
515 struct __pyx_obj_8PyClical_clifford;
516 struct __pyx_obj_8PyClical___pyx_scope_struct____iter__;
517 struct __pyx_opt_args_8PyClical_sqrt;
518 struct __pyx_opt_args_8PyClical_log;
519 struct __pyx_opt_args_8PyClical_cos;
520 struct __pyx_opt_args_8PyClical_acos;
521 struct __pyx_opt_args_8PyClical_acosh;
522 struct __pyx_opt_args_8PyClical_sin;
523 struct __pyx_opt_args_8PyClical_asin;
524 struct __pyx_opt_args_8PyClical_asinh;
525 struct __pyx_opt_args_8PyClical_tan;
526 struct __pyx_opt_args_8PyClical_atan;
527 struct __pyx_opt_args_8PyClical_atanh;
528 struct __pyx_opt_args_8PyClical_random_clifford;
529 
530 /* "PyClical.pyx":1542
531  * return clifford().wrap( glucat.complexifier(toClifford(obj)) )
532  *
533  * cpdef inline sqrt(obj, i = None): # <<<<<<<<<<<<<<
534  * """
535  * Square root of multivector with optional complexifier.
536  */
537 struct __pyx_opt_args_8PyClical_sqrt {
538  int __pyx_n;
539  PyObject *i;
540 };
541 
542 /* "PyClical.pyx":1579
543  * return clifford().wrap( glucat.exp(toClifford(obj)) )
544  *
545  * cpdef inline log(obj,i = None): # <<<<<<<<<<<<<<
546  * """
547  * Natural logarithm of multivector with optional complexifier.
548  */
549 struct __pyx_opt_args_8PyClical_log {
550  int __pyx_n;
551  PyObject *i;
552 };
553 
554 /* "PyClical.pyx":1602
555  * return clifford().wrap( glucat.log(toClifford(obj)) )
556  *
557  * cpdef inline cos(obj,i = None): # <<<<<<<<<<<<<<
558  * """
559  * Cosine of multivector with optional complexifier.
560  */
561 struct __pyx_opt_args_8PyClical_cos {
562  int __pyx_n;
563  PyObject *i;
564 };
565 
566 /* "PyClical.pyx":1619
567  * return clifford().wrap( glucat.cos(toClifford(obj)) )
568  *
569  * cpdef inline acos(obj,i = None): # <<<<<<<<<<<<<<
570  * """
571  * Inverse cosine of multivector with optional complexifier.
572  */
573 struct __pyx_opt_args_8PyClical_acos {
574  int __pyx_n;
575  PyObject *i;
576 };
577 
578 /* "PyClical.pyx":1656
579  * return clifford().wrap( glucat.cosh(toClifford(obj)) )
580  *
581  * cpdef inline acosh(obj,i = None): # <<<<<<<<<<<<<<
582  * """
583  * Inverse hyperbolic cosine of multivector with optional complexifier.
584  */
585 struct __pyx_opt_args_8PyClical_acosh {
586  int __pyx_n;
587  PyObject *i;
588 };
589 
590 /* "PyClical.pyx":1679
591  * return clifford().wrap( glucat.acosh(toClifford(obj)) )
592  *
593  * cpdef inline sin(obj,i = None): # <<<<<<<<<<<<<<
594  * """
595  * Sine of multivector with optional complexifier.
596  */
597 struct __pyx_opt_args_8PyClical_sin {
598  int __pyx_n;
599  PyObject *i;
600 };
601 
602 /* "PyClical.pyx":1698
603  * return clifford().wrap( glucat.sin(toClifford(obj)) )
604  *
605  * cpdef inline asin(obj,i = None): # <<<<<<<<<<<<<<
606  * """
607  * Inverse sine of multivector with optional complexifier.
608  */
609 struct __pyx_opt_args_8PyClical_asin {
610  int __pyx_n;
611  PyObject *i;
612 };
613 
614 /* "PyClical.pyx":1733
615  * return clifford().wrap( glucat.sinh(toClifford(obj)) )
616  *
617  * cpdef inline asinh(obj,i = None): # <<<<<<<<<<<<<<
618  * """
619  * Inverse hyperbolic sine of multivector with optional complexifier.
620  */
621 struct __pyx_opt_args_8PyClical_asinh {
622  int __pyx_n;
623  PyObject *i;
624 };
625 
626 /* "PyClical.pyx":1752
627  * return clifford().wrap( glucat.asinh(toClifford(obj)) )
628  *
629  * cpdef inline tan(obj,i = None): # <<<<<<<<<<<<<<
630  * """
631  * Tangent of multivector with optional complexifier.
632  */
633 struct __pyx_opt_args_8PyClical_tan {
634  int __pyx_n;
635  PyObject *i;
636 };
637 
638 /* "PyClical.pyx":1769
639  * return clifford().wrap( glucat.tan(toClifford(obj)) )
640  *
641  * cpdef inline atan(obj,i = None): # <<<<<<<<<<<<<<
642  * """
643  * Inverse tangent of multivector with optional complexifier.
644  */
645 struct __pyx_opt_args_8PyClical_atan {
646  int __pyx_n;
647  PyObject *i;
648 };
649 
650 /* "PyClical.pyx":1798
651  * return clifford().wrap( glucat.tanh(toClifford(obj)) )
652  *
653  * cpdef inline atanh(obj,i = None): # <<<<<<<<<<<<<<
654  * """
655  * Inverse hyperbolic tangent of multivector with optional complexifier.
656  */
657 struct __pyx_opt_args_8PyClical_atanh {
658  int __pyx_n;
659  PyObject *i;
660 };
661 
662 /* "PyClical.pyx":1815
663  * return clifford().wrap( glucat.atanh(toClifford(obj)) )
664  *
665  * cpdef inline random_clifford(index_set ixt, fill = 1.0): # <<<<<<<<<<<<<<
666  * """
667  * Random multivector within a frame.
668  */
669 struct __pyx_opt_args_8PyClical_random_clifford {
670  int __pyx_n;
671  PyObject *fill;
672 };
673 
674 /* "PyClical.pyx":37
675  *
676  * # Forward reference
677  * cdef class index_set # <<<<<<<<<<<<<<
678  *
679  * cdef inline IndexSet toIndexSet(obj):
680  */
681 struct __pyx_obj_8PyClical_index_set {
682  PyObject_HEAD
683  struct __pyx_vtabstruct_8PyClical_index_set *__pyx_vtab;
684  IndexSet *instance;
685 };
686 
687 
688 /* "PyClical.pyx":530
689  *
690  * # Forward reference.
691  * cdef class clifford # <<<<<<<<<<<<<<
692  *
693  * cdef inline Clifford toClifford(obj):
694  */
695 struct __pyx_obj_8PyClical_clifford {
696  PyObject_HEAD
697  struct __pyx_vtabstruct_8PyClical_clifford *__pyx_vtab;
698  Clifford *instance;
699 };
700 
701 
702 /* "PyClical.pyx":227
703  * return self.instance.getitem(idx)
704  *
705  * def __iter__(self): # <<<<<<<<<<<<<<
706  * """
707  * Iterate over the indices of an index_set.
708  */
709 struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ {
710  PyObject_HEAD
711  PyObject *__pyx_v_idx;
712  struct __pyx_obj_8PyClical_index_set *__pyx_v_self;
713  PyObject *__pyx_t_0;
714  Py_ssize_t __pyx_t_1;
715  PyObject *(*__pyx_t_2)(PyObject *);
716 };
717 
718 
719 
720 /* "PyClical.pyx":45
721  * return index_set(obj).instance[0]
722  *
723  * cdef class index_set: # <<<<<<<<<<<<<<
724  * """
725  * Python class index_set wraps C++ class IndexSet.
726  */
727 
728 struct __pyx_vtabstruct_8PyClical_index_set {
729  PyObject *(*wrap)(struct __pyx_obj_8PyClical_index_set *, IndexSet);
730  IndexSet (*unwrap)(struct __pyx_obj_8PyClical_index_set *);
731  PyObject *(*copy)(struct __pyx_obj_8PyClical_index_set *, int __pyx_skip_dispatch);
732 };
733 static struct __pyx_vtabstruct_8PyClical_index_set *__pyx_vtabptr_8PyClical_index_set;
734 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_9index_set_wrap(struct __pyx_obj_8PyClical_index_set *, IndexSet);
735 static CYTHON_INLINE IndexSet __pyx_f_8PyClical_9index_set_unwrap(struct __pyx_obj_8PyClical_index_set *);
736 
737 
738 /* "PyClical.pyx":535
739  * return clifford(obj).instance[0]
740  *
741  * cdef class clifford: # <<<<<<<<<<<<<<
742  * """
743  * Python class clifford wraps C++ class Clifford.
744  */
745 
746 struct __pyx_vtabstruct_8PyClical_clifford {
747  PyObject *(*wrap)(struct __pyx_obj_8PyClical_clifford *, Clifford);
748  Clifford (*unwrap)(struct __pyx_obj_8PyClical_clifford *);
749  PyObject *(*copy)(struct __pyx_obj_8PyClical_clifford *, int __pyx_skip_dispatch);
750 };
751 static struct __pyx_vtabstruct_8PyClical_clifford *__pyx_vtabptr_8PyClical_clifford;
752 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_8clifford_wrap(struct __pyx_obj_8PyClical_clifford *, Clifford);
753 static CYTHON_INLINE Clifford __pyx_f_8PyClical_8clifford_unwrap(struct __pyx_obj_8PyClical_clifford *);
754 
755 /* --- Runtime support code (head) --- */
756 #ifndef CYTHON_REFNANNY
757  #define CYTHON_REFNANNY 0
758 #endif
759 #if CYTHON_REFNANNY
760  typedef struct {
761  void (*INCREF)(void*, PyObject*, int);
762  void (*DECREF)(void*, PyObject*, int);
763  void (*GOTREF)(void*, PyObject*, int);
764  void (*GIVEREF)(void*, PyObject*, int);
765  void* (*SetupContext)(const char*, int, const char*);
766  void (*FinishContext)(void**);
767  } __Pyx_RefNannyAPIStruct;
768  static __Pyx_RefNannyAPIStruct *__Pyx_RefNanny = NULL;
769  static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname);
770  #define __Pyx_RefNannyDeclarations void *__pyx_refnanny = NULL;
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772  #define __Pyx_RefNannySetupContext(name, acquire_gil)\
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774  PyGILState_STATE __pyx_gilstate_save = PyGILState_Ensure();\
775  __pyx_refnanny = __Pyx_RefNanny->SetupContext((name), __LINE__, __FILE__);\
776  PyGILState_Release(__pyx_gilstate_save);\
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780 #else
781  #define __Pyx_RefNannySetupContext(name, acquire_gil)\
782  __pyx_refnanny = __Pyx_RefNanny->SetupContext((name), __LINE__, __FILE__)
783 #endif
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785  __Pyx_RefNanny->FinishContext(&__pyx_refnanny)
786  #define __Pyx_INCREF(r) __Pyx_RefNanny->INCREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
787  #define __Pyx_DECREF(r) __Pyx_RefNanny->DECREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
788  #define __Pyx_GOTREF(r) __Pyx_RefNanny->GOTREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
789  #define __Pyx_GIVEREF(r) __Pyx_RefNanny->GIVEREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
790  #define __Pyx_XINCREF(r) do { if((r) != NULL) {__Pyx_INCREF(r); }} while(0)
791  #define __Pyx_XDECREF(r) do { if((r) != NULL) {__Pyx_DECREF(r); }} while(0)
792  #define __Pyx_XGOTREF(r) do { if((r) != NULL) {__Pyx_GOTREF(r); }} while(0)
793  #define __Pyx_XGIVEREF(r) do { if((r) != NULL) {__Pyx_GIVEREF(r);}} while(0)
794 #else
795  #define __Pyx_RefNannyDeclarations
796  #define __Pyx_RefNannySetupContext(name, acquire_gil)
797  #define __Pyx_RefNannyFinishContext()
798  #define __Pyx_INCREF(r) Py_INCREF(r)
799  #define __Pyx_DECREF(r) Py_DECREF(r)
800  #define __Pyx_GOTREF(r)
801  #define __Pyx_GIVEREF(r)
802  #define __Pyx_XINCREF(r) Py_XINCREF(r)
803  #define __Pyx_XDECREF(r) Py_XDECREF(r)
804  #define __Pyx_XGOTREF(r)
805  #define __Pyx_XGIVEREF(r)
806 #endif
807 #define __Pyx_XDECREF_SET(r, v) do {\
808  PyObject *tmp = (PyObject *) r;\
809  r = v; __Pyx_XDECREF(tmp);\
810  } while (0)
811 #define __Pyx_DECREF_SET(r, v) do {\
812  PyObject *tmp = (PyObject *) r;\
813  r = v; __Pyx_DECREF(tmp);\
814  } while (0)
815 #define __Pyx_CLEAR(r) do { PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);} while(0)
816 #define __Pyx_XCLEAR(r) do { if((r) != NULL) {PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);}} while(0)
817 
818 #if CYTHON_COMPILING_IN_CPYTHON
819 static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name) {
820  PyTypeObject* tp = Py_TYPE(obj);
821  if (likely(tp->tp_getattro))
822  return tp->tp_getattro(obj, attr_name);
823 #if PY_MAJOR_VERSION < 3
824  if (likely(tp->tp_getattr))
825  return tp->tp_getattr(obj, PyString_AS_STRING(attr_name));
826 #endif
827  return PyObject_GetAttr(obj, attr_name);
828 }
829 #else
830 #define __Pyx_PyObject_GetAttrStr(o,n) PyObject_GetAttr(o,n)
831 #endif
832 
833 static PyObject *__Pyx_GetBuiltinName(PyObject *name);
834 
835 #if CYTHON_COMPILING_IN_CPYTHON
836 static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw);
837 #else
838 #define __Pyx_PyObject_Call(func, arg, kw) PyObject_Call(func, arg, kw)
839 #endif
840 
841 static CYTHON_INLINE void __Pyx_ErrRestore(PyObject *type, PyObject *value, PyObject *tb);
842 static CYTHON_INLINE void __Pyx_ErrFetch(PyObject **type, PyObject **value, PyObject **tb);
843 
844 static void __Pyx_WriteUnraisable(const char *name, int clineno,
845  int lineno, const char *filename,
846  int full_traceback, int nogil);
847 
848 #if CYTHON_COMPILING_IN_CPYTHON
849 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg);
850 #endif
851 
852 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg);
853 
854 #if CYTHON_COMPILING_IN_CPYTHON
855 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func);
856 #else
857 #define __Pyx_PyObject_CallNoArg(func) __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL)
858 #endif
859 
860 static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name);
861 
862 static int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject **argnames[],\
863  PyObject *kwds2, PyObject *values[], Py_ssize_t num_pos_args,\
864  const char* function_name);
865 
866 static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact,
867  Py_ssize_t num_min, Py_ssize_t num_max, Py_ssize_t num_found);
868 
869 static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name);
870 
871 static CYTHON_INLINE void __Pyx_ExceptionSave(PyObject **type, PyObject **value, PyObject **tb);
872 static void __Pyx_ExceptionReset(PyObject *type, PyObject *value, PyObject *tb);
873 
874 static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb);
875 
876 static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause);
877 
878 #if CYTHON_COMPILING_IN_CPYTHON
879 static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, long intval, int inplace);
880 #else
881 #define __Pyx_PyInt_AddObjC(op1, op2, intval, inplace)\
882  (inplace ? PyNumber_InPlaceAdd(op1, op2) : PyNumber_Add(op1, op2))
883 #endif
884 
885 static CYTHON_INLINE int __Pyx_PySequence_ContainsTF(PyObject* item, PyObject* seq, int eq) {
886  int result = PySequence_Contains(seq, item);
887  return unlikely(result < 0) ? result : (result == (eq == Py_EQ));
888 }
889 
890 #define __Pyx_SetItemInt(o, i, v, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
891  (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
892  __Pyx_SetItemInt_Fast(o, (Py_ssize_t)i, v, is_list, wraparound, boundscheck) :\
893  (is_list ? (PyErr_SetString(PyExc_IndexError, "list assignment index out of range"), -1) :\
894  __Pyx_SetItemInt_Generic(o, to_py_func(i), v)))
895 static CYTHON_INLINE int __Pyx_SetItemInt_Generic(PyObject *o, PyObject *j, PyObject *v);
896 static CYTHON_INLINE int __Pyx_SetItemInt_Fast(PyObject *o, Py_ssize_t i, PyObject *v,
897  int is_list, int wraparound, int boundscheck);
898 
899 static CYTHON_INLINE int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed,
900  const char *name, int exact);
901 
902 static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level);
903 
904 #include <string.h>
905 
906 static int __Pyx_SetVtable(PyObject *dict, void *vtable);
907 
908 #if CYTHON_COMPILING_IN_CPYTHON
909 static PyObject* __Pyx_PyFloat_DivideObjC(PyObject *op1, PyObject *op2, double floatval, int inplace);
910 #else
911 #define __Pyx_PyFloat_DivideObjC(op1, op2, floatval, inplace)\
912  ((inplace ? __Pyx_PyNumber_InPlaceDivide(op1, op2) : __Pyx_PyNumber_Divide(op1, op2)))
913  #endif
914 
915 static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals);
916 
917 static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals);
918 
919 #if PY_MAJOR_VERSION >= 3
920 #define __Pyx_PyString_Equals __Pyx_PyUnicode_Equals
921 #else
922 #define __Pyx_PyString_Equals __Pyx_PyBytes_Equals
923 #endif
924 
925 typedef struct {
926  int code_line;
927  PyCodeObject* code_object;
928 } __Pyx_CodeObjectCacheEntry;
929 struct __Pyx_CodeObjectCache {
930  int count;
931  int max_count;
932  __Pyx_CodeObjectCacheEntry* entries;
933 };
934 static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL};
935 static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line);
936 static PyCodeObject *__pyx_find_code_object(int code_line);
937 static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object);
938 
939 static void __Pyx_AddTraceback(const char *funcname, int c_line,
940  int py_line, const char *filename);
941 
942 static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *);
943 
944 #ifndef __Pyx_CppExn2PyErr
945 #include <new>
946 #include <typeinfo>
947 #include <stdexcept>
948 #include <ios>
949 static void __Pyx_CppExn2PyErr() {
950  try {
951  if (PyErr_Occurred())
952  ; // let the latest Python exn pass through and ignore the current one
953  else
954  throw;
955  } catch (const std::bad_alloc& exn) {
956  PyErr_SetString(PyExc_MemoryError, exn.what());
957  } catch (const std::bad_cast& exn) {
958  PyErr_SetString(PyExc_TypeError, exn.what());
959  } catch (const std::domain_error& exn) {
960  PyErr_SetString(PyExc_ValueError, exn.what());
961  } catch (const std::invalid_argument& exn) {
962  PyErr_SetString(PyExc_ValueError, exn.what());
963  } catch (const std::ios_base::failure& exn) {
964  PyErr_SetString(PyExc_IOError, exn.what());
965  } catch (const std::out_of_range& exn) {
966  PyErr_SetString(PyExc_IndexError, exn.what());
967  } catch (const std::overflow_error& exn) {
968  PyErr_SetString(PyExc_OverflowError, exn.what());
969  } catch (const std::range_error& exn) {
970  PyErr_SetString(PyExc_ArithmeticError, exn.what());
971  } catch (const std::underflow_error& exn) {
972  PyErr_SetString(PyExc_ArithmeticError, exn.what());
973  } catch (const std::exception& exn) {
974  PyErr_SetString(PyExc_RuntimeError, exn.what());
975  }
976  catch (...)
977  {
978  PyErr_SetString(PyExc_RuntimeError, "Unknown exception");
979  }
980 }
981 #endif
982 
983 static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value);
984 
985 static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value);
986 
987 static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *);
988 
989 static PyTypeObject* __Pyx_FetchCommonType(PyTypeObject* type);
990 
991 static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb);
992 
993 static PyObject* __Pyx_PyObject_CallMethod1(PyObject* obj, PyObject* method_name, PyObject* arg);
994 
995 typedef PyObject *(*__pyx_coroutine_body_t)(PyObject *, PyObject *);
996 typedef struct {
997  PyObject_HEAD
998  __pyx_coroutine_body_t body;
999  PyObject *closure;
1000  PyObject *exc_type;
1001  PyObject *exc_value;
1002  PyObject *exc_traceback;
1003  PyObject *gi_weakreflist;
1004  PyObject *classobj;
1005  PyObject *yieldfrom;
1006  PyObject *gi_name;
1007  PyObject *gi_qualname;
1008  int resume_label;
1009  char is_running;
1010 } __pyx_CoroutineObject;
1011 static __pyx_CoroutineObject *__Pyx__Coroutine_New(PyTypeObject *type, __pyx_coroutine_body_t body,
1012  PyObject *closure, PyObject *name, PyObject *qualname);
1013 static int __Pyx_Coroutine_clear(PyObject *self);
1014 #if 1 || PY_VERSION_HEX < 0x030300B0
1015 static int __Pyx_PyGen_FetchStopIterationValue(PyObject **pvalue);
1016 #else
1017 #define __Pyx_PyGen_FetchStopIterationValue(pvalue) PyGen_FetchStopIterationValue(pvalue)
1018 #endif
1019 
1020 static PyObject* __Pyx_Coroutine_patch_module(PyObject* module, const char* py_code);
1021 
1022 static int __Pyx_patch_abc(void);
1023 
1024 #define __Pyx_Generator_USED
1025 static PyTypeObject *__pyx_GeneratorType = 0;
1026 #define __Pyx_Generator_CheckExact(obj) (Py_TYPE(obj) == __pyx_GeneratorType)
1027 #define __Pyx_Generator_New(body, closure, name, qualname)\
1028  __Pyx__Coroutine_New(__pyx_GeneratorType, body, closure, name, qualname)
1029 static PyObject *__Pyx_Generator_Next(PyObject *self);
1030 static int __pyx_Generator_init(void);
1031 
1032 static int __Pyx_check_binary_version(void);
1033 
1034 static int __Pyx_InitStrings(__Pyx_StringTabEntry *t);
1035 
1036 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_9index_set_wrap(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, IndexSet __pyx_v_other); /* proto*/
1037 static CYTHON_INLINE IndexSet __pyx_f_8PyClical_9index_set_unwrap(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto*/
1038 static PyObject *__pyx_f_8PyClical_9index_set_copy(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, int __pyx_skip_dispatch); /* proto*/
1039 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_8clifford_wrap(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, Clifford __pyx_v_other); /* proto*/
1040 static CYTHON_INLINE Clifford __pyx_f_8PyClical_8clifford_unwrap(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto*/
1041 static PyObject *__pyx_f_8PyClical_8clifford_copy(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, int __pyx_skip_dispatch); /* proto*/
1042 
1043 /* Module declarations from 'libcpp.vector' */
1044 
1045 /* Module declarations from 'glucat' */
1046 
1047 /* Module declarations from 'PyClical' */
1048 static PyTypeObject *__pyx_ptype_8PyClical_index_set = 0;
1049 static PyTypeObject *__pyx_ptype_8PyClical_clifford = 0;
1050 static PyTypeObject *__pyx_ptype_8PyClical___pyx_scope_struct____iter__ = 0;
1051 static CYTHON_INLINE IndexSet __pyx_f_8PyClical_toIndexSet(PyObject *); /*proto*/
1052 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_compare(PyObject *, PyObject *, int __pyx_skip_dispatch); /*proto*/
1053 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_min_neg(PyObject *, int __pyx_skip_dispatch); /*proto*/
1054 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_max_pos(PyObject *, int __pyx_skip_dispatch); /*proto*/
1055 static CYTHON_INLINE std::vector<scalar_t> __pyx_f_8PyClical_list_to_vector(PyObject *); /*proto*/
1056 static CYTHON_INLINE Clifford __pyx_f_8PyClical_toClifford(PyObject *); /*proto*/
1057 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_inv(PyObject *, int __pyx_skip_dispatch); /*proto*/
1058 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_scalar(PyObject *, int __pyx_skip_dispatch); /*proto*/
1059 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_real(PyObject *, int __pyx_skip_dispatch); /*proto*/
1060 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_imag(PyObject *, int __pyx_skip_dispatch); /*proto*/
1061 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_pure(PyObject *, int __pyx_skip_dispatch); /*proto*/
1062 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_even(PyObject *, int __pyx_skip_dispatch); /*proto*/
1063 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_odd(PyObject *, int __pyx_skip_dispatch); /*proto*/
1064 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_involute(PyObject *, int __pyx_skip_dispatch); /*proto*/
1065 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_reverse(PyObject *, int __pyx_skip_dispatch); /*proto*/
1066 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_conj(PyObject *, int __pyx_skip_dispatch); /*proto*/
1067 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_quad(PyObject *, int __pyx_skip_dispatch); /*proto*/
1068 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_norm(PyObject *, int __pyx_skip_dispatch); /*proto*/
1069 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_abs(PyObject *, int __pyx_skip_dispatch); /*proto*/
1070 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_max_abs(PyObject *, int __pyx_skip_dispatch); /*proto*/
1071 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_pow(PyObject *, PyObject *, int __pyx_skip_dispatch); /*proto*/
1072 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_outer_pow(PyObject *, PyObject *, int __pyx_skip_dispatch); /*proto*/
1073 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_complexifier(PyObject *, int __pyx_skip_dispatch); /*proto*/
1074 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_sqrt(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_sqrt *__pyx_optional_args); /*proto*/
1075 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_exp(PyObject *, int __pyx_skip_dispatch); /*proto*/
1076 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_log(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_log *__pyx_optional_args); /*proto*/
1077 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_cos(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_cos *__pyx_optional_args); /*proto*/
1078 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_acos(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_acos *__pyx_optional_args); /*proto*/
1079 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_cosh(PyObject *, int __pyx_skip_dispatch); /*proto*/
1080 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_acosh(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_acosh *__pyx_optional_args); /*proto*/
1081 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_sin(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_sin *__pyx_optional_args); /*proto*/
1082 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_asin(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_asin *__pyx_optional_args); /*proto*/
1083 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_sinh(PyObject *, int __pyx_skip_dispatch); /*proto*/
1084 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_asinh(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_asinh *__pyx_optional_args); /*proto*/
1085 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_tan(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_tan *__pyx_optional_args); /*proto*/
1086 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_atan(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_atan *__pyx_optional_args); /*proto*/
1087 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_tanh(PyObject *, int __pyx_skip_dispatch); /*proto*/
1088 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_atanh(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_atanh *__pyx_optional_args); /*proto*/
1089 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_random_clifford(struct __pyx_obj_8PyClical_index_set *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_random_clifford *__pyx_optional_args); /*proto*/
1090 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_cga3(PyObject *, int __pyx_skip_dispatch); /*proto*/
1091 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_cga3std(PyObject *, int __pyx_skip_dispatch); /*proto*/
1092 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_agc3(PyObject *, int __pyx_skip_dispatch); /*proto*/
1093 #define __Pyx_MODULE_NAME "PyClical"
1094 int __pyx_module_is_main_PyClical = 0;
1095 
1096 /* Implementation of 'PyClical' */
1097 static PyObject *__pyx_builtin_IndexError;
1098 static PyObject *__pyx_builtin_RuntimeError;
1099 static PyObject *__pyx_builtin_TypeError;
1100 static PyObject *__pyx_builtin_ValueError;
1101 static PyObject *__pyx_builtin_NotImplemented;
1102 static PyObject *__pyx_builtin_range;
1103 static PyObject *__pyx_builtin_xrange;
1104 static char __pyx_k_[] = ".";
1105 static char __pyx_k_e[] = "e";
1106 static char __pyx_k_i[] = "i";
1107 static char __pyx_k_m[] = "m";
1108 static char __pyx_k_p[] = "p";
1109 static char __pyx_k_q[] = "q";
1110 static char __pyx_k__2[] = " ";
1111 static char __pyx_k__3[] = ":";
1112 static char __pyx_k__4[] = "\n\t";
1113 static char __pyx_k__5[] = " (";
1114 static char __pyx_k__6[] = ", ";
1115 static char __pyx_k__7[] = ").";
1116 static char __pyx_k_cl[] = "cl";
1117 static char __pyx_k_pi[] = "pi";
1118 static char __pyx_k_cos[] = "cos";
1119 static char __pyx_k_exp[] = "exp";
1120 static char __pyx_k_frm[] = "frm";
1121 static char __pyx_k_inv[] = "inv";
1122 static char __pyx_k_ist[] = "ist";
1123 static char __pyx_k_ixt[] = "ixt";
1124 static char __pyx_k_lhs[] = "lhs";
1125 static char __pyx_k_log[] = "log";
1126 static char __pyx_k_max[] = "max";
1127 static char __pyx_k_min[] = "min";
1128 static char __pyx_k_obj[] = "obj";
1129 static char __pyx_k_odd[] = "odd";
1130 static char __pyx_k_pow[] = "pow";
1131 static char __pyx_k_rhs[] = "rhs";
1132 static char __pyx_k_sin[] = "sin";
1133 static char __pyx_k_tan[] = "tan";
1134 static char __pyx_k_tau[] = "tau";
1135 static char __pyx_k_Real[] = "Real";
1136 static char __pyx_k_acos[] = "acos";
1137 static char __pyx_k_args[] = "args";
1138 static char __pyx_k_asin[] = "asin";
1139 static char __pyx_k_atan[] = "atan";
1140 static char __pyx_k_conj[] = "conj";
1141 static char __pyx_k_copy[] = "copy";
1142 static char __pyx_k_cosh[] = "cosh";
1143 static char __pyx_k_even[] = "even";
1144 static char __pyx_k_fill[] = "fill";
1145 static char __pyx_k_from[] = " from ";
1146 static char __pyx_k_iter[] = "__iter__";
1147 static char __pyx_k_main[] = "__main__";
1148 static char __pyx_k_math[] = "math";
1149 static char __pyx_k_name[] = "__name__";
1150 static char __pyx_k_norm[] = "norm";
1151 static char __pyx_k_pure[] = "pure";
1152 static char __pyx_k_quad[] = "quad";
1153 static char __pyx_k_send[] = "send";
1154 static char __pyx_k_sinh[] = "sinh";
1155 static char __pyx_k_sqrt[] = "sqrt";
1156 static char __pyx_k_tanh[] = "tanh";
1157 static char __pyx_k_test[] = "_test";
1158 static char __pyx_k_0_8_2[] = "0.8.2";
1159 static char __pyx_k_acosh[] = "acosh";
1160 static char __pyx_k_asinh[] = "asinh";
1161 static char __pyx_k_atanh[] = "atanh";
1162 static char __pyx_k_close[] = "close";
1163 static char __pyx_k_grade[] = "grade";
1164 static char __pyx_k_istpq[] = "istpq";
1165 static char __pyx_k_nbar3[] = "nbar3";
1166 static char __pyx_k_ninf3[] = "ninf3";
1167 static char __pyx_k_other[] = "other";
1168 static char __pyx_k_range[] = "range";
1169 static char __pyx_k_throw[] = "throw";
1170 static char __pyx_k_using[] = " using (";
1171 static char __pyx_k_value[] = " value ";
1172 static char __pyx_k_import[] = "__import__";
1173 static char __pyx_k_scalar[] = "scalar";
1174 static char __pyx_k_test_2[] = "__test__";
1175 static char __pyx_k_xrange[] = "xrange";
1176 static char __pyx_k_doctest[] = "doctest";
1177 static char __pyx_k_invalid[] = " invalid ";
1178 static char __pyx_k_numbers[] = "numbers";
1179 static char __pyx_k_reverse[] = "reverse";
1180 static char __pyx_k_testmod[] = "testmod";
1181 static char __pyx_k_version[] = "__version__";
1182 static char __pyx_k_Integral[] = "Integral";
1183 static char __pyx_k_PyClical[] = "PyClical";
1184 static char __pyx_k_Sequence[] = "Sequence";
1185 static char __pyx_k_as_frame[] = " as frame:\n\t";
1186 static char __pyx_k_involute[] = "involute";
1187 static char __pyx_k_to_frame[] = " to frame ";
1188 static char __pyx_k_TypeError[] = "TypeError";
1189 static char __pyx_k_outer_pow[] = "outer_pow";
1190 static char __pyx_k_IndexError[] = "IndexError";
1191 static char __pyx_k_ValueError[] = "ValueError";
1192 static char __pyx_k_pyx_vtable[] = "__pyx_vtable__";
1193 static char __pyx_k_collections[] = "collections";
1194 static char __pyx_k_e_line_1887[] = "e (line 1887)";
1195 static char __pyx_k_RuntimeError[] = "RuntimeError";
1196 static char __pyx_k_abs_line_1473[] = "abs (line 1473)";
1197 static char __pyx_k_cos_line_1602[] = "cos (line 1602)";
1198 static char __pyx_k_exp_line_1565[] = "exp (line 1565)";
1199 static char __pyx_k_inv_line_1329[] = "inv (line 1329)";
1200 static char __pyx_k_log_line_1579[] = "log (line 1579)";
1201 static char __pyx_k_odd_line_1397[] = "odd (line 1397)";
1202 static char __pyx_k_pow_line_1494[] = "pow (line 1494)";
1203 static char __pyx_k_sin_line_1679[] = "sin (line 1679)";
1204 static char __pyx_k_tan_line_1752[] = "tan (line 1752)";
1205 static char __pyx_k_using_invalid[] = " using invalid ";
1206 static char __pyx_k_Cannot_reframe[] = "Cannot reframe";
1207 static char __pyx_k_NotImplemented[] = "NotImplemented";
1208 static char __pyx_k_Not_applicable[] = "Not applicable.";
1209 static char __pyx_k_acos_line_1619[] = "acos (line 1619)";
1210 static char __pyx_k_agc3_line_1844[] = "agc3 (line 1844)";
1211 static char __pyx_k_asin_line_1698[] = "asin (line 1698)";
1212 static char __pyx_k_atan_line_1769[] = "atan (line 1769)";
1213 static char __pyx_k_cga3_line_1824[] = "cga3 (line 1824)";
1214 static char __pyx_k_conj_line_1436[] = "conj (line 1436)";
1215 static char __pyx_k_cosh_line_1640[] = "cosh (line 1640)";
1216 static char __pyx_k_even_line_1388[] = "even (line 1388)";
1217 static char __pyx_k_imag_line_1366[] = "imag (line 1366)";
1218 static char __pyx_k_invalid_string[] = " invalid string ";
1219 static char __pyx_k_norm_line_1462[] = "norm (line 1462)";
1220 static char __pyx_k_pure_line_1377[] = "pure (line 1377)";
1221 static char __pyx_k_quad_line_1451[] = "quad (line 1451)";
1222 static char __pyx_k_real_line_1355[] = "real (line 1355)";
1223 static char __pyx_k_sinh_line_1719[] = "sinh (line 1719)";
1224 static char __pyx_k_sqrt_line_1542[] = "sqrt (line 1542)";
1225 static char __pyx_k_tanh_line_1786[] = "tanh (line 1786)";
1226 static char __pyx_k_acosh_line_1656[] = "acosh (line 1656)";
1227 static char __pyx_k_asinh_line_1733[] = "asinh (line 1733)";
1228 static char __pyx_k_atanh_line_1798[] = "atanh (line 1798)";
1229 static char __pyx_k_istpq_line_1900[] = "istpq (line 1900)";
1230 static char __pyx_k_compare_line_490[] = "compare (line 490)";
1231 static char __pyx_k_index_set___iter[] = "index_set.__iter__";
1232 static char __pyx_k_max_pos_line_511[] = "max_pos (line 511)";
1233 static char __pyx_k_min_neg_line_502[] = "min_neg (line 502)";
1234 static char __pyx_k_scalar_line_1344[] = "scalar (line 1344)";
1235 static char __pyx_k_cga3std_line_1833[] = "cga3std (line 1833)";
1236 static char __pyx_k_max_abs_line_1482[] = "max_abs (line 1482)";
1237 static char __pyx_k_reverse_line_1421[] = "reverse (line 1421)";
1238 static char __pyx_k_involute_line_1406[] = "involute (line 1406)";
1239 static char __pyx_k_outer_pow_line_1518[] = "outer_pow (line 1518)";
1240 static char __pyx_k_clifford_inv_line_925[] = "clifford.inv (line 925)";
1241 static char __pyx_k_clifford_pow_line_979[] = "clifford.pow (line 979)";
1242 static char __pyx_k_clifford_abs_line_1174[] = "clifford.abs (line 1174)";
1243 static char __pyx_k_clifford_copy_line_554[] = "clifford.copy (line 554)";
1244 static char __pyx_k_clifford_odd_line_1069[] = "clifford.odd (line 1069)";
1245 static char __pyx_k_complexifier_line_1527[] = "complexifier (line 1527)";
1246 static char __pyx_k_index_set_copy_line_64[] = "index_set.copy (line 64)";
1247 static char __pyx_k_index_set_max_line_349[] = "index_set.max (line 349)";
1248 static char __pyx_k_index_set_min_line_340[] = "index_set.min (line 340)";
1249 static char __pyx_k_clifford_conj_line_1137[] = "clifford.conj (line 1137)";
1250 static char __pyx_k_clifford_even_line_1060[] = "clifford.even (line 1060)";
1251 static char __pyx_k_clifford_norm_line_1163[] = "clifford.norm (line 1163)";
1252 static char __pyx_k_clifford_pure_line_1049[] = "clifford.pure (line 1049)";
1253 static char __pyx_k_clifford_quad_line_1152[] = "clifford.quad (line 1152)";
1254 static char __pyx_k_Unary_print_clifford_1_1[] = "\n Unary -.\n\n >>> print -clifford(\"{1}\")\n -{1}\n ";
1255 static char __pyx_k_clifford___or___line_938[] = "clifford.__or__ (line 938)";
1256 static char __pyx_k_clifford_frame_line_1214[] = "clifford.frame (line 1214)";
1257 static char __pyx_k_clifford_hidden_doctests[] = "clifford_hidden_doctests";
1258 static char __pyx_k_clifford_isnan_line_1205[] = "clifford.isnan (line 1205)";
1259 static char __pyx_k_index_set_count_line_313[] = "index_set.count (line 313)";
1260 static char __pyx_k_clifford___add___line_739[] = "clifford.__add__ (line 739)";
1261 static char __pyx_k_clifford___and___line_835[] = "clifford.__and__ (line 835)";
1262 static char __pyx_k_clifford___div___line_895[] = "clifford.__div__ (line 895)";
1263 static char __pyx_k_clifford___ior___line_949[] = "clifford.__ior__ (line 949)";
1264 static char __pyx_k_clifford___mod___line_805[] = "clifford.__mod__ (line 805)";
1265 static char __pyx_k_clifford___mul___line_779[] = "clifford.__mul__ (line 779)";
1266 static char __pyx_k_clifford___neg___line_721[] = "clifford.__neg__ (line 721)";
1267 static char __pyx_k_clifford___pos___line_730[] = "clifford.__pos__ (line 730)";
1268 static char __pyx_k_clifford___pow___line_960[] = "clifford.__pow__ (line 960)";
1269 static char __pyx_k_clifford___sub___line_759[] = "clifford.__sub__ (line 759)";
1270 static char __pyx_k_clifford___xor___line_865[] = "clifford.__xor__ (line 865)";
1271 static char __pyx_k_clifford_reframe_line_648[] = "clifford.reframe (line 648)";
1272 static char __pyx_k_clifford_scalar_line_1038[] = "clifford.scalar (line 1038)";
1273 static char __pyx_k_index_set___or___line_291[] = "index_set.__or__ (line 291)";
1274 static char __pyx_k_index_set_hidden_doctests[] = "index_set_hidden_doctests";
1275 static char __pyx_k_random_clifford_line_1815[] = "random_clifford (line 1815)";
1276 static char __pyx_k_Cannot_take_vector_part_of[] = "Cannot take vector part of ";
1277 static char __pyx_k_Unary_print_clifford_1_1_2[] = "\n Unary +.\n\n >>> print +clifford(\"{1}\")\n {1}\n ";
1278 static char __pyx_k_clifford___iadd___line_750[] = "clifford.__iadd__ (line 750)";
1279 static char __pyx_k_clifford___iand___line_850[] = "clifford.__iand__ (line 850)";
1280 static char __pyx_k_clifford___idiv___line_910[] = "clifford.__idiv__ (line 910)";
1281 static char __pyx_k_clifford___imod___line_820[] = "clifford.__imod__ (line 820)";
1282 static char __pyx_k_clifford___imul___line_792[] = "clifford.__imul__ (line 792)";
1283 static char __pyx_k_clifford___isub___line_770[] = "clifford.__isub__ (line 770)";
1284 static char __pyx_k_clifford___iter___line_637[] = "clifford.__iter__ (line 637)";
1285 static char __pyx_k_clifford___ixor___line_880[] = "clifford.__ixor__ (line 880)";
1286 static char __pyx_k_clifford___str___line_1234[] = "clifford.__str__ (line 1234)";
1287 static char __pyx_k_clifford_max_abs_line_1183[] = "clifford.max_abs (line 1183)";
1288 static char __pyx_k_clifford_reverse_line_1122[] = "clifford.reverse (line 1122)";
1289 static char __pyx_k_index_set___and___line_269[] = "index_set.__and__ (line 269)";
1290 static char __pyx_k_index_set___ior___line_302[] = "index_set.__ior__ (line 302)";
1291 static char __pyx_k_index_set___str___line_393[] = "index_set.__str__ (line 393)";
1292 static char __pyx_k_index_set___xor___line_247[] = "index_set.__xor__ (line 247)";
1293 static char __pyx_k_clifford___call___line_1019[] = "clifford.__call__ (line 1019)";
1294 static char __pyx_k_clifford___repr___line_1225[] = "clifford.__repr__ (line 1225)";
1295 static char __pyx_k_clifford_involute_line_1106[] = "clifford.involute (line 1106)";
1296 static char __pyx_k_index_set___iand___line_280[] = "index_set.__iand__ (line 280)";
1297 static char __pyx_k_index_set___iter___line_227[] = "index_set.__iter__ (line 227)";
1298 static char __pyx_k_index_set___ixor___line_258[] = "index_set.__ixor__ (line 258)";
1299 static char __pyx_k_index_set___repr___line_382[] = "index_set.__repr__ (line 382)";
1300 static char __pyx_k_clifford_outer_pow_line_1003[] = "clifford.outer_pow (line 1003)";
1301 static char __pyx_k_clifford_truncated_line_1194[] = "clifford.truncated (line 1194)";
1302 static char __pyx_k_index_set_count_neg_line_322[] = "index_set.count_neg (line 322)";
1303 static char __pyx_k_index_set_count_pos_line_331[] = "index_set.count_pos (line 331)";
1304 static char __pyx_k_clifford___getitem___line_706[] = "clifford.__getitem__ (line 706)";
1305 static char __pyx_k_index_set___invert___line_238[] = "index_set.__invert__ (line 238)";
1306 static char __pyx_k_Abbreviation_for_index_set_q_p[] = "\n Abbreviation for index_set({-q,...p}).\n\n >>> print istpq(2,3)\n {-3,-2,-1,1,2}\n ";
1307 static char __pyx_k_Conjugation_reverse_o_involute[] = "\n Conjugation, reverse o involute == involute o reverse.\n\n >>> print (clifford(\"{1}\")).conj()\n -{1}\n >>> print (clifford(\"{2}\") * clifford(\"{1}\")).conj()\n {1,2}\n >>> print (clifford(\"{1}\") * clifford(\"{2}\")).conj()\n -{1,2}\n >>> print clifford(\"1+{1}+{1,2}\").conj()\n 1-{1}-{1,2}\n ";
1308 static char __pyx_k_Geometric_product_x_clifford_2[] = "\n Geometric product.\n\n >>> x = clifford(2); x *= clifford(\"{2}\"); print x\n 2{2}\n >>> x = clifford(\"{1}\"); x *= clifford(\"{2}\"); print x\n {1,2}\n >>> x = clifford(\"{1}\"); x *= clifford(\"{1,2}\"); print x\n {2}\n ";
1309 static char __pyx_k_Geometric_sum_print_clifford_1[] = "\n Geometric sum.\n\n >>> print clifford(1) + clifford(\"{2}\")\n 1+{2}\n >>> print clifford(\"{1}\") + clifford(\"{2}\")\n {1}+{2}\n ";
1310 static char __pyx_k_Hyperbolic_sine_of_multivector[] = "\n Hyperbolic sine of multivector.\n\n >>> x=clifford(\"{1,2}\") * pi/2; print sinh(x)\n {1,2}\n >>> x=clifford(\"{1,2}\") * pi/6; print sinh(x)\n 0.5{1,2}\n ";
1311 static char __pyx_k_Inner_product_print_clifford_1[] = "\n Inner product.\n\n >>> print clifford(\"{1}\") & clifford(\"{2}\")\n 0\n >>> print clifford(2) & clifford(\"{2}\")\n 0\n >>> print clifford(\"{1}\") & clifford(\"{1}\")\n 1\n >>> print clifford(\"{1}\") & clifford(\"{1,2}\")\n {2}\n ";
1312 static char __pyx_k_Inverse_tangent_of_multivector[] = "\n Inverse tangent of multivector with optional complexifier.\n\n >>> s=index_set({1,2,3}); x=clifford(\"{1}\"); print tan(atan(x,s),s)\n {1}\n >>> x=clifford(\"{1}\"); print tan(atan(x))\n {1}\n ";
1313 static char __pyx_k_Iterate_over_the_indices_of_an[] = "\n Iterate over the indices of an index_set.\n\n >>> for i in index_set({-3,4,7}): print i,\n -3 4 7\n ";
1314 static char __pyx_k_Maximum_member_index_set_1_1_2[] = "\n Maximum member.\n\n >>> index_set({-1,1,2}).max()\n 2\n ";
1315 static char __pyx_k_Maximum_positive_index_or_0_if[] = "\n Maximum positive index, or 0 if none.\n\n >>> max_pos(index_set({1,2}))\n 2\n ";
1316 static char __pyx_k_Minimum_member_index_set_1_1_2[] = "\n Minimum member.\n\n >>> index_set({-1,1,2}).min()\n -1\n ";
1317 static char __pyx_k_Minimum_negative_index_or_0_if[] = "\n Minimum negative index, or 0 if none.\n\n >>> min_neg(index_set({1,2}))\n 0\n ";
1318 static char __pyx_k_Odd_part_of_multivector_sum_of[] = "\n Odd part of multivector, sum of odd grade terms.\n\n >>> print clifford(\"1+{1}+{1,2}\").odd()\n {1}\n ";
1319 static char __pyx_k_Outer_product_power_x_clifford[] = "\n Outer product power.\n\n >>> x=clifford(\"2+{1}\"); print x.outer_pow(0)\n 1\n >>> x=clifford(\"2+{1}\"); print x.outer_pow(1)\n 2+{1}\n >>> x=clifford(\"2+{1}\"); print x.outer_pow(2)\n 4+4{1}\n >>> print clifford(\"1+{1}+{1,2}\").outer_pow(3)\n 1+3{1}+3{1,2}\n\n ";
1320 static char __pyx_k_Outer_product_print_clifford_1[] = "\n Outer product.\n\n >>> print clifford(\"{1}\") ^ clifford(\"{2}\")\n {1,2}\n >>> print clifford(2) ^ clifford(\"{2}\")\n 2{2}\n >>> print clifford(\"{1}\") ^ clifford(\"{1}\")\n 0\n >>> print clifford(\"{1}\") ^ clifford(\"{1,2}\")\n 0\n ";
1321 static char __pyx_k_Power_self_to_the_m_x_clifford[] = "\n Power: self to the m.\n\n >>> x=clifford(\"{1}\"); print x ** 2\n 1\n >>> x=clifford(\"2\"); print x ** 2\n 4\n >>> x=clifford(\"2+{1}\"); print x ** 0\n 1\n >>> x=clifford(\"2+{1}\"); print x ** 1\n 2+{1}\n >>> x=clifford(\"2+{1}\"); print x ** 2\n 5+4{1}\n >>> i=clifford(\"{1,2}\");print exp(pi/2) * (i ** i)\n 1\n ";
1322 static char __pyx_k_Pure_part_print_clifford_1_1_1[] = "\n Pure part.\n\n >>> print clifford(\"1+{1}+{1,2}\").pure()\n {1}+{1,2}\n >>> print clifford(\"{1,2}\").pure()\n {1,2}\n ";
1323 static char __pyx_k_Quadratic_form_rev_x_x_0_print[] = "\n Quadratic form == (rev(x)*x)(0).\n\n >>> print clifford(\"1+{1}+{1,2}\").quad()\n 3.0\n >>> print clifford(\"1+{-1}+{1,2}+{1,2,3}\").quad()\n 2.0\n ";
1324 static char __pyx_k_Set_complement_not_print_index[] = "\n Set complement: not.\n\n >>> print ~index_set({-16,-15,-14,-13,-12,-11,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16})\n {-32,-31,-30,-29,-28,-27,-26,-25,-24,-23,-22,-21,-20,-19,-18,-17,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32}\n ";
1325 static char __pyx_k_Set_union_or_print_index_set_1[] = "\n Set union: or.\n\n >>> print index_set({1}) | index_set({2})\n {1,2}\n >>> print index_set({1,2}) | index_set({2})\n {1,2}\n ";
1326 static char __pyx_k_Transform_left_hand_side_using[] = "\n Transform left hand side, using right hand side as a transformation.\n\n >>> x=clifford(\"{1,2}\") * pi/2; y=clifford(\"{1}\"); print y|x\n -{1}\n >>> x=clifford(\"{1,2}\") * pi/2; y=clifford(\"{1}\"); print y|exp(x)\n -{1}\n ";
1327 static char __pyx_k_clifford_vector_part_line_1078[] = "clifford.vector_part (line 1078)";
1328 static char __pyx_k_index_set___getitem___line_189[] = "index_set.__getitem__ (line 189)";
1329 static char __pyx_k_index_set___setitem___line_177[] = "index_set.__setitem__ (line 177)";
1330 static char __pyx_k_lexicographic_compare_eg_3_4_5[] = "\n \"lexicographic compare\" eg. {3,4,5} is less than {3,7,8};\n -1 if a<b, +1 if a>b, 0 if a==b.\n\n >>> compare(index_set({1,2}),index_set({-1,3}))\n -1\n >>> compare(index_set({-1,4}),index_set({-1,3}))\n 1\n ";
1331 static char __pyx_k_Abbreviation_for_clifford_index[] = "\n Abbreviation for clifford(index_set(obj)).\n\n >>> print e(1)\n {1}\n >>> print e(-1)\n {-1}\n >>> print e(0)\n 1\n ";
1332 static char __pyx_k_Absolute_value_of_multivector_m[] = "\n Absolute value of multivector: multivector 2-norm.\n\n >>> abs(clifford(\"1+{-1}+{1,2}+{1,2,3}\"))\n 2.0\n ";
1333 static char __pyx_k_Absolute_value_square_root_of_n[] = "\n Absolute value: square root of norm.\n\n >>> clifford(\"1+{-1}+{1,2}+{1,2,3}\").abs()\n 2.0\n ";
1334 static char __pyx_k_Cardinality_Number_of_indices_i[] = "\n Cardinality: Number of indices included in set.\n\n >>> index_set({-1,1,2}).count()\n 3\n ";
1335 static char __pyx_k_Check_if_a_multivector_contains[] = "\n Check if a multivector contains any IEEE NaN values.\n\n >>> clifford().isnan()\n False\n ";
1336 static char __pyx_k_Contraction_print_clifford_1_cl[] = "\n Contraction.\n\n >>> print clifford(\"{1}\") % clifford(\"{2}\")\n 0\n >>> print clifford(2) % clifford(\"{2}\")\n 2{2}\n >>> print clifford(\"{1}\") % clifford(\"{1}\")\n 1\n >>> print clifford(\"{1}\") % clifford(\"{1,2}\")\n {2}\n ";
1337 static char __pyx_k_Contraction_x_clifford_1_x_clif[] = "\n Contraction.\n\n >>> x = clifford(\"{1}\"); x %= clifford(\"{2}\"); print x\n 0\n >>> x = clifford(2); x %= clifford(\"{2}\"); print x\n 2{2}\n >>> x = clifford(\"{1}\"); x %= clifford(\"{1}\"); print x\n 1\n >>> x = clifford(\"{1}\"); x %= clifford(\"{1,2}\"); print x\n {2}\n ";
1338 static char __pyx_k_Convert_CGA3_null_vector_to_Euc[] = "\n Convert CGA3 null vector to Euclidean 3D vector using Doran and Lasenby definition.\n\n >>> x=clifford(\"2{1}+9{2}+{3}\"); print agc3(cga3(x))\n 2{1}+9{2}+{3}\n >>> x=clifford(\"2{1}+9{2}+{3}\"); print agc3(cga3(x))-x\n 0\n ";
1339 static char __pyx_k_Convert_CGA3_null_vector_to_sta[] = "\n Convert CGA3 null vector to standard conformal null vector using Doran and Lasenby definition.\n\n >>> x=clifford(\"2{1}+9{2}+{3}\"); print cga3std(cga3(x))\n 87{-1}+4{1}+18{2}+2{3}+85{4}\n >>> x=clifford(\"2{1}+9{2}+{3}\"); print cga3std(cga3(x))-cga3(x)\n 0\n ";
1340 static char __pyx_k_Convert_Euclidean_3D_multivecto[] = "\n Convert Euclidean 3D multivector to Conformal Geometric Algebra using Doran and Lasenby definition.\n\n >>> x=clifford(\"2{1}+9{2}+{3}\"); print cga3(x)\n 87{-1}+4{1}+18{2}+2{3}+85{4}\n ";
1341 static char __pyx_k_Copy_this_clifford_object_x_cli[] = "\n Copy this clifford object.\n\n >>> x=clifford(\"1{2}\"); y=x.copy(); print y\n {2}\n ";
1342 static char __pyx_k_Copy_this_index_set_object_s_in[] = "\n Copy this index_set object.\n\n >>> s=index_set(1); t=s.copy(); print t\n {1}\n ";
1343 static char __pyx_k_Cosine_of_multivector_with_opti[] = "\n Cosine of multivector with optional complexifier.\n\n >>> x=clifford(\"{1,2}\"); print cos(acos(x),\"{1,2,3}\")\n {1,2}\n >>> x=clifford(\"{1,2}\"); print cos(acos(x))\n {1,2}\n ";
1344 static char __pyx_k_Even_part_of_multivector_sum_of[] = "\n Even part of multivector, sum of even grade terms.\n\n >>> print clifford(\"1+{1}+{1,2}\").even()\n 1+{1,2}\n ";
1345 static char __pyx_k_Exponential_of_multivector_x_cl[] = "\n Exponential of multivector.\n\n >>> x=clifford(\"{1,2}\") * pi/4; print exp(x)\n 0.7071+0.7071{1,2}\n >>> x=clifford(\"{1,2}\") * pi/2; print exp(x)\n {1,2}\n ";
1346 static char __pyx_k_Geometric_difference_print_clif[] = "\n Geometric difference.\n\n >>> print clifford(1) - clifford(\"{2}\")\n 1-{2}\n >>> print clifford(\"{1}\") - clifford(\"{2}\")\n {1}-{2}\n ";
1347 static char __pyx_k_Geometric_difference_x_clifford[] = "\n Geometric difference.\n\n >>> x = clifford(1); x -= clifford(\"{2}\"); print x\n 1-{2}\n ";
1348 static char __pyx_k_Geometric_multiplicative_invers[] = "\n Geometric multiplicative inverse.\n\n >>> x = clifford(\"{1}\"); print x.inv()\n {1}\n >>> x = clifford(2); print x.inv()\n 0.5\n >>> x = clifford(\"{1,2}\"); print x.inv()\n -{1,2}\n ";
1349 static char __pyx_k_Geometric_product_print_cliffor[] = "\n Geometric product.\n\n >>> print clifford(\"{1}\") * clifford(\"{2}\")\n {1,2}\n >>> print clifford(2) * clifford(\"{2}\")\n 2{2}\n >>> print clifford(\"{1}\") * clifford(\"{1,2}\")\n {2}\n ";
1350 static char __pyx_k_Geometric_quotient_print_cliffo[] = "\n Geometric quotient.\n\n >>> print clifford(\"{1}\") / clifford(\"{2}\")\n {1,2}\n >>> print clifford(2) / clifford(\"{2}\")\n 2{2}\n >>> print clifford(\"{1}\") / clifford(\"{1}\")\n 1\n >>> print clifford(\"{1}\") / clifford(\"{1,2}\")\n -{2}\n ";
1351 static char __pyx_k_Geometric_quotient_x_clifford_1[] = "\n Geometric quotient.\n\n >>> x = clifford(\"{1}\"); x /= clifford(\"{2}\"); print x\n {1,2}\n >>> x = clifford(2); x /= clifford(\"{2}\"); print x\n 2{2}\n >>> x = clifford(\"{1}\"); x /= clifford(\"{1}\"); print x\n 1\n >>> x = clifford(\"{1}\"); x /= clifford(\"{1,2}\"); print x\n -{2}\n ";
1352 static char __pyx_k_Geometric_sum_x_clifford_1_x_cl[] = "\n Geometric sum.\n\n >>> x = clifford(1); x += clifford(\"{2}\"); print x\n 1+{2}\n ";
1353 static char __pyx_k_Get_the_value_of_an_index_set_o[] = "\n Get the value of an index_set object at an index.\n\n >>> index_set({1})[1]\n True\n >>> index_set({1})[2]\n False\n >>> index_set({2})[-1]\n False\n >>> index_set({2})[1]\n False\n >>> index_set({2})[2]\n True\n >>> index_set({2})[33]\n False\n ";
1354 static char __pyx_k_Hyperbolic_cosine_of_multivecto[] = "\n Hyperbolic cosine of multivector.\n\n >>> x=clifford(\"{1,2}\") * pi; print cosh(x)\n -1\n >>> x=clifford(\"{1,2,3}\"); print cosh(acosh(x))\n {1,2,3}\n >>> x=clifford(\"{1,2}\"); print cosh(acosh(x))\n {1,2}\n ";
1355 static char __pyx_k_Hyperbolic_tangent_of_multivect[] = "\n Hyperbolic tangent of multivector.\n\n >>> x=clifford(\"{1,2}\") * pi/4; print tanh(x)\n {1,2}\n ";
1356 static char __pyx_k_Imaginary_part_deprecated_alway[] = "\n Imaginary part: deprecated (always 0).\n\n >>> imag(clifford(\"1+{1}+{1,2}\"))\n 0.0\n >>> imag(clifford(\"{1,2}\"))\n 0.0\n ";
1357 static char __pyx_k_Inner_product_x_clifford_1_x_cl[] = "\n Inner product.\n\n >>> x = clifford(\"{1}\"); x &= clifford(\"{2}\"); print x\n 0\n >>> x = clifford(2); x &= clifford(\"{2}\"); print x\n 0\n >>> x = clifford(\"{1}\"); x &= clifford(\"{1}\"); print x\n 1\n >>> x = clifford(\"{1}\"); x &= clifford(\"{1,2}\"); print x\n {2}\n ";
1358 static char __pyx_k_Integer_power_of_multivector_ob[] = "\n Integer power of multivector: obj to the m.\n\n >>> x=clifford(\"{1}\"); print pow(x,2)\n 1\n >>> x=clifford(\"2\"); print pow(x,2)\n 4\n >>> x=clifford(\"2+{1}\"); print pow(x,0)\n 1\n >>> x=clifford(\"2+{1}\"); print pow(x,1)\n 2+{1}\n >>> x=clifford(\"2+{1}\"); print pow(x,2)\n 5+4{1}\n >>> print pow(clifford(\"1+{1}+{1,2}\"),3)\n 1+3{1}+3{1,2}\n >>> i=clifford(\"{1,2}\");print exp(pi/2) * pow(i, i)\n 1\n ";
1359 static char __pyx_k_Inverse_cosine_of_multivector_w[] = "\n Inverse cosine of multivector with optional complexifier.\n\n >>> x=clifford(\"{1,2}\"); print cos(acos(x),\"{1,2,3}\")\n {1,2}\n >>> x=clifford(\"{1,2}\"); print cos(acos(x),\"{-1,1,2,3,4}\")\n {1,2}\n >>> print acos(0) / pi\n 0.5\n >>> x=clifford(\"{1,2}\"); print cos(acos(x))\n {1,2}\n ";
1360 static char __pyx_k_Inverse_hyperbolic_cosine_of_mu[] = "\n Inverse hyperbolic cosine of multivector with optional complexifier.\n\n >>> print acosh(0,\"{-2,-1,1}\")\n 1.571{-2,-1,1}\n >>> x=clifford(\"{1,2,3}\"); print cosh(acosh(x,\"{-1,1,2,3,4}\"))\n {1,2,3}\n >>> print acosh(0)\n 1.571{-1}\n >>> x=clifford(\"{1,2,3}\"); print cosh(acosh(x))\n {1,2,3}\n >>> x=clifford(\"{1,2}\"); print cosh(acosh(x))\n {1,2}\n ";
1361 static char __pyx_k_Inverse_hyperbolic_sine_of_mult[] = "\n Inverse hyperbolic sine of multivector with optional complexifier.\n\n >>> x=clifford(\"{1,2}\"); print asinh(x,\"{1,2,3}\") * 2/pi\n {1,2}\n >>> x=clifford(\"{1,2}\"); print asinh(x) * 2/pi\n {1,2}\n >>> x=clifford(\"{1,2}\") / 2; print asinh(x) * 6/pi\n {1,2}\n ";
1362 static char __pyx_k_Inverse_hyperbolic_tangent_of_m[] = "\n Inverse hyperbolic tangent of multivector with optional complexifier.\n\n >>> s=index_set({1,2,3}); x=clifford(\"{1,2}\"); print tanh(atanh(x,s))\n {1,2}\n >>> x=clifford(\"{1,2}\"); print tanh(atanh(x))\n {1,2}\n ";
1363 static char __pyx_k_Inverse_sine_of_multivector_wit[] = "\n Inverse sine of multivector with optional complexifier.\n\n >>> s=\"{-1}\"; x=clifford(s); print asin(sin(x,s),s)\n {-1}\n >>> s=\"{-1}\"; x=clifford(s); print asin(sin(x,s),\"{-2,-1,1}\")\n {-1}\n >>> print asin(1) / pi\n 0.5\n >>> x=clifford(\"{1,2,3}\"); print asin(sin(x))\n {1,2,3}\n ";
1364 static char __pyx_k_Main_involution_each_i_is_repla[] = "\n Main involution, each {i} is replaced by -{i} in each term,\n eg. clifford(\"{1}\") -> -clifford(\"{1}\").\n\n >>> print clifford(\"{1}\").involute()\n -{1}\n >>> print (clifford(\"{2}\") * clifford(\"{1}\")).involute()\n -{1,2}\n >>> print (clifford(\"{1}\") * clifford(\"{2}\")).involute()\n {1,2}\n >>> print clifford(\"1+{1}+{1,2}\").involute()\n 1-{1}+{1,2}\n ";
1365 static char __pyx_k_Maximum_absolute_value_of_coord[] = "\n Maximum absolute value of coordinates multivector: multivector infinity-norm.\n\n >>> max_abs(clifford(\"1+{-1}+{1,2}+{1,2,3}\"))\n 1.0\n >>> max_abs(clifford(\"3+2{1}+{1,2}\"))\n 3.0\n\n ";
1366 static char __pyx_k_Maximum_of_absolute_values_of_c[] = "\n Maximum of absolute values of components of multivector: multivector infinity norm.\n\n >>> clifford(\"1+{-1}+{1,2}+{1,2,3}\").max_abs()\n 1.0\n >>> clifford(\"3+2{1}+{1,2}\").max_abs()\n 3.0\n ";
1367 static char __pyx_k_Natural_logarithm_of_multivecto[] = "\n Natural logarithm of multivector with optional complexifier.\n\n >>> x=clifford(\"{-1}\"); print (log(x,\"{-1}\") * 2/pi)\n {-1}\n >>> x=clifford(\"{1,2}\"); print (log(x,\"{1,2,3}\") * 2/pi)\n {1,2}\n >>> x=clifford(\"{1,2}\"); print (log(x) * 2/pi)\n {1,2}\n >>> x=clifford(\"{1,2}\"); print (log(x,\"{1,2}\") * 2/pi)\n Traceback (most recent call last):\n ...\n RuntimeError: check_complex(val, i): i is not a valid complexifier for val\n ";
1368 static char __pyx_k_Norm_sum_of_squares_of_coordina[] = "\n Norm == sum of squares of coordinates.\n\n >>> clifford(\"1+{1}+{1,2}\").norm()\n 3.0\n >>> clifford(\"1+{-1}+{1,2}+{1,2,3}\").norm()\n 4.0\n ";
1369 static char __pyx_k_Not_applicable_for_a_in_cliffor[] = "\n Not applicable.\n\n >>> for a in clifford(index_set({-3,4,7})): print a,\n Traceback (most recent call last):\n ...\n TypeError: Not applicable.\n ";
1370 static char __pyx_k_Number_of_negative_indices_incl[] = "\n Number of negative indices included in set.\n\n >>> index_set({-1,1,2}).count_neg()\n 1\n ";
1371 static char __pyx_k_Number_of_positive_indices_incl[] = "\n Number of positive indices included in set.\n\n >>> index_set({-1,1,2}).count_pos()\n 2\n ";
1372 static char __pyx_k_Outer_product_power_of_multivec[] = "\n Outer product power of multivector.\n\n >>> print outer_pow(clifford(\"1+{1}+{1,2}\"),3)\n 1+3{1}+3{1,2}\n ";
1373 static char __pyx_k_Outer_product_x_clifford_1_x_cl[] = "\n Outer product.\n\n >>> x = clifford(\"{1}\"); x ^= clifford(\"{2}\"); print x\n {1,2}\n >>> x = clifford(2); x ^= clifford(\"{2}\"); print x\n 2{2}\n >>> x = clifford(\"{1}\"); x ^= clifford(\"{1}\"); print x\n 0\n >>> x = clifford(\"{1}\"); x ^= clifford(\"{1,2}\"); print x\n 0\n ";
1374 static char __pyx_k_Pure_grade_vector_part_print_cl[] = "\n Pure grade-vector part.\n\n >>> print clifford(\"{1}\")(1)\n {1}\n >>> print clifford(\"{1}\")(0)\n 0\n >>> print clifford(\"1+{1}+{1,2}\")(0)\n 1\n >>> print clifford(\"1+{1}+{1,2}\")(1)\n {1}\n >>> print clifford(\"1+{1}+{1,2}\")(2)\n {1,2}\n >>> print clifford(\"1+{1}+{1,2}\")(3)\n 0\n ";
1375 static char __pyx_k_Pure_part_print_pure_clifford_1[] = "\n Pure part\n\n >>> print pure(clifford(\"1+{1}+{1,2}\"))\n {1}+{1,2}\n >>> print pure(clifford(\"{1,2}\"))\n {1,2}\n ";
1376 static char __pyx_k_Put_self_into_a_larger_frame_co[] = "\n Put self into a larger frame, containing the union of self.frame() and index set ixt.\n This can be used to make multiplication faster, by multiplying within a common frame.\n\n >>> clifford(\"2+3{1}\").reframe(index_set({1,2,3}))\n clifford(\"2+3{1}\")\n >>> s=index_set({1,2,3});t=index_set({-3,-2,-1});x=random_clifford(s); x.reframe(t).frame() == (s|t);\n True\n ";
1377 static char __pyx_k_Random_multivector_within_a_fra[] = "\n Random multivector within a frame.\n\n >>> print random_clifford(index_set({-3,-1,2})).frame()\n {-3,-1,2}\n ";
1378 static char __pyx_k_Real_part_synonym_for_scalar_pa[] = "\n Real part: synonym for scalar part.\n\n >>> real(clifford(\"1+{1}+{1,2}\"))\n 1.0\n >>> real(clifford(\"{1,2}\"))\n 0.0\n ";
1379 static char __pyx_k_Remove_all_terms_of_self_with_r[] = "\n Remove all terms of self with relative size smaller than limit.\n\n >>> clifford(\"1e8+{1}+1e-8{1,2}\").truncated(1.0e-6)\n clifford(\"100000000\")\n >>> clifford(\"1e4+{1}+1e-4{1,2}\").truncated(1.0e-6)\n clifford(\"10000+{1}\")\n ";
1380 static char __pyx_k_Reversion_eg_1_2_2_1_print_reve[] = "\n Reversion, eg. {1}*{2} -> {2}*{1}\n\n >>> print reverse(clifford(\"{1}\"))\n {1}\n >>> print reverse(clifford(\"{2}\") * clifford(\"{1}\"))\n {1,2}\n >>> print reverse(clifford(\"{1}\") * clifford(\"{2}\"))\n -{1,2}\n >>> print reverse(clifford(\"1+{1}+{1,2}\"))\n 1+{1}-{1,2}\n ";
1381 static char __pyx_k_Reversion_eg_clifford_1_cliffor[] = "\n Reversion, eg. clifford(\"{1}\")*clifford(\"{2}\") -> clifford(\"{2}\")*clifford(\"{1}\").\n\n >>> print clifford(\"{1}\").reverse()\n {1}\n >>> print (clifford(\"{2}\") * clifford(\"{1}\")).reverse()\n {1,2}\n >>> print (clifford(\"{1}\") * clifford(\"{2}\")).reverse()\n -{1,2}\n >>> print clifford(\"1+{1}+{1,2}\").reverse()\n 1+{1}-{1,2}\n ";
1382 static char __pyx_k_Scalar_part_clifford_1_1_1_2_sc[] = "\n Scalar part.\n\n >>> clifford(\"1+{1}+{1,2}\").scalar()\n 1.0\n >>> clifford(\"{1,2}\").scalar()\n 0.0\n ";
1383 static char __pyx_k_Scalar_part_scalar_clifford_1_1[] = "\n Scalar part.\n\n >>> scalar(clifford(\"1+{1}+{1,2}\"))\n 1.0\n >>> scalar(clifford(\"{1,2}\"))\n 0.0\n ";
1384 static char __pyx_k_Set_intersection_and_print_inde[] = "\n Set intersection: and.\n\n >>> print index_set({1}) & index_set({2})\n {}\n >>> print index_set({1,2}) & index_set({2})\n {2}\n ";
1385 static char __pyx_k_Set_intersection_and_x_index_se[] = "\n Set intersection: and.\n\n >>> x = index_set({1}); x &= index_set({2}); print x\n {}\n >>> x = index_set({1,2}); x &= index_set({2}); print x\n {2}\n ";
1386 static char __pyx_k_Set_the_value_of_an_index_set_o[] = "\n Set the value of an index_set object at index idx to value val.\n\n >>> s=index_set({1}); s[2] = True; print s\n {1,2}\n >>> s=index_set({1,2}); s[1] = False; print s\n {2}\n ";
1387 static char __pyx_k_Set_union_or_x_index_set_1_x_in[] = "\n Set union: or.\n\n >>> x = index_set({1}); x |= index_set({2}); print x\n {1,2}\n >>> x = index_set({1,2}); x |= index_set({2}); print x\n {1,2}\n ";
1388 static char __pyx_k_Sign_of_geometric_product_of_tw[] = "\n Sign of geometric product of two Clifford basis elements.\n\n >>> s = index_set({1,2}); t=index_set({-1}); s.sign_of_mult(t)\n 1\n ";
1389 static char __pyx_k_Sign_of_geometric_square_of_a_C[] = "\n Sign of geometric square of a Clifford basis element.\n\n >>> s = index_set({1,2}); s.sign_of_square()\n -1\n ";
1390 static char __pyx_k_Sine_of_multivector_with_option[] = "\n Sine of multivector with optional complexifier.\n\n >>> s=\"{-1}\"; x=clifford(s); print asin(sin(x,s),s)\n {-1}\n >>> s=\"{-1}\"; x=clifford(s); print asin(sin(x,s),\"{-2,-1,1}\")\n {-1}\n >>> x=clifford(\"{1,2,3}\"); print asin(sin(x))\n {1,2,3}\n ";
1391 static char __pyx_k_Square_root_of_1_which_commutes[] = "\n Square root of -1 which commutes with all members of the frame of the given multivector.\n\n >>> print complexifier(clifford(index_set({1})))\n {1,2,3}\n >>> print complexifier(clifford(index_set({-1})))\n {-1}\n >>> print complexifier(index_set({1}))\n {1,2,3}\n >>> print complexifier(index_set({-1}))\n {-1}\n ";
1392 static char __pyx_k_Square_root_of_multivector_with[] = "\n Square root of multivector with optional complexifier.\n\n >>> print sqrt(-1)\n {-1}\n >>> print sqrt(clifford(\"2{-1}\"))\n 1+{-1}\n >>> j=sqrt(-1,complexifier(index_set({1}))); print j; print j*j\n {1,2,3}\n -1\n >>> j=sqrt(-1,\"{1,2,3}\"); print j; print j*j\n {1,2,3}\n -1\n ";
1393 static char __pyx_k_Subalgebra_generated_by_all_gen[] = "\n Subalgebra generated by all generators of terms of given multivector.\n\n >>> print clifford(\"1+3{-1}+2{1,2}+4{-2,7}\").frame()\n {-2,-1,1,2,7}\n >>> s=clifford(\"1+3{-1}+2{1,2}+4{-2,7}\").frame(); type(s)\n <type 'PyClical.index_set'>\n ";
1394 static char __pyx_k_Subscripting_map_from_index_set[] = "\n Subscripting: map from index set to scalar coordinate.\n\n >>> clifford(\"{1}\")[index_set(1)]\n 1.0\n >>> clifford(\"{1}\")[index_set({1})]\n 1.0\n >>> clifford(\"{1}\")[index_set({1,2})]\n 0.0\n >>> clifford(\"2{1,2}\")[index_set({1,2})]\n 2.0\n ";
1395 static char __pyx_k_Symmetric_set_difference_exclus[] = "\n Symmetric set difference: exclusive or.\n\n >>> print index_set({1}) ^ index_set({2})\n {1,2}\n >>> print index_set({1,2}) ^ index_set({2})\n {1}\n ";
1396 static char __pyx_k_Tangent_of_multivector_with_opt[] = "\n Tangent of multivector with optional complexifier.\n\n >>> x=clifford(\"{1,2}\"); print tan(x,\"{1,2,3}\")\n 0.7616{1,2}\n >>> x=clifford(\"{1,2}\"); print tan(x)\n 0.7616{1,2}\n ";
1397 static char __pyx_k_Tests_for_functions_that_Doctes[] = "\n Tests for functions that Doctest cannot see.\n\n For index_set.__cinit__: Construct index_set.\n\n >>> print index_set(1)\n {1}\n >>> print index_set({1,2})\n {1,2}\n >>> print index_set(index_set({1,2}))\n {1,2}\n >>> print index_set({1,2})\n {1,2}\n >>> print index_set({1,2,1})\n {1,2}\n >>> print index_set({1,2,1})\n {1,2}\n >>> print index_set(\"\")\n {}\n >>> print index_set(\"{\")\n Traceback (most recent call last):\n ...\n ValueError: Cannot initialize index_set object from invalid string '{'.\n >>> print index_set(\"{1\")\n Traceback (most recent call last):\n ...\n ValueError: Cannot initialize index_set object from invalid string '{1'.\n >>> print index_set(\"{1,2,100}\")\n Traceback (most recent call last):\n ...\n ValueError: Cannot initialize index_set object from invalid string '{1,2,100}'.\n >>> print index_set({1,2,100})\n Traceback (most recent call last):\n ...\n IndexError: Cannot initialize index_set object from invalid set([1, 2, 100]).\n >>> print index_set([1,2])\n Traceback (most recent call last):\n ...\n TypeError: Cannot initialize index_set object from <type 'list'>.\n\n For index_set.__richcmp__: Compare two objects of class index_set.\n\n >>> index_set(1) == index_set({1})\n True\n >>> index_set({1}) != index_set({1})\n False\n >>> index_set({1}) != index_set({2})\n True\n >>> index_set({1}) == index_set({2})\n False\n >>> index_set({1}) < index_set({2})\n True\n >>> index_set({1}) <= index_set({2})\n True\n >>> index_set({1}) > index_set({2})\n False\n >>> index_set({1}) >= index_set({2})\n False\n >>> None == index_set({1,2})\n False\n >>> None != index_set({1,2})\n True\n >>> None < index_set({1,2})\n False\n >>> None <= index_set({1,2})\n False\n >>> None > index_set({1,2})\n False\n >>> None >= index_set({1,2})\n False\n >>> index_se""t({1,2}) == None\n False\n >>> index_set({1,2}) != None\n True\n >>> index_set({1,2}) < None\n False\n >>> index_set({1,2}) <= None\n False\n >>> index_set({1,2}) > None\n False\n >>> index_set({1,2}) >= None\n False\n ";
1398  static char __pyx_k_The_informal_string_representat[] = "\n The \342\200\234informal\342\200\235 string representation of self.\n\n >>> index_set({1,2}).__str__()\n '{1,2}'\n >>> str(index_set({1,2}))\n '{1,2}'\n ";
1399  static char __pyx_k_The_official_string_representat[] = "\n The \342\200\234official\342\200\235 string representation of self.\n\n >>> index_set({1,2}).__repr__()\n 'index_set({1,2})'\n >>> repr(index_set({1,2}))\n 'index_set({1,2})'\n ";
1400  static char __pyx_k_This_comparison_operator_is_not[] = "This comparison operator is not implemented for ";
1401  static char __pyx_k_Vector_part_of_multivector_as_a[] = "\n Vector part of multivector, as a Python list, with respect to frm.\n\n >>> print clifford(\"1+2{1}+3{2}+4{1,2}\").vector_part()\n [2.0, 3.0]\n >>> print clifford(\"1+2{1}+3{2}+4{1,2}\").vector_part(index_set({-1,1,2}))\n [0.0, 2.0, 3.0]\n ";
1402  static char __pyx_k_home_abuild_rpmbuild_BUILD_gluc[] = "/home/abuild/rpmbuild/BUILD/glucat-0.8.2/pyclical/PyClical.pyx";
1403  static char __pyx_k_index_set_sign_of_mult_line_364[] = "index_set.sign_of_mult (line 364)";
1404  static char __pyx_k_norm_sum_of_squares_of_coordina[] = "\n norm == sum of squares of coordinates.\n\n >>> norm(clifford(\"1+{1}+{1,2}\"))\n 3.0\n >>> norm(clifford(\"1+{-1}+{1,2}+{1,2,3}\"))\n 4.0\n ";
1405  static char __pyx_k_Cannot_initialize_clifford_objec[] = "Cannot initialize clifford object from";
1406  static char __pyx_k_Cannot_initialize_index_set_obje[] = "Cannot initialize index_set object from";
1407  static char __pyx_k_Conjugation_reverse_o_involute_2[] = "\n Conjugation, reverse o involute == involute o reverse.\n\n >>> print conj(clifford(\"{1}\"))\n -{1}\n >>> print conj(clifford(\"{2}\") * clifford(\"{1}\"))\n {1,2}\n >>> print conj(clifford(\"{1}\") * clifford(\"{2}\"))\n -{1,2}\n >>> print conj(clifford(\"1+{1}+{1,2}\"))\n 1-{1}-{1,2}\n ";
1408  static char __pyx_k_Odd_part_of_multivector_sum_of_2[] = "\n Odd part of multivector, sum of odd grade terms.\n\n >>> print odd(clifford(\"1+{1}+{1,2}\"))\n {1}\n ";
1409  static char __pyx_k_Power_self_to_the_m_x_clifford_2[] = "\n Power: self to the m.\n\n >>> x=clifford(\"{1}\"); print x.pow(2)\n 1\n >>> x=clifford(\"2\"); print x.pow(2)\n 4\n >>> x=clifford(\"2+{1}\"); print x.pow(0)\n 1\n >>> x=clifford(\"2+{1}\"); print x.pow(1)\n 2+{1}\n >>> x=clifford(\"2+{1}\"); print x.pow(2)\n 5+4{1}\n >>> print clifford(\"1+{1}+{1,2}\").pow(3)\n 1+3{1}+3{1,2}\n >>> i=clifford(\"{1,2}\");print exp(pi/2) * i.pow(i)\n 1\n ";
1410  static char __pyx_k_Quadratic_form_rev_x_x_0_print_2[] = "\n Quadratic form == (rev(x)*x)(0).\n\n >>> print quad(clifford(\"1+{1}+{1,2}\"))\n 3.0\n >>> print quad(clifford(\"1+{-1}+{1,2}+{1,2,3}\"))\n 2.0\n ";
1411  static char __pyx_k_Transform_left_hand_side_using_2[] = "\n Transform left hand side, using right hand side as a transformation.\n\n >>> x=clifford(\"{1,2}\") * pi/2; y=clifford(\"{1}\"); y|=x; print y\n -{1}\n >>> x=clifford(\"{1,2}\") * pi/2; y=clifford(\"{1}\"); y|=exp(x); print y\n -{1}\n ";
1412  static char __pyx_k_clifford_hidden_doctests_line_12[] = "clifford_hidden_doctests (line 1243)";
1413  static char __pyx_k_index_set_hidden_doctests_line_4[] = "index_set_hidden_doctests (line 404)";
1414  static char __pyx_k_index_set_sign_of_square_line_37[] = "index_set.sign_of_square (line 373)";
1415  static char __pyx_k_Even_part_of_multivector_sum_of_2[] = "\n Even part of multivector, sum of even grade terms.\n\n >>> print even(clifford(\"1+{1}+{1,2}\"))\n 1+{1,2}\n ";
1416  static char __pyx_k_Geometric_multiplicative_invers_2[] = "\n Geometric multiplicative inverse.\n\n >>> print inv(clifford(\"{1}\"))\n {1}\n >>> print inv(clifford(\"{-1}\"))\n -{-1}\n >>> print inv(clifford(\"{-2,-1}\"))\n -{-2,-1}\n >>> print inv(clifford(\"{-1}+{1}\"))\n nan\n ";
1417  static char __pyx_k_Main_involution_each_i_is_repla_2[] = "\n Main involution, each {i} is replaced by -{i} in each term, eg. {1}*{2} -> (-{2})*(-{1})\n\n >>> print involute(clifford(\"{1}\"))\n -{1}\n >>> print involute(clifford(\"{2}\") * clifford(\"{1}\"))\n -{1,2}\n >>> print involute(clifford(\"{1}\") * clifford(\"{2}\"))\n {1,2}\n >>> print involute(clifford(\"1+{1}+{1,2}\"))\n 1-{1}+{1,2}\n ";
1418  static char __pyx_k_Symmetric_set_difference_exclus_2[] = "\n Symmetric set difference: exclusive or.\n\n >>> x = index_set({1}); x ^= index_set({2}); print x\n {1,2}\n >>> x = index_set({1,2}); x ^= index_set({2}); print x\n {1}\n ";
1419  static char __pyx_k_Tests_for_functions_that_Doctes_2[] = "\n Tests for functions that Doctest cannot see.\n\n For clifford.__cinit__: Construct an object of type clifford.\n\n >>> print clifford(2)\n 2\n >>> print clifford(2L)\n 2\n >>> print clifford(2.0)\n 2\n >>> print clifford(1.0e-1)\n 0.1\n >>> print clifford(\"2\")\n 2\n >>> print clifford(\"2{1,2,3}\")\n 2{1,2,3}\n >>> print clifford(clifford(\"2{1,2,3}\"))\n 2{1,2,3}\n >>> print clifford(\"-{1}\")\n -{1}\n >>> print clifford(2,index_set({1,2}))\n 2{1,2}\n >>> print clifford([2,3],index_set({1,2}))\n 2{1}+3{2}\n >>> print clifford([1,2])\n Traceback (most recent call last):\n ...\n TypeError: Cannot initialize clifford object from <type 'list'>.\n >>> print clifford(None)\n Traceback (most recent call last):\n ...\n TypeError: Cannot initialize clifford object from <type 'NoneType'>.\n >>> print clifford(None,[1,2])\n Traceback (most recent call last):\n ...\n TypeError: Cannot initialize clifford object from (<type 'NoneType'>, <type 'list'>).\n >>> print clifford([1,2],[1,2])\n Traceback (most recent call last):\n ...\n TypeError: Cannot initialize clifford object from (<type 'list'>, <type 'list'>).\n >>> print clifford(\"\")\n Traceback (most recent call last):\n ...\n ValueError: Cannot initialize clifford object from invalid string ''.\n >>> print clifford(\"{\")\n Traceback (most recent call last):\n ...\n ValueError: Cannot initialize clifford object from invalid string '{'.\n >>> print clifford(\"{1\")\n Traceback (most recent call last):\n ...\n ValueError: Cannot initialize clifford object from invalid string '{1'.\n >>> print clifford(\"+\")\n Traceback (most recent call last):\n ...\n ValueError: Cannot initialize clifford object from invalid string '+'.\n >>> print clifford(\"-\")\n Traceback (most recent call last):\n ...\n ValueError: Cannot initialize clifford"" object from invalid string '-'.\n >>> print clifford(\"{1}+\")\n Traceback (most recent call last):\n ...\n ValueError: Cannot initialize clifford object from invalid string '{1}+'.\n\n For clifford.__richcmp__: Compare objects of type clifford.\n\n >>> clifford(\"{1}\") == clifford(\"1{1}\")\n True\n >>> clifford(\"{1}\") != clifford(\"1.0{1}\")\n False\n >>> clifford(\"{1}\") != clifford(\"1.0\")\n True\n >>> clifford(\"{1,2}\") == None\n False\n >>> clifford(\"{1,2}\") != None\n True\n >>> None == clifford(\"{1,2}\")\n False\n >>> None != clifford(\"{1,2}\")\n True\n ";
1420  static char __pyx_k_The_informal_string_representat_2[] = "\n The \342\200\234informal\342\200\235 string representation of self.\n\n >>> clifford(\"1+3{-1}+2{1,2}+4{-2,7}\").__str__()\n '1+3{-1}+2{1,2}+4{-2,7}'\n ";
1421  static char __pyx_k_The_official_string_representat_2[] = "\n The \342\200\234official\342\200\235 string representation of self.\n\n >>> clifford(\"1+3{-1}+2{1,2}+4{-2,7}\").__repr__()\n 'clifford(\"1+3{-1}+2{1,2}+4{-2,7}\")'\n ";
1422  static PyObject *__pyx_kp_s_;
1423  static PyObject *__pyx_kp_s_0_8_2;
1424  static PyObject *__pyx_kp_u_Abbreviation_for_clifford_index;
1425  static PyObject *__pyx_kp_u_Abbreviation_for_index_set_q_p;
1426  static PyObject *__pyx_kp_u_Absolute_value_of_multivector_m;
1427  static PyObject *__pyx_kp_u_Absolute_value_square_root_of_n;
1428  static PyObject *__pyx_kp_s_Cannot_initialize_clifford_objec;
1429  static PyObject *__pyx_kp_s_Cannot_initialize_index_set_obje;
1430  static PyObject *__pyx_kp_s_Cannot_reframe;
1431  static PyObject *__pyx_kp_s_Cannot_take_vector_part_of;
1432  static PyObject *__pyx_kp_u_Cardinality_Number_of_indices_i;
1433  static PyObject *__pyx_kp_u_Check_if_a_multivector_contains;
1434  static PyObject *__pyx_kp_u_Conjugation_reverse_o_involute;
1435  static PyObject *__pyx_kp_u_Conjugation_reverse_o_involute_2;
1436  static PyObject *__pyx_kp_u_Contraction_print_clifford_1_cl;
1437  static PyObject *__pyx_kp_u_Contraction_x_clifford_1_x_clif;
1438  static PyObject *__pyx_kp_u_Convert_CGA3_null_vector_to_Euc;
1439  static PyObject *__pyx_kp_u_Convert_CGA3_null_vector_to_sta;
1440  static PyObject *__pyx_kp_u_Convert_Euclidean_3D_multivecto;
1441  static PyObject *__pyx_kp_u_Copy_this_clifford_object_x_cli;
1442  static PyObject *__pyx_kp_u_Copy_this_index_set_object_s_in;
1443  static PyObject *__pyx_kp_u_Cosine_of_multivector_with_opti;
1444  static PyObject *__pyx_kp_u_Even_part_of_multivector_sum_of;
1445  static PyObject *__pyx_kp_u_Even_part_of_multivector_sum_of_2;
1446  static PyObject *__pyx_kp_u_Exponential_of_multivector_x_cl;
1447  static PyObject *__pyx_kp_u_Geometric_difference_print_clif;
1448  static PyObject *__pyx_kp_u_Geometric_difference_x_clifford;
1449  static PyObject *__pyx_kp_u_Geometric_multiplicative_invers;
1450  static PyObject *__pyx_kp_u_Geometric_multiplicative_invers_2;
1451  static PyObject *__pyx_kp_u_Geometric_product_print_cliffor;
1452  static PyObject *__pyx_kp_u_Geometric_product_x_clifford_2;
1453  static PyObject *__pyx_kp_u_Geometric_quotient_print_cliffo;
1454  static PyObject *__pyx_kp_u_Geometric_quotient_x_clifford_1;
1455  static PyObject *__pyx_kp_u_Geometric_sum_print_clifford_1;
1456  static PyObject *__pyx_kp_u_Geometric_sum_x_clifford_1_x_cl;
1457  static PyObject *__pyx_kp_u_Get_the_value_of_an_index_set_o;
1458  static PyObject *__pyx_kp_u_Hyperbolic_cosine_of_multivecto;
1459  static PyObject *__pyx_kp_u_Hyperbolic_sine_of_multivector;
1460  static PyObject *__pyx_kp_u_Hyperbolic_tangent_of_multivect;
1461  static PyObject *__pyx_kp_u_Imaginary_part_deprecated_alway;
1462  static PyObject *__pyx_n_s_IndexError;
1463  static PyObject *__pyx_kp_u_Inner_product_print_clifford_1;
1464  static PyObject *__pyx_kp_u_Inner_product_x_clifford_1_x_cl;
1465  static PyObject *__pyx_kp_u_Integer_power_of_multivector_ob;
1466  static PyObject *__pyx_n_s_Integral;
1467  static PyObject *__pyx_kp_u_Inverse_cosine_of_multivector_w;
1468  static PyObject *__pyx_kp_u_Inverse_hyperbolic_cosine_of_mu;
1469  static PyObject *__pyx_kp_u_Inverse_hyperbolic_sine_of_mult;
1470  static PyObject *__pyx_kp_u_Inverse_hyperbolic_tangent_of_m;
1471  static PyObject *__pyx_kp_u_Inverse_sine_of_multivector_wit;
1472  static PyObject *__pyx_kp_u_Inverse_tangent_of_multivector;
1473  static PyObject *__pyx_kp_u_Iterate_over_the_indices_of_an;
1474  static PyObject *__pyx_kp_u_Main_involution_each_i_is_repla;
1475  static PyObject *__pyx_kp_u_Main_involution_each_i_is_repla_2;
1476  static PyObject *__pyx_kp_u_Maximum_absolute_value_of_coord;
1477  static PyObject *__pyx_kp_u_Maximum_member_index_set_1_1_2;
1478  static PyObject *__pyx_kp_u_Maximum_of_absolute_values_of_c;
1479  static PyObject *__pyx_kp_u_Maximum_positive_index_or_0_if;
1480  static PyObject *__pyx_kp_u_Minimum_member_index_set_1_1_2;
1481  static PyObject *__pyx_kp_u_Minimum_negative_index_or_0_if;
1482  static PyObject *__pyx_kp_u_Natural_logarithm_of_multivecto;
1483  static PyObject *__pyx_kp_u_Norm_sum_of_squares_of_coordina;
1484  static PyObject *__pyx_n_s_NotImplemented;
1485  static PyObject *__pyx_kp_s_Not_applicable;
1486  static PyObject *__pyx_kp_u_Not_applicable_for_a_in_cliffor;
1487  static PyObject *__pyx_kp_u_Number_of_negative_indices_incl;
1488  static PyObject *__pyx_kp_u_Number_of_positive_indices_incl;
1489  static PyObject *__pyx_kp_u_Odd_part_of_multivector_sum_of;
1490  static PyObject *__pyx_kp_u_Odd_part_of_multivector_sum_of_2;
1491  static PyObject *__pyx_kp_u_Outer_product_power_of_multivec;
1492  static PyObject *__pyx_kp_u_Outer_product_power_x_clifford;
1493  static PyObject *__pyx_kp_u_Outer_product_print_clifford_1;
1494  static PyObject *__pyx_kp_u_Outer_product_x_clifford_1_x_cl;
1495  static PyObject *__pyx_kp_u_Power_self_to_the_m_x_clifford;
1496  static PyObject *__pyx_kp_u_Power_self_to_the_m_x_clifford_2;
1497  static PyObject *__pyx_kp_u_Pure_grade_vector_part_print_cl;
1498  static PyObject *__pyx_kp_u_Pure_part_print_clifford_1_1_1;
1499  static PyObject *__pyx_kp_u_Pure_part_print_pure_clifford_1;
1500  static PyObject *__pyx_kp_u_Put_self_into_a_larger_frame_co;
1501  static PyObject *__pyx_n_s_PyClical;
1502  static PyObject *__pyx_kp_u_Quadratic_form_rev_x_x_0_print;
1503  static PyObject *__pyx_kp_u_Quadratic_form_rev_x_x_0_print_2;
1504  static PyObject *__pyx_kp_u_Random_multivector_within_a_fra;
1505  static PyObject *__pyx_n_s_Real;
1506  static PyObject *__pyx_kp_u_Real_part_synonym_for_scalar_pa;
1507  static PyObject *__pyx_kp_u_Remove_all_terms_of_self_with_r;
1508  static PyObject *__pyx_kp_u_Reversion_eg_1_2_2_1_print_reve;
1509  static PyObject *__pyx_kp_u_Reversion_eg_clifford_1_cliffor;
1510  static PyObject *__pyx_n_s_RuntimeError;
1511  static PyObject *__pyx_kp_u_Scalar_part_clifford_1_1_1_2_sc;
1512  static PyObject *__pyx_kp_u_Scalar_part_scalar_clifford_1_1;
1513  static PyObject *__pyx_n_s_Sequence;
1514  static PyObject *__pyx_kp_u_Set_complement_not_print_index;
1515  static PyObject *__pyx_kp_u_Set_intersection_and_print_inde;
1516  static PyObject *__pyx_kp_u_Set_intersection_and_x_index_se;
1517  static PyObject *__pyx_kp_u_Set_the_value_of_an_index_set_o;
1518  static PyObject *__pyx_kp_u_Set_union_or_print_index_set_1;
1519  static PyObject *__pyx_kp_u_Set_union_or_x_index_set_1_x_in;
1520  static PyObject *__pyx_kp_u_Sign_of_geometric_product_of_tw;
1521  static PyObject *__pyx_kp_u_Sign_of_geometric_square_of_a_C;
1522  static PyObject *__pyx_kp_u_Sine_of_multivector_with_option;
1523  static PyObject *__pyx_kp_u_Square_root_of_1_which_commutes;
1524  static PyObject *__pyx_kp_u_Square_root_of_multivector_with;
1525  static PyObject *__pyx_kp_u_Subalgebra_generated_by_all_gen;
1526  static PyObject *__pyx_kp_u_Subscripting_map_from_index_set;
1527  static PyObject *__pyx_kp_u_Symmetric_set_difference_exclus;
1528  static PyObject *__pyx_kp_u_Symmetric_set_difference_exclus_2;
1529  static PyObject *__pyx_kp_u_Tangent_of_multivector_with_opt;
1530  static PyObject *__pyx_kp_u_Tests_for_functions_that_Doctes;
1531  static PyObject *__pyx_kp_u_Tests_for_functions_that_Doctes_2;
1532  static PyObject *__pyx_kp_u_The_informal_string_representat;
1533  static PyObject *__pyx_kp_u_The_informal_string_representat_2;
1534  static PyObject *__pyx_kp_u_The_official_string_representat;
1535  static PyObject *__pyx_kp_u_The_official_string_representat_2;
1536  static PyObject *__pyx_kp_s_This_comparison_operator_is_not;
1537  static PyObject *__pyx_kp_u_Transform_left_hand_side_using;
1538  static PyObject *__pyx_kp_u_Transform_left_hand_side_using_2;
1539  static PyObject *__pyx_n_s_TypeError;
1540  static PyObject *__pyx_kp_u_Unary_print_clifford_1_1;
1541  static PyObject *__pyx_kp_u_Unary_print_clifford_1_1_2;
1542  static PyObject *__pyx_n_s_ValueError;
1543  static PyObject *__pyx_kp_u_Vector_part_of_multivector_as_a;
1544  static PyObject *__pyx_kp_s__2;
1545  static PyObject *__pyx_kp_s__3;
1546  static PyObject *__pyx_kp_s__4;
1547  static PyObject *__pyx_kp_s__5;
1548  static PyObject *__pyx_kp_s__6;
1549  static PyObject *__pyx_kp_s__7;
1550  static PyObject *__pyx_kp_u_abs_line_1473;
1551  static PyObject *__pyx_n_s_acos;
1552  static PyObject *__pyx_kp_u_acos_line_1619;
1553  static PyObject *__pyx_n_s_acosh;
1554  static PyObject *__pyx_kp_u_acosh_line_1656;
1555  static PyObject *__pyx_kp_u_agc3_line_1844;
1556  static PyObject *__pyx_n_s_args;
1557  static PyObject *__pyx_kp_s_as_frame;
1558  static PyObject *__pyx_n_s_asin;
1559  static PyObject *__pyx_kp_u_asin_line_1698;
1560  static PyObject *__pyx_n_s_asinh;
1561  static PyObject *__pyx_kp_u_asinh_line_1733;
1562  static PyObject *__pyx_n_s_atan;
1563  static PyObject *__pyx_kp_u_atan_line_1769;
1564  static PyObject *__pyx_n_s_atanh;
1565  static PyObject *__pyx_kp_u_atanh_line_1798;
1566  static PyObject *__pyx_kp_u_cga3_line_1824;
1567  static PyObject *__pyx_kp_u_cga3std_line_1833;
1568  static PyObject *__pyx_n_s_cl;
1569  static PyObject *__pyx_kp_u_clifford___add___line_739;
1570  static PyObject *__pyx_kp_u_clifford___and___line_835;
1571  static PyObject *__pyx_kp_u_clifford___call___line_1019;
1572  static PyObject *__pyx_kp_u_clifford___div___line_895;
1573  static PyObject *__pyx_kp_u_clifford___getitem___line_706;
1574  static PyObject *__pyx_kp_u_clifford___iadd___line_750;
1575  static PyObject *__pyx_kp_u_clifford___iand___line_850;
1576  static PyObject *__pyx_kp_u_clifford___idiv___line_910;
1577  static PyObject *__pyx_kp_u_clifford___imod___line_820;
1578  static PyObject *__pyx_kp_u_clifford___imul___line_792;
1579  static PyObject *__pyx_kp_u_clifford___ior___line_949;
1580  static PyObject *__pyx_kp_u_clifford___isub___line_770;
1581  static PyObject *__pyx_kp_u_clifford___iter___line_637;
1582  static PyObject *__pyx_kp_u_clifford___ixor___line_880;
1583  static PyObject *__pyx_kp_u_clifford___mod___line_805;
1584  static PyObject *__pyx_kp_u_clifford___mul___line_779;
1585  static PyObject *__pyx_kp_u_clifford___neg___line_721;
1586  static PyObject *__pyx_kp_u_clifford___or___line_938;
1587  static PyObject *__pyx_kp_u_clifford___pos___line_730;
1588  static PyObject *__pyx_kp_u_clifford___pow___line_960;
1589  static PyObject *__pyx_kp_u_clifford___repr___line_1225;
1590  static PyObject *__pyx_kp_u_clifford___str___line_1234;
1591  static PyObject *__pyx_kp_u_clifford___sub___line_759;
1592  static PyObject *__pyx_kp_u_clifford___xor___line_865;
1593  static PyObject *__pyx_kp_u_clifford_abs_line_1174;
1594  static PyObject *__pyx_kp_u_clifford_conj_line_1137;
1595  static PyObject *__pyx_kp_u_clifford_copy_line_554;
1596  static PyObject *__pyx_kp_u_clifford_even_line_1060;
1597  static PyObject *__pyx_kp_u_clifford_frame_line_1214;
1598  static PyObject *__pyx_n_s_clifford_hidden_doctests;
1599  static PyObject *__pyx_kp_u_clifford_hidden_doctests_line_12;
1600  static PyObject *__pyx_kp_u_clifford_inv_line_925;
1601  static PyObject *__pyx_kp_u_clifford_involute_line_1106;
1602  static PyObject *__pyx_kp_u_clifford_isnan_line_1205;
1603  static PyObject *__pyx_kp_u_clifford_max_abs_line_1183;
1604  static PyObject *__pyx_kp_u_clifford_norm_line_1163;
1605  static PyObject *__pyx_kp_u_clifford_odd_line_1069;
1606  static PyObject *__pyx_kp_u_clifford_outer_pow_line_1003;
1607  static PyObject *__pyx_kp_u_clifford_pow_line_979;
1608  static PyObject *__pyx_kp_u_clifford_pure_line_1049;
1609  static PyObject *__pyx_kp_u_clifford_quad_line_1152;
1610  static PyObject *__pyx_kp_u_clifford_reframe_line_648;
1611  static PyObject *__pyx_kp_u_clifford_reverse_line_1122;
1612  static PyObject *__pyx_kp_u_clifford_scalar_line_1038;
1613  static PyObject *__pyx_kp_u_clifford_truncated_line_1194;
1614  static PyObject *__pyx_kp_u_clifford_vector_part_line_1078;
1615  static PyObject *__pyx_n_s_close;
1616  static PyObject *__pyx_n_s_collections;
1617  static PyObject *__pyx_kp_u_compare_line_490;
1618  static PyObject *__pyx_kp_u_complexifier_line_1527;
1619  static PyObject *__pyx_n_s_conj;
1620  static PyObject *__pyx_kp_u_conj_line_1436;
1621  static PyObject *__pyx_n_s_copy;
1622  static PyObject *__pyx_n_s_cos;
1623  static PyObject *__pyx_kp_u_cos_line_1602;
1624  static PyObject *__pyx_n_s_cosh;
1625  static PyObject *__pyx_kp_u_cosh_line_1640;
1626  static PyObject *__pyx_n_s_doctest;
1627  static PyObject *__pyx_n_s_e;
1628  static PyObject *__pyx_kp_u_e_line_1887;
1629  static PyObject *__pyx_n_s_even;
1630  static PyObject *__pyx_kp_u_even_line_1388;
1631  static PyObject *__pyx_n_s_exp;
1632  static PyObject *__pyx_kp_u_exp_line_1565;
1633  static PyObject *__pyx_n_s_fill;
1634  static PyObject *__pyx_n_s_frm;
1635  static PyObject *__pyx_kp_s_from;
1636  static PyObject *__pyx_n_s_grade;
1637  static PyObject *__pyx_kp_s_home_abuild_rpmbuild_BUILD_gluc;
1638  static PyObject *__pyx_n_s_i;
1639  static PyObject *__pyx_kp_u_imag_line_1366;
1640  static PyObject *__pyx_n_s_import;
1641  static PyObject *__pyx_kp_u_index_set___and___line_269;
1642  static PyObject *__pyx_kp_u_index_set___getitem___line_189;
1643  static PyObject *__pyx_kp_u_index_set___iand___line_280;
1644  static PyObject *__pyx_kp_u_index_set___invert___line_238;
1645  static PyObject *__pyx_kp_u_index_set___ior___line_302;
1646  static PyObject *__pyx_n_s_index_set___iter;
1647  static PyObject *__pyx_kp_u_index_set___iter___line_227;
1648  static PyObject *__pyx_kp_u_index_set___ixor___line_258;
1649  static PyObject *__pyx_kp_u_index_set___or___line_291;
1650  static PyObject *__pyx_kp_u_index_set___repr___line_382;
1651  static PyObject *__pyx_kp_u_index_set___setitem___line_177;
1652  static PyObject *__pyx_kp_u_index_set___str___line_393;
1653  static PyObject *__pyx_kp_u_index_set___xor___line_247;
1654  static PyObject *__pyx_kp_u_index_set_copy_line_64;
1655  static PyObject *__pyx_kp_u_index_set_count_line_313;
1656  static PyObject *__pyx_kp_u_index_set_count_neg_line_322;
1657  static PyObject *__pyx_kp_u_index_set_count_pos_line_331;
1658  static PyObject *__pyx_n_s_index_set_hidden_doctests;
1659  static PyObject *__pyx_kp_u_index_set_hidden_doctests_line_4;
1660  static PyObject *__pyx_kp_u_index_set_max_line_349;
1661  static PyObject *__pyx_kp_u_index_set_min_line_340;
1662  static PyObject *__pyx_kp_u_index_set_sign_of_mult_line_364;
1663  static PyObject *__pyx_kp_u_index_set_sign_of_square_line_37;
1664  static PyObject *__pyx_n_s_inv;
1665  static PyObject *__pyx_kp_u_inv_line_1329;
1666  static PyObject *__pyx_kp_s_invalid;
1667  static PyObject *__pyx_kp_s_invalid_string;
1668  static PyObject *__pyx_n_s_involute;
1669  static PyObject *__pyx_kp_u_involute_line_1406;
1670  static PyObject *__pyx_n_s_ist;
1671  static PyObject *__pyx_n_s_istpq;
1672  static PyObject *__pyx_kp_u_istpq_line_1900;
1673  static PyObject *__pyx_n_s_iter;
1674  static PyObject *__pyx_n_s_ixt;
1675  static PyObject *__pyx_kp_u_lexicographic_compare_eg_3_4_5;
1676  static PyObject *__pyx_n_s_lhs;
1677  static PyObject *__pyx_n_s_log;
1678  static PyObject *__pyx_kp_u_log_line_1579;
1679  static PyObject *__pyx_n_s_m;
1680  static PyObject *__pyx_n_s_main;
1681  static PyObject *__pyx_n_s_math;
1682  static PyObject *__pyx_n_s_max;
1683  static PyObject *__pyx_kp_u_max_abs_line_1482;
1684  static PyObject *__pyx_kp_u_max_pos_line_511;
1685  static PyObject *__pyx_n_s_min;
1686  static PyObject *__pyx_kp_u_min_neg_line_502;
1687  static PyObject *__pyx_n_s_name;
1688  static PyObject *__pyx_n_s_nbar3;
1689  static PyObject *__pyx_n_s_ninf3;
1690  static PyObject *__pyx_n_s_norm;
1691  static PyObject *__pyx_kp_u_norm_line_1462;
1692  static PyObject *__pyx_kp_u_norm_sum_of_squares_of_coordina;
1693  static PyObject *__pyx_n_s_numbers;
1694  static PyObject *__pyx_n_s_obj;
1695  static PyObject *__pyx_n_s_odd;
1696  static PyObject *__pyx_kp_u_odd_line_1397;
1697  static PyObject *__pyx_n_s_other;
1698  static PyObject *__pyx_n_s_outer_pow;
1699  static PyObject *__pyx_kp_u_outer_pow_line_1518;
1700  static PyObject *__pyx_n_s_p;
1701  static PyObject *__pyx_n_s_pi;
1702  static PyObject *__pyx_n_s_pow;
1703  static PyObject *__pyx_kp_u_pow_line_1494;
1704  static PyObject *__pyx_n_s_pure;
1705  static PyObject *__pyx_kp_u_pure_line_1377;
1706  static PyObject *__pyx_n_s_pyx_vtable;
1707  static PyObject *__pyx_n_s_q;
1708  static PyObject *__pyx_n_s_quad;
1709  static PyObject *__pyx_kp_u_quad_line_1451;
1710  static PyObject *__pyx_kp_u_random_clifford_line_1815;
1711  static PyObject *__pyx_n_s_range;
1712  static PyObject *__pyx_kp_u_real_line_1355;
1713  static PyObject *__pyx_n_s_reverse;
1714  static PyObject *__pyx_kp_u_reverse_line_1421;
1715  static PyObject *__pyx_n_s_rhs;
1716  static PyObject *__pyx_n_s_scalar;
1717  static PyObject *__pyx_kp_u_scalar_line_1344;
1718  static PyObject *__pyx_n_s_send;
1719  static PyObject *__pyx_n_s_sin;
1720  static PyObject *__pyx_kp_u_sin_line_1679;
1721  static PyObject *__pyx_n_s_sinh;
1722  static PyObject *__pyx_kp_u_sinh_line_1719;
1723  static PyObject *__pyx_n_s_sqrt;
1724  static PyObject *__pyx_kp_u_sqrt_line_1542;
1725  static PyObject *__pyx_n_s_tan;
1726  static PyObject *__pyx_kp_u_tan_line_1752;
1727  static PyObject *__pyx_n_s_tanh;
1728  static PyObject *__pyx_kp_u_tanh_line_1786;
1729  static PyObject *__pyx_n_s_tau;
1730  static PyObject *__pyx_n_s_test;
1731  static PyObject *__pyx_n_s_test_2;
1732  static PyObject *__pyx_n_s_testmod;
1733  static PyObject *__pyx_n_s_throw;
1734  static PyObject *__pyx_kp_s_to_frame;
1735  static PyObject *__pyx_kp_s_using;
1736  static PyObject *__pyx_kp_s_using_invalid;
1737  static PyObject *__pyx_kp_s_value;
1738  static PyObject *__pyx_n_s_version;
1739  static PyObject *__pyx_n_s_xrange;
1740 static PyObject *__pyx_pf_8PyClical_9index_set_copy(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
1741 static int __pyx_pf_8PyClical_9index_set_2__cinit__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_other); /* proto */
1742 static void __pyx_pf_8PyClical_9index_set_4__dealloc__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
1743 static PyObject *__pyx_pf_8PyClical_9index_set_6__richcmp__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs, int __pyx_v_op); /* proto */
1744 static int __pyx_pf_8PyClical_9index_set_8__setitem__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_idx, PyObject *__pyx_v_val); /* proto */
1745 static PyObject *__pyx_pf_8PyClical_9index_set_10__getitem__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_idx); /* proto */
1746 static int __pyx_pf_8PyClical_9index_set_12__contains__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_idx); /* proto */
1747 static PyObject *__pyx_pf_8PyClical_9index_set_14__iter__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
1748 static PyObject *__pyx_pf_8PyClical_9index_set_17__invert__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
1749 static PyObject *__pyx_pf_8PyClical_9index_set_19__xor__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
1750 static PyObject *__pyx_pf_8PyClical_9index_set_21__ixor__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
1751 static PyObject *__pyx_pf_8PyClical_9index_set_23__and__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
1752 static PyObject *__pyx_pf_8PyClical_9index_set_25__iand__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
1753 static PyObject *__pyx_pf_8PyClical_9index_set_27__or__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
1754 static PyObject *__pyx_pf_8PyClical_9index_set_29__ior__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
1755 static PyObject *__pyx_pf_8PyClical_9index_set_31count(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
1756 static PyObject *__pyx_pf_8PyClical_9index_set_33count_neg(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
1757 static PyObject *__pyx_pf_8PyClical_9index_set_35count_pos(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
1758 static PyObject *__pyx_pf_8PyClical_9index_set_37min(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
1759 static PyObject *__pyx_pf_8PyClical_9index_set_39max(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
1760 static PyObject *__pyx_pf_8PyClical_9index_set_41hash_fn(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
1761 static PyObject *__pyx_pf_8PyClical_9index_set_43sign_of_mult(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
1762 static PyObject *__pyx_pf_8PyClical_9index_set_45sign_of_square(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
1763 static PyObject *__pyx_pf_8PyClical_9index_set_47__repr__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
1764 static PyObject *__pyx_pf_8PyClical_9index_set_49__str__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
1765 static PyObject *__pyx_pf_8PyClical_index_set_hidden_doctests(CYTHON_UNUSED PyObject *__pyx_self); /* proto */
1766 static PyObject *__pyx_pf_8PyClical_2compare(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
1767 static PyObject *__pyx_pf_8PyClical_4min_neg(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1768 static PyObject *__pyx_pf_8PyClical_6max_pos(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1769 static PyObject *__pyx_pf_8PyClical_8clifford_copy(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1770 static int __pyx_pf_8PyClical_8clifford_2__cinit__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_other, PyObject *__pyx_v_ixt); /* proto */
1771 static void __pyx_pf_8PyClical_8clifford_4__dealloc__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1772 static int __pyx_pf_8PyClical_8clifford_6__contains__(CYTHON_UNUSED struct __pyx_obj_8PyClical_clifford *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v_x); /* proto */
1773 static PyObject *__pyx_pf_8PyClical_8clifford_8__iter__(CYTHON_UNUSED struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1774 static PyObject *__pyx_pf_8PyClical_8clifford_10reframe(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_ixt); /* proto */
1775 static PyObject *__pyx_pf_8PyClical_8clifford_12__richcmp__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs, int __pyx_v_op); /* proto */
1776 static PyObject *__pyx_pf_8PyClical_8clifford_14__getitem__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_ixt); /* proto */
1777 static PyObject *__pyx_pf_8PyClical_8clifford_16__neg__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1778 static PyObject *__pyx_pf_8PyClical_8clifford_18__pos__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1779 static PyObject *__pyx_pf_8PyClical_8clifford_20__add__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
1780 static PyObject *__pyx_pf_8PyClical_8clifford_22__iadd__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
1781 static PyObject *__pyx_pf_8PyClical_8clifford_24__sub__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
1782 static PyObject *__pyx_pf_8PyClical_8clifford_26__isub__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
1783 static PyObject *__pyx_pf_8PyClical_8clifford_28__mul__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
1784 static PyObject *__pyx_pf_8PyClical_8clifford_30__imul__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
1785 static PyObject *__pyx_pf_8PyClical_8clifford_32__mod__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
1786 static PyObject *__pyx_pf_8PyClical_8clifford_34__imod__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
1787 static PyObject *__pyx_pf_8PyClical_8clifford_36__and__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
1788 static PyObject *__pyx_pf_8PyClical_8clifford_38__iand__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
1789 static PyObject *__pyx_pf_8PyClical_8clifford_40__xor__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
1790 static PyObject *__pyx_pf_8PyClical_8clifford_42__ixor__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
1791 #if PY_MAJOR_VERSION < 3 || CYTHON_COMPILING_IN_PYPY
1792 static PyObject *__pyx_pf_8PyClical_8clifford_44__div__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
1793 #endif
1794 #if PY_MAJOR_VERSION < 3 || CYTHON_COMPILING_IN_PYPY
1795 static PyObject *__pyx_pf_8PyClical_8clifford_46__idiv__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
1796 #endif
1797 static PyObject *__pyx_pf_8PyClical_8clifford_48inv(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1798 static PyObject *__pyx_pf_8PyClical_8clifford_50__or__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
1799 static PyObject *__pyx_pf_8PyClical_8clifford_52__ior__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
1800 static PyObject *__pyx_pf_8PyClical_8clifford_54__pow__(PyObject *__pyx_v_self, PyObject *__pyx_v_m, CYTHON_UNUSED PyObject *__pyx_v_dummy); /* proto */
1801 static PyObject *__pyx_pf_8PyClical_8clifford_56pow(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_m); /* proto */
1802 static PyObject *__pyx_pf_8PyClical_8clifford_58outer_pow(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_m); /* proto */
1803 static PyObject *__pyx_pf_8PyClical_8clifford_60__call__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_grade); /* proto */
1804 static PyObject *__pyx_pf_8PyClical_8clifford_62scalar(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1805 static PyObject *__pyx_pf_8PyClical_8clifford_64pure(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1806 static PyObject *__pyx_pf_8PyClical_8clifford_66even(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1807 static PyObject *__pyx_pf_8PyClical_8clifford_68odd(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1808 static PyObject *__pyx_pf_8PyClical_8clifford_70vector_part(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_frm); /* proto */
1809 static PyObject *__pyx_pf_8PyClical_8clifford_72involute(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1810 static PyObject *__pyx_pf_8PyClical_8clifford_74reverse(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1811 static PyObject *__pyx_pf_8PyClical_8clifford_76conj(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1812 static PyObject *__pyx_pf_8PyClical_8clifford_78quad(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1813 static PyObject *__pyx_pf_8PyClical_8clifford_80norm(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1814 static PyObject *__pyx_pf_8PyClical_8clifford_82abs(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1815 static PyObject *__pyx_pf_8PyClical_8clifford_84max_abs(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1816 static PyObject *__pyx_pf_8PyClical_8clifford_86truncated(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_limit); /* proto */
1817 static PyObject *__pyx_pf_8PyClical_8clifford_88isnan(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1818 static PyObject *__pyx_pf_8PyClical_8clifford_90frame(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1819 static PyObject *__pyx_pf_8PyClical_8clifford_92__repr__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1820 static PyObject *__pyx_pf_8PyClical_8clifford_94__str__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
1821 static PyObject *__pyx_pf_8PyClical_8clifford_hidden_doctests(CYTHON_UNUSED PyObject *__pyx_self); /* proto */
1822 static PyObject *__pyx_pf_8PyClical_10inv(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1823 static PyObject *__pyx_pf_8PyClical_12scalar(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1824 static PyObject *__pyx_pf_8PyClical_14real(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1825 static PyObject *__pyx_pf_8PyClical_16imag(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1826 static PyObject *__pyx_pf_8PyClical_18pure(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1827 static PyObject *__pyx_pf_8PyClical_20even(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1828 static PyObject *__pyx_pf_8PyClical_22odd(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1829 static PyObject *__pyx_pf_8PyClical_24involute(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1830 static PyObject *__pyx_pf_8PyClical_26reverse(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1831 static PyObject *__pyx_pf_8PyClical_28conj(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1832 static PyObject *__pyx_pf_8PyClical_30quad(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1833 static PyObject *__pyx_pf_8PyClical_32norm(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1834 static PyObject *__pyx_pf_8PyClical_34abs(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1835 static PyObject *__pyx_pf_8PyClical_36max_abs(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1836 static PyObject *__pyx_pf_8PyClical_38pow(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_m); /* proto */
1837 static PyObject *__pyx_pf_8PyClical_40outer_pow(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_m); /* proto */
1838 static PyObject *__pyx_pf_8PyClical_42complexifier(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1839 static PyObject *__pyx_pf_8PyClical_44sqrt(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
1840 static PyObject *__pyx_pf_8PyClical_46exp(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1841 static PyObject *__pyx_pf_8PyClical_48log(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
1842 static PyObject *__pyx_pf_8PyClical_50cos(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
1843 static PyObject *__pyx_pf_8PyClical_52acos(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
1844 static PyObject *__pyx_pf_8PyClical_54cosh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1845 static PyObject *__pyx_pf_8PyClical_56acosh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
1846 static PyObject *__pyx_pf_8PyClical_58sin(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
1847 static PyObject *__pyx_pf_8PyClical_60asin(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
1848 static PyObject *__pyx_pf_8PyClical_62sinh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1849 static PyObject *__pyx_pf_8PyClical_64asinh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
1850 static PyObject *__pyx_pf_8PyClical_66tan(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
1851 static PyObject *__pyx_pf_8PyClical_68atan(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
1852 static PyObject *__pyx_pf_8PyClical_70tanh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1853 static PyObject *__pyx_pf_8PyClical_72atanh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
1854 static PyObject *__pyx_pf_8PyClical_74random_clifford(CYTHON_UNUSED PyObject *__pyx_self, struct __pyx_obj_8PyClical_index_set *__pyx_v_ixt, PyObject *__pyx_v_fill); /* proto */
1855 static PyObject *__pyx_pf_8PyClical_76cga3(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1856 static PyObject *__pyx_pf_8PyClical_78cga3std(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1857 static PyObject *__pyx_pf_8PyClical_80agc3(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1858 static PyObject *__pyx_pf_8PyClical_82e(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
1859 static PyObject *__pyx_pf_8PyClical_84istpq(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_p, PyObject *__pyx_v_q); /* proto */
1860 static PyObject *__pyx_pf_8PyClical_86_test(CYTHON_UNUSED PyObject *__pyx_self); /* proto */
1861 static PyObject *__pyx_tp_new_8PyClical_index_set(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
1862 static PyObject *__pyx_tp_new_8PyClical_clifford(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
1863 static PyObject *__pyx_tp_new_8PyClical___pyx_scope_struct____iter__(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
1864 static PyObject *__pyx_float_0_0;
1865 static PyObject *__pyx_float_1_0;
1866 static PyObject *__pyx_float_2_0;
1867 static PyObject *__pyx_float_8_0;
1868 static PyObject *__pyx_int_0;
1869 static PyObject *__pyx_int_1;
1870 static PyObject *__pyx_int_4;
1871 static PyObject *__pyx_int_neg_1;
1872 static PyObject *__pyx_tuple__8;
1873 static PyObject *__pyx_tuple__9;
1874 static PyObject *__pyx_tuple__12;
1875 static PyObject *__pyx_tuple__13;
1876 static PyObject *__pyx_tuple__15;
1877 static PyObject *__pyx_tuple__17;
1878 static PyObject *__pyx_tuple__18;
1879 static PyObject *__pyx_tuple__19;
1880 static PyObject *__pyx_tuple__20;
1881 static PyObject *__pyx_tuple__21;
1882 static PyObject *__pyx_codeobj__10;
1883 static PyObject *__pyx_codeobj__11;
1884 static PyObject *__pyx_codeobj__14;
1885 static PyObject *__pyx_codeobj__16;
1886 static PyObject *__pyx_codeobj__22;
1887 
1888 /* "PyClical.pyx":39
1889  * cdef class index_set
1890  *
1891  * cdef inline IndexSet toIndexSet(obj): # <<<<<<<<<<<<<<
1892  * """
1893  * Return the C++ IndexSet instance wrapped by index_set(obj).
1894  */
1895 
1896 static CYTHON_INLINE IndexSet __pyx_f_8PyClical_toIndexSet(PyObject *__pyx_v_obj) {
1897  IndexSet __pyx_r;
1898  __Pyx_RefNannyDeclarations
1899  PyObject *__pyx_t_1 = NULL;
1900  PyObject *__pyx_t_2 = NULL;
1901  int __pyx_lineno = 0;
1902  const char *__pyx_filename = NULL;
1903  int __pyx_clineno = 0;
1904  __Pyx_RefNannySetupContext("toIndexSet", 0);
1905 
1906  /* "PyClical.pyx":43
1907  * Return the C++ IndexSet instance wrapped by index_set(obj).
1908  * """
1909  * return index_set(obj).instance[0] # <<<<<<<<<<<<<<
1910  *
1911  * cdef class index_set:
1912  */
1913  __pyx_t_1 = PyTuple_New(1); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 43; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
1914  __Pyx_GOTREF(__pyx_t_1);
1915  __Pyx_INCREF(__pyx_v_obj);
1916  __Pyx_GIVEREF(__pyx_v_obj);
1917  PyTuple_SET_ITEM(__pyx_t_1, 0, __pyx_v_obj);
1918  __pyx_t_2 = __Pyx_PyObject_Call(((PyObject *)__pyx_ptype_8PyClical_index_set), __pyx_t_1, NULL); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 43; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
1919  __Pyx_GOTREF(__pyx_t_2);
1920  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
1921  __pyx_r = (((struct __pyx_obj_8PyClical_index_set *)__pyx_t_2)->instance[0]);
1922  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
1923  goto __pyx_L0;
1924 
1925  /* "PyClical.pyx":39
1926  * cdef class index_set
1927  *
1928  * cdef inline IndexSet toIndexSet(obj): # <<<<<<<<<<<<<<
1929  * """
1930  * Return the C++ IndexSet instance wrapped by index_set(obj).
1931  */
1932 
1933  /* function exit code */
1934  __pyx_L1_error:;
1935  __Pyx_XDECREF(__pyx_t_1);
1936  __Pyx_XDECREF(__pyx_t_2);
1937  __Pyx_WriteUnraisable("PyClical.toIndexSet", __pyx_clineno, __pyx_lineno, __pyx_filename, 0, 0);
1938  __pyx_L0:;
1939  __Pyx_RefNannyFinishContext();
1940  return __pyx_r;
1941 }
1942 
1943 /* "PyClical.pyx":51
1944  * cdef IndexSet *instance # Wrapped instance of C++ class IndexSet.
1945  *
1946  * cdef inline wrap(index_set self, IndexSet other): # <<<<<<<<<<<<<<
1947  * """
1948  * Wrap an instance of the C++ class IndexSet.
1949  */
1950 
1951 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_9index_set_wrap(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, IndexSet __pyx_v_other) {
1952  PyObject *__pyx_r = NULL;
1953  __Pyx_RefNannyDeclarations
1954  __Pyx_RefNannySetupContext("wrap", 0);
1955 
1956  /* "PyClical.pyx":55
1957  * Wrap an instance of the C++ class IndexSet.
1958  * """
1959  * self.instance[0] = other # <<<<<<<<<<<<<<
1960  * return self
1961  *
1962  */
1963  (__pyx_v_self->instance[0]) = __pyx_v_other;
1964 
1965  /* "PyClical.pyx":56
1966  * """
1967  * self.instance[0] = other
1968  * return self # <<<<<<<<<<<<<<
1969  *
1970  * cdef inline IndexSet unwrap(index_set self):
1971  */
1972  __Pyx_XDECREF(__pyx_r);
1973  __Pyx_INCREF(((PyObject *)__pyx_v_self));
1974  __pyx_r = ((PyObject *)__pyx_v_self);
1975  goto __pyx_L0;
1976 
1977  /* "PyClical.pyx":51
1978  * cdef IndexSet *instance # Wrapped instance of C++ class IndexSet.
1979  *
1980  * cdef inline wrap(index_set self, IndexSet other): # <<<<<<<<<<<<<<
1981  * """
1982  * Wrap an instance of the C++ class IndexSet.
1983  */
1984 
1985  /* function exit code */
1986  __pyx_L0:;
1987  __Pyx_XGIVEREF(__pyx_r);
1988  __Pyx_RefNannyFinishContext();
1989  return __pyx_r;
1990 }
1991 
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2410  #if CYTHON_COMPILING_IN_CPYTHON
2411  __pyx_t_4 = PyList_GET_ITEM(__pyx_t_5, __pyx_t_11); __Pyx_INCREF(__pyx_t_4); __pyx_t_11++; if (unlikely(0 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 100; __pyx_clineno = __LINE__; goto __pyx_L6_error;}
2412  #else
2413  __pyx_t_4 = PySequence_ITEM(__pyx_t_5, __pyx_t_11); __pyx_t_11++; if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 100; __pyx_clineno = __LINE__; goto __pyx_L6_error;}
2414  __Pyx_GOTREF(__pyx_t_4);
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2417  if (__pyx_t_11 >= PyTuple_GET_SIZE(__pyx_t_5)) break;
2418  #if CYTHON_COMPILING_IN_CPYTHON
2419  __pyx_t_4 = PyTuple_GET_ITEM(__pyx_t_5, __pyx_t_11); __Pyx_INCREF(__pyx_t_4); __pyx_t_11++; if (unlikely(0 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 100; __pyx_clineno = __LINE__; goto __pyx_L6_error;}
2420  #else
2421  __pyx_t_4 = PySequence_ITEM(__pyx_t_5, __pyx_t_11); __pyx_t_11++; if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 100; __pyx_clineno = __LINE__; goto __pyx_L6_error;}
2422  __Pyx_GOTREF(__pyx_t_4);
2423  #endif
2424  }
2425  } else {
2426  __pyx_t_4 = __pyx_t_12(__pyx_t_5);
2427  if (unlikely(!__pyx_t_4)) {
2428  PyObject* exc_type = PyErr_Occurred();
2429  if (exc_type) {
2430  if (likely(exc_type == PyExc_StopIteration || PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) PyErr_Clear();
2431  else {__pyx_filename = __pyx_f[0]; __pyx_lineno = 100; __pyx_clineno = __LINE__; goto __pyx_L6_error;}
2432  }
2433  break;
2434  }
2435  __Pyx_GOTREF(__pyx_t_4);
2436  }
2437  __Pyx_XDECREF_SET(__pyx_v_idx, __pyx_t_4);
2438  __pyx_t_4 = 0;
2439 
2440  /* "PyClical.pyx":101
2441  * self.instance = new IndexSet()
2442  * for idx in other:
2443  * self[idx] = True # <<<<<<<<<<<<<<
2444  * except IndexError:
2445  * raise IndexError(error_msg_prefix + " invalid " + repr(other) + ".")
2446  */
2447  if (unlikely(PyObject_SetItem(((PyObject *)__pyx_v_self), __pyx_v_idx, Py_True) < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 101; __pyx_clineno = __LINE__; goto __pyx_L6_error;}
2448 
2449  /* "PyClical.pyx":100
2450  * try:
2451  * self.instance = new IndexSet()
2452  * for idx in other: # <<<<<<<<<<<<<<
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2454  * except IndexError:
2455  */
2456  }
2457  __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
2458 
2459  /* "PyClical.pyx":98
2460  * self.instance = new IndexSet(<int>other)
2461  * elif isinstance(other, (set, frozenset)):
2462  * try: # <<<<<<<<<<<<<<
2463  * self.instance = new IndexSet()
2464  * for idx in other:
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2466  }
2467  __Pyx_XDECREF(__pyx_t_8); __pyx_t_8 = 0;
2468  __Pyx_XDECREF(__pyx_t_9); __pyx_t_9 = 0;
2469  __Pyx_XDECREF(__pyx_t_10); __pyx_t_10 = 0;
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2471  __pyx_L6_error:;
2472  __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0;
2473  __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
2474 
2475  /* "PyClical.pyx":102
2476  * for idx in other:
2477  * self[idx] = True
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2486  __Pyx_GOTREF(__pyx_t_5);
2487  __Pyx_GOTREF(__pyx_t_4);
2488  __Pyx_GOTREF(__pyx_t_13);
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2491  * self[idx] = True
2492  * except IndexError:
2493  * raise IndexError(error_msg_prefix + " invalid " + repr(other) + ".") # <<<<<<<<<<<<<<
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2497  __pyx_t_14 = PyNumber_Add(__pyx_v_error_msg_prefix, __pyx_kp_s_invalid); if (unlikely(!__pyx_t_14)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 103; __pyx_clineno = __LINE__; goto __pyx_L8_except_error;}
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2500  __Pyx_GOTREF(__pyx_t_15);
2501  __pyx_t_16 = PyNumber_Add(__pyx_t_14, __pyx_t_15); if (unlikely(!__pyx_t_16)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 103; __pyx_clineno = __LINE__; goto __pyx_L8_except_error;}
2502  __Pyx_GOTREF(__pyx_t_16);
2503  __Pyx_DECREF(__pyx_t_14); __pyx_t_14 = 0;
2504  __Pyx_DECREF(__pyx_t_15); __pyx_t_15 = 0;
2505  __pyx_t_15 = PyNumber_Add(__pyx_t_16, __pyx_kp_s_); if (unlikely(!__pyx_t_15)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 103; __pyx_clineno = __LINE__; goto __pyx_L8_except_error;}
2506  __Pyx_GOTREF(__pyx_t_15);
2507  __Pyx_DECREF(__pyx_t_16); __pyx_t_16 = 0;
2508  __pyx_t_16 = PyTuple_New(1); if (unlikely(!__pyx_t_16)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 103; __pyx_clineno = __LINE__; goto __pyx_L8_except_error;}
2509  __Pyx_GOTREF(__pyx_t_16);
2510  __Pyx_GIVEREF(__pyx_t_15);
2511  PyTuple_SET_ITEM(__pyx_t_16, 0, __pyx_t_15);
2512  __pyx_t_15 = 0;
2513  __pyx_t_15 = __Pyx_PyObject_Call(__pyx_builtin_IndexError, __pyx_t_16, NULL); if (unlikely(!__pyx_t_15)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 103; __pyx_clineno = __LINE__; goto __pyx_L8_except_error;}
2514  __Pyx_GOTREF(__pyx_t_15);
2515  __Pyx_DECREF(__pyx_t_16); __pyx_t_16 = 0;
2516  __Pyx_Raise(__pyx_t_15, 0, 0, 0);
2517  __Pyx_DECREF(__pyx_t_15); __pyx_t_15 = 0;
2518  {__pyx_filename = __pyx_f[0]; __pyx_lineno = 103; __pyx_clineno = __LINE__; goto __pyx_L8_except_error;}
2519  }
2520 
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2523  * raise IndexError(error_msg_prefix + " invalid " + repr(other) + ".")
2524  * except (RuntimeError, TypeError): # <<<<<<<<<<<<<<
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2527  */
2528  __pyx_t_6 = PyErr_ExceptionMatches(__pyx_builtin_RuntimeError) || PyErr_ExceptionMatches(__pyx_builtin_TypeError);
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2532  __Pyx_GOTREF(__pyx_t_13);
2533  __Pyx_GOTREF(__pyx_t_4);
2534  __Pyx_GOTREF(__pyx_t_5);
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2544  __Pyx_GOTREF(__pyx_t_15);
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2546  __Pyx_GOTREF(__pyx_t_16);
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2548  __Pyx_GOTREF(__pyx_t_14);
2549  __Pyx_DECREF(__pyx_t_15); __pyx_t_15 = 0;
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2551  __pyx_t_16 = PyNumber_Add(__pyx_t_14, __pyx_kp_s_); if (unlikely(!__pyx_t_16)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 105; __pyx_clineno = __LINE__; goto __pyx_L8_except_error;}
2552  __Pyx_GOTREF(__pyx_t_16);
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2555  __Pyx_GOTREF(__pyx_t_14);
2556  __Pyx_GIVEREF(__pyx_t_16);
2557  PyTuple_SET_ITEM(__pyx_t_14, 0, __pyx_t_16);
2558  __pyx_t_16 = 0;
2559  __pyx_t_16 = __Pyx_PyObject_Call(__pyx_builtin_ValueError, __pyx_t_14, NULL); if (unlikely(!__pyx_t_16)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 105; __pyx_clineno = __LINE__; goto __pyx_L8_except_error;}
2560  __Pyx_GOTREF(__pyx_t_16);
2561  __Pyx_DECREF(__pyx_t_14); __pyx_t_14 = 0;
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2563  __Pyx_DECREF(__pyx_t_16); __pyx_t_16 = 0;
2564  {__pyx_filename = __pyx_f[0]; __pyx_lineno = 105; __pyx_clineno = __LINE__; goto __pyx_L8_except_error;}
2565  }
2566  goto __pyx_L8_except_error;
2567  __pyx_L8_except_error:;
2568 
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2570  * self.instance = new IndexSet(<int>other)
2571  * elif isinstance(other, (set, frozenset)):
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2573  * self.instance = new IndexSet()
2574  * for idx in other:
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2576  __Pyx_XGIVEREF(__pyx_t_8);
2577  __Pyx_XGIVEREF(__pyx_t_9);
2578  __Pyx_XGIVEREF(__pyx_t_10);
2579  __Pyx_ExceptionReset(__pyx_t_8, __pyx_t_9, __pyx_t_10);
2580  goto __pyx_L1_error;
2581  __pyx_L13_try_end:;
2582  }
2583 
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2585  * elif isinstance(other, numbers.Integral):
2586  * self.instance = new IndexSet(<int>other)
2587  * elif isinstance(other, (set, frozenset)): # <<<<<<<<<<<<<<
2588  * try:
2589  * self.instance = new IndexSet()
2590  */
2591  goto __pyx_L3;
2592  }
2593 
2594  /* "PyClical.pyx":106
2595  * except (RuntimeError, TypeError):
2596  * raise ValueError(error_msg_prefix + " invalid " + repr(other) + ".")
2597  * elif isinstance(other, str): # <<<<<<<<<<<<<<
2598  * try:
2599  * self.instance = new IndexSet(<char *>other)
2600  */
2601  __pyx_t_2 = PyString_Check(__pyx_v_other);
2602  __pyx_t_1 = (__pyx_t_2 != 0);
2603  if (__pyx_t_1) {
2604 
2605  /* "PyClical.pyx":107
2606  * raise ValueError(error_msg_prefix + " invalid " + repr(other) + ".")
2607  * elif isinstance(other, str):
2608  * try: # <<<<<<<<<<<<<<
2609  * self.instance = new IndexSet(<char *>other)
2610  * except RuntimeError:
2611  */
2612  {
2613  __Pyx_ExceptionSave(&__pyx_t_10, &__pyx_t_9, &__pyx_t_8);
2614  __Pyx_XGOTREF(__pyx_t_10);
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2616  __Pyx_XGOTREF(__pyx_t_8);
2617  /*try:*/ {
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2620  * elif isinstance(other, str):
2621  * try:
2622  * self.instance = new IndexSet(<char *>other) # <<<<<<<<<<<<<<
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2624  * raise ValueError(error_msg_prefix + " invalid string " + repr(other) + ".")
2625  */
2626  __pyx_t_17 = __Pyx_PyObject_AsString(__pyx_v_other); if (unlikely((!__pyx_t_17) && PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 108; __pyx_clineno = __LINE__; goto __pyx_L20_error;}
2627  try {
2628  __pyx_t_3 = new IndexSet(((char *)__pyx_t_17));
2629  } catch(...) {
2630  __Pyx_CppExn2PyErr();
2631  {__pyx_filename = __pyx_f[0]; __pyx_lineno = 108; __pyx_clineno = __LINE__; goto __pyx_L20_error;}
2632  }
2633  __pyx_v_self->instance = __pyx_t_3;
2634 
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2636  * raise ValueError(error_msg_prefix + " invalid " + repr(other) + ".")
2637  * elif isinstance(other, str):
2638  * try: # <<<<<<<<<<<<<<
2639  * self.instance = new IndexSet(<char *>other)
2640  * except RuntimeError:
2641  */
2642  }
2643  __Pyx_XDECREF(__pyx_t_10); __pyx_t_10 = 0;
2644  __Pyx_XDECREF(__pyx_t_9); __pyx_t_9 = 0;
2645  __Pyx_XDECREF(__pyx_t_8); __pyx_t_8 = 0;
2646  goto __pyx_L27_try_end;
2647  __pyx_L20_error:;
2648  __Pyx_XDECREF(__pyx_t_15); __pyx_t_15 = 0;
2649  __Pyx_XDECREF(__pyx_t_14); __pyx_t_14 = 0;
2650  __Pyx_XDECREF(__pyx_t_16); __pyx_t_16 = 0;
2651  __Pyx_XDECREF(__pyx_t_13); __pyx_t_13 = 0;
2652  __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0;
2653  __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
2654 
2655  /* "PyClical.pyx":109
2656  * try:
2657  * self.instance = new IndexSet(<char *>other)
2658  * except RuntimeError: # <<<<<<<<<<<<<<
2659  * raise ValueError(error_msg_prefix + " invalid string " + repr(other) + ".")
2660  * else:
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2663  if (__pyx_t_6) {
2664  __Pyx_AddTraceback("PyClical.index_set.__cinit__", __pyx_clineno, __pyx_lineno, __pyx_filename);
2665  if (__Pyx_GetException(&__pyx_t_5, &__pyx_t_4, &__pyx_t_13) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 109; __pyx_clineno = __LINE__; goto __pyx_L22_except_error;}
2666  __Pyx_GOTREF(__pyx_t_5);
2667  __Pyx_GOTREF(__pyx_t_4);
2668  __Pyx_GOTREF(__pyx_t_13);
2669 
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2671  * self.instance = new IndexSet(<char *>other)
2672  * except RuntimeError:
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2678  __Pyx_GOTREF(__pyx_t_16);
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2680  __Pyx_GOTREF(__pyx_t_14);
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2682  __Pyx_GOTREF(__pyx_t_15);
2683  __Pyx_DECREF(__pyx_t_16); __pyx_t_16 = 0;
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2685  __pyx_t_14 = PyNumber_Add(__pyx_t_15, __pyx_kp_s_); if (unlikely(!__pyx_t_14)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 110; __pyx_clineno = __LINE__; goto __pyx_L22_except_error;}
2686  __Pyx_GOTREF(__pyx_t_14);
2687  __Pyx_DECREF(__pyx_t_15); __pyx_t_15 = 0;
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2689  __Pyx_GOTREF(__pyx_t_15);
2690  __Pyx_GIVEREF(__pyx_t_14);
2691  PyTuple_SET_ITEM(__pyx_t_15, 0, __pyx_t_14);
2692  __pyx_t_14 = 0;
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2694  __Pyx_GOTREF(__pyx_t_14);
2695  __Pyx_DECREF(__pyx_t_15); __pyx_t_15 = 0;
2696  __Pyx_Raise(__pyx_t_14, 0, 0, 0);
2697  __Pyx_DECREF(__pyx_t_14); __pyx_t_14 = 0;
2698  {__pyx_filename = __pyx_f[0]; __pyx_lineno = 110; __pyx_clineno = __LINE__; goto __pyx_L22_except_error;}
2699  }
2700  goto __pyx_L22_except_error;
2701  __pyx_L22_except_error:;
2702 
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2704  * raise ValueError(error_msg_prefix + " invalid " + repr(other) + ".")
2705  * elif isinstance(other, str):
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2707  * self.instance = new IndexSet(<char *>other)
2708  * except RuntimeError:
2709  */
2710  __Pyx_XGIVEREF(__pyx_t_10);
2711  __Pyx_XGIVEREF(__pyx_t_9);
2712  __Pyx_XGIVEREF(__pyx_t_8);
2713  __Pyx_ExceptionReset(__pyx_t_10, __pyx_t_9, __pyx_t_8);
2714  goto __pyx_L1_error;
2715  __pyx_L27_try_end:;
2716  }
2717 
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2719  * except (RuntimeError, TypeError):
2720  * raise ValueError(error_msg_prefix + " invalid " + repr(other) + ".")
2721  * elif isinstance(other, str): # <<<<<<<<<<<<<<
2722  * try:
2723  * self.instance = new IndexSet(<char *>other)
2724  */
2725  goto __pyx_L3;
2726  }
2727 
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2729  * raise ValueError(error_msg_prefix + " invalid string " + repr(other) + ".")
2730  * else:
2731  * raise TypeError(error_msg_prefix + " " + str(type(other)) + ".") # <<<<<<<<<<<<<<
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2734  */
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3956  * def __xor__(lhs, rhs): # <<<<<<<<<<<<<<
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4008  * def __xor__(lhs, rhs): # <<<<<<<<<<<<<<
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5966  goto __pyx_L12;
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6091  * elif isinstance(other, str):
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6121  * self.instance = new Clifford(<char *>other)
6122  * except RuntimeError:
6123  * raise ValueError(error_msg_prefix + " invalid string " + repr(other) + ".") # <<<<<<<<<<<<<<
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6136  __Pyx_GOTREF(__pyx_t_17);
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6139  __Pyx_GOTREF(__pyx_t_18);
6140  __Pyx_GIVEREF(__pyx_t_17);
6141  PyTuple_SET_ITEM(__pyx_t_18, 0, __pyx_t_17);
6142  __pyx_t_17 = 0;
6143  __pyx_t_17 = __Pyx_PyObject_Call(__pyx_builtin_ValueError, __pyx_t_18, NULL); if (unlikely(!__pyx_t_17)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 601; __pyx_clineno = __LINE__; goto __pyx_L15_except_error;}
6144  __Pyx_GOTREF(__pyx_t_17);
6145  __Pyx_DECREF(__pyx_t_18); __pyx_t_18 = 0;
6146  __Pyx_Raise(__pyx_t_17, 0, 0, 0);
6147  __Pyx_DECREF(__pyx_t_17); __pyx_t_17 = 0;
6148  {__pyx_filename = __pyx_f[0]; __pyx_lineno = 601; __pyx_clineno = __LINE__; goto __pyx_L15_except_error;}
6149  }
6150  goto __pyx_L15_except_error;
6151  __pyx_L15_except_error:;
6152 
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6154  * self.instance = new Clifford(<scalar_t>other)
6155  * elif isinstance(other, str):
6156  * try: # <<<<<<<<<<<<<<
6157  * self.instance = new Clifford(<char *>other)
6158  * except RuntimeError:
6159  */
6160  __Pyx_XGIVEREF(__pyx_t_10);
6161  __Pyx_XGIVEREF(__pyx_t_11);
6162  __Pyx_XGIVEREF(__pyx_t_12);
6163  __Pyx_ExceptionReset(__pyx_t_10, __pyx_t_11, __pyx_t_12);
6164  goto __pyx_L4_error;
6165  __pyx_L20_try_end:;
6166  }
6167 
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6169  * elif isinstance(other, numbers.Real):
6170  * self.instance = new Clifford(<scalar_t>other)
6171  * elif isinstance(other, str): # <<<<<<<<<<<<<<
6172  * try:
6173  * self.instance = new Clifford(<char *>other)
6174  */
6175  goto __pyx_L12;
6176  }
6177 
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6179  * raise ValueError(error_msg_prefix + " invalid string " + repr(other) + ".")
6180  * else:
6181  * raise TypeError(error_msg_prefix + " " + str(type(other)) + ".") # <<<<<<<<<<<<<<
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6184  */
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6187  __Pyx_GOTREF(__pyx_t_15);
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6190  __Pyx_INCREF(((PyObject *)Py_TYPE(__pyx_v_other)));
6191  __Pyx_GIVEREF(((PyObject *)Py_TYPE(__pyx_v_other)));
6192  PyTuple_SET_ITEM(__pyx_t_7, 0, ((PyObject *)Py_TYPE(__pyx_v_other)));
6193  __pyx_t_8 = __Pyx_PyObject_Call(((PyObject *)(&PyString_Type)), __pyx_t_7, NULL); if (unlikely(!__pyx_t_8)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 603; __pyx_clineno = __LINE__; goto __pyx_L4_error;}
6194  __Pyx_GOTREF(__pyx_t_8);
6195  __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
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6197  __Pyx_GOTREF(__pyx_t_7);
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6201  __Pyx_GOTREF(__pyx_t_8);
6202  __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
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6204  __Pyx_GOTREF(__pyx_t_7);
6205  __Pyx_GIVEREF(__pyx_t_8);
6206  PyTuple_SET_ITEM(__pyx_t_7, 0, __pyx_t_8);
6207  __pyx_t_8 = 0;
6208  __pyx_t_8 = __Pyx_PyObject_Call(__pyx_builtin_TypeError, __pyx_t_7, NULL); if (unlikely(!__pyx_t_8)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 603; __pyx_clineno = __LINE__; goto __pyx_L4_error;}
6209  __Pyx_GOTREF(__pyx_t_8);
6210  __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
6211  __Pyx_Raise(__pyx_t_8, 0, 0, 0);
6212  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
6213  {__pyx_filename = __pyx_f[0]; __pyx_lineno = 603; __pyx_clineno = __LINE__; goto __pyx_L4_error;}
6214  }
6215  __pyx_L12:;
6216 
6217  /* "PyClical.pyx":590
6218  * error_msg_prefix = "Cannot initialize clifford object from"
6219  * if ixt is None:
6220  * try: # <<<<<<<<<<<<<<
6221  * if isinstance(other, clifford):
6222  * self.instance = new Clifford((<clifford>other).unwrap())
6223  */
6224  }
6225  __Pyx_XDECREF(__pyx_t_3); __pyx_t_3 = 0;
6226  __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0;
6227  __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
6228  goto __pyx_L11_try_end;
6229  __pyx_L4_error:;
6230  __Pyx_XDECREF(__pyx_t_16); __pyx_t_16 = 0;
6231  __Pyx_XDECREF(__pyx_t_18); __pyx_t_18 = 0;
6232  __Pyx_XDECREF(__pyx_t_17); __pyx_t_17 = 0;
6233  __Pyx_XDECREF(__pyx_t_15); __pyx_t_15 = 0;
6234  __Pyx_XDECREF(__pyx_t_7); __pyx_t_7 = 0;
6235  __Pyx_XDECREF(__pyx_t_8); __pyx_t_8 = 0;
6236 
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6238  * else:
6239  * raise TypeError(error_msg_prefix + " " + str(type(other)) + ".")
6240  * except RuntimeError as err: # <<<<<<<<<<<<<<
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6242  * + " value " + repr(other) + ":"
6243  */
6244  __pyx_t_14 = PyErr_ExceptionMatches(__pyx_builtin_RuntimeError);
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6246  __Pyx_AddTraceback("PyClical.clifford.__cinit__", __pyx_clineno, __pyx_lineno, __pyx_filename);
6247  if (__Pyx_GetException(&__pyx_t_8, &__pyx_t_7, &__pyx_t_15) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 604; __pyx_clineno = __LINE__; goto __pyx_L6_except_error;}
6248  __Pyx_GOTREF(__pyx_t_8);
6249  __Pyx_GOTREF(__pyx_t_7);
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6257  * raise ValueError(error_msg_prefix + " " + str(type(other)) # <<<<<<<<<<<<<<
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6259  * + "\n\t" + str(err))
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6266  __Pyx_GIVEREF(((PyObject *)Py_TYPE(__pyx_v_other)));
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6270  __Pyx_DECREF(__pyx_t_18); __pyx_t_18 = 0;
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6272  __Pyx_GOTREF(__pyx_t_18);
6273  __Pyx_DECREF(__pyx_t_17); __pyx_t_17 = 0;
6274  __Pyx_DECREF(__pyx_t_16); __pyx_t_16 = 0;
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6277  * except RuntimeError as err:
6278  * raise ValueError(error_msg_prefix + " " + str(type(other))
6279  * + " value " + repr(other) + ":" # <<<<<<<<<<<<<<
6280  * + "\n\t" + str(err))
6281  * elif isinstance(ixt, index_set):
6282  */
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6284  __Pyx_GOTREF(__pyx_t_16);
6285  __Pyx_DECREF(__pyx_t_18); __pyx_t_18 = 0;
6286  __pyx_t_18 = PyObject_Repr(__pyx_v_other); if (unlikely(!__pyx_t_18)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 606; __pyx_clineno = __LINE__; goto __pyx_L6_except_error;}
6287  __Pyx_GOTREF(__pyx_t_18);
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6289  __Pyx_GOTREF(__pyx_t_17);
6290  __Pyx_DECREF(__pyx_t_16); __pyx_t_16 = 0;
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6293  __Pyx_GOTREF(__pyx_t_18);
6294  __Pyx_DECREF(__pyx_t_17); __pyx_t_17 = 0;
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6298  * + " value " + repr(other) + ":"
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6300  * elif isinstance(ixt, index_set):
6301  * if isinstance(other, numbers.Real):
6302  */
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6304  __Pyx_GOTREF(__pyx_t_17);
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6307  __Pyx_GOTREF(__pyx_t_18);
6308  __Pyx_INCREF(__pyx_v_err);
6309  __Pyx_GIVEREF(__pyx_v_err);
6310  PyTuple_SET_ITEM(__pyx_t_18, 0, __pyx_v_err);
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6315  __Pyx_GOTREF(__pyx_t_18);
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6317  __Pyx_DECREF(__pyx_t_16); __pyx_t_16 = 0;
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6320  * raise TypeError(error_msg_prefix + " " + str(type(other)) + ".")
6321  * except RuntimeError as err:
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6324  * + "\n\t" + str(err))
6325  */
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6328  __Pyx_GIVEREF(__pyx_t_18);
6329  PyTuple_SET_ITEM(__pyx_t_16, 0, __pyx_t_18);
6330  __pyx_t_18 = 0;
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6332  __Pyx_GOTREF(__pyx_t_18);
6333  __Pyx_DECREF(__pyx_t_16); __pyx_t_16 = 0;
6334  __Pyx_Raise(__pyx_t_18, 0, 0, 0);
6335  __Pyx_DECREF(__pyx_t_18); __pyx_t_18 = 0;
6336  {__pyx_filename = __pyx_f[0]; __pyx_lineno = 605; __pyx_clineno = __LINE__; goto __pyx_L6_except_error;}
6337  }
6338  goto __pyx_L6_except_error;
6339  __pyx_L6_except_error:;
6340 
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6342  * error_msg_prefix = "Cannot initialize clifford object from"
6343  * if ixt is None:
6344  * try: # <<<<<<<<<<<<<<
6345  * if isinstance(other, clifford):
6346  * self.instance = new Clifford((<clifford>other).unwrap())
6347  */
6348  __Pyx_XGIVEREF(__pyx_t_3);
6349  __Pyx_XGIVEREF(__pyx_t_4);
6350  __Pyx_XGIVEREF(__pyx_t_5);
6351  __Pyx_ExceptionReset(__pyx_t_3, __pyx_t_4, __pyx_t_5);
6352  goto __pyx_L1_error;
6353  __pyx_L11_try_end:;
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6355 
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6357  * """
6358  * error_msg_prefix = "Cannot initialize clifford object from"
6359  * if ixt is None: # <<<<<<<<<<<<<<
6360  * try:
6361  * if isinstance(other, clifford):
6362  */
6363  goto __pyx_L3;
6364  }
6365 
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6367  * + " value " + repr(other) + ":"
6368  * + "\n\t" + str(err))
6369  * elif isinstance(ixt, index_set): # <<<<<<<<<<<<<<
6370  * if isinstance(other, numbers.Real):
6371  * self.instance = new Clifford((<index_set>ixt).unwrap(), <scalar_t>other)
6372  */
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6374  __pyx_t_1 = (__pyx_t_2 != 0);
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6379  * elif isinstance(ixt, index_set):
6380  * if isinstance(other, numbers.Real): # <<<<<<<<<<<<<<
6381  * self.instance = new Clifford((<index_set>ixt).unwrap(), <scalar_t>other)
6382  * elif isinstance(other, collections.Sequence):
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6387  __Pyx_GOTREF(__pyx_t_7);
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6395  * elif isinstance(ixt, index_set):
6396  * if isinstance(other, numbers.Real):
6397  * self.instance = new Clifford((<index_set>ixt).unwrap(), <scalar_t>other) # <<<<<<<<<<<<<<
6398  * elif isinstance(other, collections.Sequence):
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6400  */
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6404  } catch(...) {
6405  __Pyx_CppExn2PyErr();
6406  {__pyx_filename = __pyx_f[0]; __pyx_lineno = 610; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
6407  }
6408  __pyx_v_self->instance = __pyx_t_6;
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6411  * + "\n\t" + str(err))
6412  * elif isinstance(ixt, index_set):
6413  * if isinstance(other, numbers.Real): # <<<<<<<<<<<<<<
6414  * self.instance = new Clifford((<index_set>ixt).unwrap(), <scalar_t>other)
6415  * elif isinstance(other, collections.Sequence):
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6417  goto __pyx_L25;
6418  }
6419 
6420  /* "PyClical.pyx":611
6421  * if isinstance(other, numbers.Real):
6422  * self.instance = new Clifford((<index_set>ixt).unwrap(), <scalar_t>other)
6423  * elif isinstance(other, collections.Sequence): # <<<<<<<<<<<<<<
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6425  * else:
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6428  __Pyx_GOTREF(__pyx_t_7);
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6433  __Pyx_DECREF(__pyx_t_15); __pyx_t_15 = 0;
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6435  if (__pyx_t_1) {
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6437  /* "PyClical.pyx":612
6438  * self.instance = new Clifford((<index_set>ixt).unwrap(), <scalar_t>other)
6439  * elif isinstance(other, collections.Sequence):
6440  * self.instance = new Clifford(list_to_vector(other), (<index_set>ixt).unwrap()) # <<<<<<<<<<<<<<
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6442  * raise TypeError(error_msg_prefix + " (" + str(type(other))
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6444  try {
6445  __pyx_t_6 = new Clifford(__pyx_f_8PyClical_list_to_vector(__pyx_v_other), __pyx_f_8PyClical_9index_set_unwrap(((struct __pyx_obj_8PyClical_index_set *)__pyx_v_ixt)));
6446  } catch(...) {
6447  __Pyx_CppExn2PyErr();
6448  {__pyx_filename = __pyx_f[0]; __pyx_lineno = 612; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
6449  }
6450  __pyx_v_self->instance = __pyx_t_6;
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6453  * if isinstance(other, numbers.Real):
6454  * self.instance = new Clifford((<index_set>ixt).unwrap(), <scalar_t>other)
6455  * elif isinstance(other, collections.Sequence): # <<<<<<<<<<<<<<
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6457  * else:
6458  */
6459  goto __pyx_L25;
6460  }
6461 
6462  /* "PyClical.pyx":614
6463  * self.instance = new Clifford(list_to_vector(other), (<index_set>ixt).unwrap())
6464  * else:
6465  * raise TypeError(error_msg_prefix + " (" + str(type(other)) # <<<<<<<<<<<<<<
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6467  * else:
6468  */
6469  /*else*/ {
6470  __pyx_t_15 = PyNumber_Add(__pyx_v_error_msg_prefix, __pyx_kp_s__5); if (unlikely(!__pyx_t_15)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 614; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
6471  __Pyx_GOTREF(__pyx_t_15);
6472  __pyx_t_7 = PyTuple_New(1); if (unlikely(!__pyx_t_7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 614; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
6473  __Pyx_GOTREF(__pyx_t_7);
6474  __Pyx_INCREF(((PyObject *)Py_TYPE(__pyx_v_other)));
6475  __Pyx_GIVEREF(((PyObject *)Py_TYPE(__pyx_v_other)));
6476  PyTuple_SET_ITEM(__pyx_t_7, 0, ((PyObject *)Py_TYPE(__pyx_v_other)));
6477  __pyx_t_8 = __Pyx_PyObject_Call(((PyObject *)(&PyString_Type)), __pyx_t_7, NULL); if (unlikely(!__pyx_t_8)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 614; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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6479  __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
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6481  __Pyx_GOTREF(__pyx_t_7);
6482  __Pyx_DECREF(__pyx_t_15); __pyx_t_15 = 0;
6483  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
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6485  /* "PyClical.pyx":615
6486  * else:
6487  * raise TypeError(error_msg_prefix + " (" + str(type(other))
6488  * + ", " + repr(ixt) + ").") # <<<<<<<<<<<<<<
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6490  * raise TypeError(error_msg_prefix + " (" + str(type(other))
6491  */
6492  __pyx_t_8 = PyNumber_Add(__pyx_t_7, __pyx_kp_s__6); if (unlikely(!__pyx_t_8)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 615; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
6493  __Pyx_GOTREF(__pyx_t_8);
6494  __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
6495  __pyx_t_7 = PyObject_Repr(__pyx_v_ixt); if (unlikely(!__pyx_t_7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 615; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
6496  __Pyx_GOTREF(__pyx_t_7);
6497  __pyx_t_15 = PyNumber_Add(__pyx_t_8, __pyx_t_7); if (unlikely(!__pyx_t_15)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 615; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
6498  __Pyx_GOTREF(__pyx_t_15);
6499  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
6500  __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
6501  __pyx_t_7 = PyNumber_Add(__pyx_t_15, __pyx_kp_s__7); if (unlikely(!__pyx_t_7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 615; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
6502  __Pyx_GOTREF(__pyx_t_7);
6503  __Pyx_DECREF(__pyx_t_15); __pyx_t_15 = 0;
6504 
6505  /* "PyClical.pyx":614
6506  * self.instance = new Clifford(list_to_vector(other), (<index_set>ixt).unwrap())
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6508  * raise TypeError(error_msg_prefix + " (" + str(type(other)) # <<<<<<<<<<<<<<
6509  * + ", " + repr(ixt) + ").")
6510  * else:
6511  */
6512  __pyx_t_15 = PyTuple_New(1); if (unlikely(!__pyx_t_15)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 614; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
6513  __Pyx_GOTREF(__pyx_t_15);
6514  __Pyx_GIVEREF(__pyx_t_7);
6515  PyTuple_SET_ITEM(__pyx_t_15, 0, __pyx_t_7);
6516  __pyx_t_7 = 0;
6517  __pyx_t_7 = __Pyx_PyObject_Call(__pyx_builtin_TypeError, __pyx_t_15, NULL); if (unlikely(!__pyx_t_7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 614; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
6518  __Pyx_GOTREF(__pyx_t_7);
6519  __Pyx_DECREF(__pyx_t_15); __pyx_t_15 = 0;
6520  __Pyx_Raise(__pyx_t_7, 0, 0, 0);
6521  __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
6522  {__pyx_filename = __pyx_f[0]; __pyx_lineno = 614; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
6523  }
6524  __pyx_L25:;
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6530  * if isinstance(other, numbers.Real):
6531  * self.instance = new Clifford((<index_set>ixt).unwrap(), <scalar_t>other)
6532  */
6533  goto __pyx_L3;
6534  }
6535 
6536  /* "PyClical.pyx":617
6537  * + ", " + repr(ixt) + ").")
6538  * else:
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6545  __Pyx_GOTREF(__pyx_t_7);
6546  __pyx_t_15 = PyTuple_New(1); if (unlikely(!__pyx_t_15)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 617; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
6547  __Pyx_GOTREF(__pyx_t_15);
6548  __Pyx_INCREF(((PyObject *)Py_TYPE(__pyx_v_other)));
6549  __Pyx_GIVEREF(((PyObject *)Py_TYPE(__pyx_v_other)));
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6566  __pyx_t_8 = PyNumber_Add(__pyx_t_15, __pyx_kp_s__6); if (unlikely(!__pyx_t_8)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 618; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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6578  __Pyx_GOTREF(__pyx_t_15);
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6582  __Pyx_GOTREF(__pyx_t_7);
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6598  __Pyx_GOTREF(__pyx_t_7);
6599  __Pyx_DECREF(__pyx_t_15); __pyx_t_15 = 0;
6600  __Pyx_Raise(__pyx_t_7, 0, 0, 0);
6601  __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
6602  {__pyx_filename = __pyx_f[0]; __pyx_lineno = 617; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
6603  }
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6608  *
6609  * def __cinit__(self, other = 0, ixt = None): # <<<<<<<<<<<<<<
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6614  /* function exit code */
6615  __pyx_r = 0;
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6617  __pyx_L1_error:;
6618  __Pyx_XDECREF(__pyx_t_7);
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6621  __Pyx_XDECREF(__pyx_t_16);
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6635  *
6636  * def __dealloc__(self): # <<<<<<<<<<<<<<
6637  * """
6638  * Clean up by deallocating the instance of C++ class Clifford.
6639  */
6640 
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6668  * def __dealloc__(self): # <<<<<<<<<<<<<<
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6725  * del self.instance
6726  *
6727  * def __contains__(self, x): # <<<<<<<<<<<<<<
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6730  */
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6733  __pyx_L1_error:;
6734  __Pyx_XDECREF(__pyx_t_1);
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6744  * def __iter__(self): # <<<<<<<<<<<<<<
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6747  */
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6796  /* function exit code */
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6838  PyObject *__pyx_t_5 = NULL;
6839  PyObject *__pyx_t_6 = NULL;
6840  Clifford *__pyx_t_7;
6841  int __pyx_t_8;
6842  PyObject *__pyx_t_9 = NULL;
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6848  const char *__pyx_filename = NULL;
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6865  * if isinstance(ixt, index_set): # <<<<<<<<<<<<<<
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6890  * result = clifford() # <<<<<<<<<<<<<<
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6991  __Pyx_GOTREF(__pyx_t_11);
6992  __Pyx_DECREF(__pyx_t_12); __pyx_t_12 = 0;
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7037  __pyx_L6_except_error:;
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7048  __Pyx_XGIVEREF(__pyx_t_5);
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7051  __pyx_L11_try_end:;
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18132  * def _test():
18133  * import PyClical, doctest # <<<<<<<<<<<<<<
18134  * return doctest.testmod(PyClical)
18135  *
18136  */
18137  __pyx_t_1 = __Pyx_Import(__pyx_n_s_PyClical, 0, -1); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1914; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
18138  __Pyx_GOTREF(__pyx_t_1);
18139  __pyx_v_PyClical = __pyx_t_1;
18140  __pyx_t_1 = 0;
18141  __pyx_t_1 = __Pyx_Import(__pyx_n_s_doctest, 0, -1); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1914; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
18142  __Pyx_GOTREF(__pyx_t_1);
18143  __pyx_v_doctest = __pyx_t_1;
18144  __pyx_t_1 = 0;
18145 
18146  /* "PyClical.pyx":1915
18147  * def _test():
18148  * import PyClical, doctest
18149  * return doctest.testmod(PyClical) # <<<<<<<<<<<<<<
18150  *
18151  * if __name__ == "__main__":
18152  */
18153  __Pyx_XDECREF(__pyx_r);
18154  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_doctest, __pyx_n_s_testmod); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1915; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
18155  __Pyx_GOTREF(__pyx_t_2);
18156  __pyx_t_3 = NULL;
18157  if (CYTHON_COMPILING_IN_CPYTHON && likely(PyMethod_Check(__pyx_t_2))) {
18158  __pyx_t_3 = PyMethod_GET_SELF(__pyx_t_2);
18159  if (likely(__pyx_t_3)) {
18160  PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_2);
18161  __Pyx_INCREF(__pyx_t_3);
18162  __Pyx_INCREF(function);
18163  __Pyx_DECREF_SET(__pyx_t_2, function);
18164  }
18165  }
18166  if (!__pyx_t_3) {
18167  __pyx_t_1 = __Pyx_PyObject_CallOneArg(__pyx_t_2, __pyx_v_PyClical); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1915; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
18168  __Pyx_GOTREF(__pyx_t_1);
18169  } else {
18170  __pyx_t_4 = PyTuple_New(1+1); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1915; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
18171  __Pyx_GOTREF(__pyx_t_4);
18172  __Pyx_GIVEREF(__pyx_t_3); PyTuple_SET_ITEM(__pyx_t_4, 0, __pyx_t_3); __pyx_t_3 = NULL;
18173  __Pyx_INCREF(__pyx_v_PyClical);
18174  __Pyx_GIVEREF(__pyx_v_PyClical);
18175  PyTuple_SET_ITEM(__pyx_t_4, 0+1, __pyx_v_PyClical);
18176  __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_2, __pyx_t_4, NULL); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1915; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
18177  __Pyx_GOTREF(__pyx_t_1);
18178  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
18179  }
18180  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
18181  __pyx_r = __pyx_t_1;
18182  __pyx_t_1 = 0;
18183  goto __pyx_L0;
18184 
18185  /* "PyClical.pyx":1913
18186  *
18187  * # Doctest interface.
18188  * def _test(): # <<<<<<<<<<<<<<
18189  * import PyClical, doctest
18190  * return doctest.testmod(PyClical)
18191  */
18192 
18193  /* function exit code */
18194  __pyx_L1_error:;
18195  __Pyx_XDECREF(__pyx_t_1);
18196  __Pyx_XDECREF(__pyx_t_2);
18197  __Pyx_XDECREF(__pyx_t_3);
18198  __Pyx_XDECREF(__pyx_t_4);
18199  __Pyx_AddTraceback("PyClical._test", __pyx_clineno, __pyx_lineno, __pyx_filename);
18200  __pyx_r = NULL;
18201  __pyx_L0:;
18202  __Pyx_XDECREF(__pyx_v_PyClical);
18203  __Pyx_XDECREF(__pyx_v_doctest);
18204  __Pyx_XGIVEREF(__pyx_r);
18205  __Pyx_RefNannyFinishContext();
18206  return __pyx_r;
18207  }
18208  static struct __pyx_vtabstruct_8PyClical_index_set __pyx_vtable_8PyClical_index_set;
18209 
18210  static PyObject *__pyx_tp_new_8PyClical_index_set(PyTypeObject *t, PyObject *a, PyObject *k) {
18211  struct __pyx_obj_8PyClical_index_set *p;
18212  PyObject *o;
18213  if (likely((t->tp_flags & Py_TPFLAGS_IS_ABSTRACT) == 0)) {
18214  o = (*t->tp_alloc)(t, 0);
18215  } else {
18216  o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_empty_tuple, 0);
18217  }
18218  if (unlikely(!o)) return 0;
18219  p = ((struct __pyx_obj_8PyClical_index_set *)o);
18220  p->__pyx_vtab = __pyx_vtabptr_8PyClical_index_set;
18221  if (unlikely(__pyx_pw_8PyClical_9index_set_3__cinit__(o, a, k) < 0)) {
18222  Py_DECREF(o); o = 0;
18223  }
18224  return o;
18225  }
18226 
18227  static void __pyx_tp_dealloc_8PyClical_index_set(PyObject *o) {
18228  #if PY_VERSION_HEX >= 0x030400a1
18229  if (unlikely(Py_TYPE(o)->tp_finalize) && (!PyType_IS_GC(Py_TYPE(o)) || !_PyGC_FINALIZED(o))) {
18230  if (PyObject_CallFinalizerFromDealloc(o)) return;
18231  }
18232  #endif
18233  {
18234  PyObject *etype, *eval, *etb;
18235  PyErr_Fetch(&etype, &eval, &etb);
18236  ++Py_REFCNT(o);
18237  __pyx_pw_8PyClical_9index_set_5__dealloc__(o);
18238  --Py_REFCNT(o);
18239  PyErr_Restore(etype, eval, etb);
18240  }
18241  (*Py_TYPE(o)->tp_free)(o);
18242  }
18243  static PyObject *__pyx_sq_item_8PyClical_index_set(PyObject *o, Py_ssize_t i) {
18244  PyObject *r;
18245  PyObject *x = PyInt_FromSsize_t(i); if(!x) return 0;
18246  r = Py_TYPE(o)->tp_as_mapping->mp_subscript(o, x);
18247  Py_DECREF(x);
18248  return r;
18249  }
18250 
18251  static int __pyx_mp_ass_subscript_8PyClical_index_set(PyObject *o, PyObject *i, PyObject *v) {
18252  if (v) {
18253  return __pyx_pw_8PyClical_9index_set_9__setitem__(o, i, v);
18254  }
18255  else {
18256  PyErr_Format(PyExc_NotImplementedError,
18257  "Subscript deletion not supported by %.200s", Py_TYPE(o)->tp_name);
18258  return -1;
18259  }
18260  }
18261 
18262  static PyMethodDef __pyx_methods_8PyClical_index_set[] = {
18263  {"copy", (PyCFunction)__pyx_pw_8PyClical_9index_set_1copy, METH_NOARGS, __pyx_doc_8PyClical_9index_set_copy},
18264  {"count", (PyCFunction)__pyx_pw_8PyClical_9index_set_32count, METH_NOARGS, __pyx_doc_8PyClical_9index_set_31count},
18265  {"count_neg", (PyCFunction)__pyx_pw_8PyClical_9index_set_34count_neg, METH_NOARGS, __pyx_doc_8PyClical_9index_set_33count_neg},
18266  {"count_pos", (PyCFunction)__pyx_pw_8PyClical_9index_set_36count_pos, METH_NOARGS, __pyx_doc_8PyClical_9index_set_35count_pos},
18267  {"min", (PyCFunction)__pyx_pw_8PyClical_9index_set_38min, METH_NOARGS, __pyx_doc_8PyClical_9index_set_37min},
18268  {"max", (PyCFunction)__pyx_pw_8PyClical_9index_set_40max, METH_NOARGS, __pyx_doc_8PyClical_9index_set_39max},
18269  {"hash_fn", (PyCFunction)__pyx_pw_8PyClical_9index_set_42hash_fn, METH_NOARGS, __pyx_doc_8PyClical_9index_set_41hash_fn},
18270  {"sign_of_mult", (PyCFunction)__pyx_pw_8PyClical_9index_set_44sign_of_mult, METH_O, __pyx_doc_8PyClical_9index_set_43sign_of_mult},
18271  {"sign_of_square", (PyCFunction)__pyx_pw_8PyClical_9index_set_46sign_of_square, METH_NOARGS, __pyx_doc_8PyClical_9index_set_45sign_of_square},
18272  {0, 0, 0, 0}
18273  };
18274 
18275  static PyNumberMethods __pyx_tp_as_number_index_set = {
18276  0, /*nb_add*/
18277  0, /*nb_subtract*/
18278  0, /*nb_multiply*/
18279  #if PY_MAJOR_VERSION < 3 || CYTHON_COMPILING_IN_PYPY
18280  0, /*nb_divide*/
18281  #endif
18282  0, /*nb_remainder*/
18283  0, /*nb_divmod*/
18284  0, /*nb_power*/
18285  0, /*nb_negative*/
18286  0, /*nb_positive*/
18287  0, /*nb_absolute*/
18288  0, /*nb_nonzero*/
18289  __pyx_pw_8PyClical_9index_set_18__invert__, /*nb_invert*/
18290  0, /*nb_lshift*/
18291  0, /*nb_rshift*/
18292  __pyx_pw_8PyClical_9index_set_24__and__, /*nb_and*/
18293  __pyx_pw_8PyClical_9index_set_20__xor__, /*nb_xor*/
18294  __pyx_pw_8PyClical_9index_set_28__or__, /*nb_or*/
18295  #if PY_MAJOR_VERSION < 3 || CYTHON_COMPILING_IN_PYPY
18296  0, /*nb_coerce*/
18297  #endif
18298  0, /*nb_int*/
18299  #if PY_MAJOR_VERSION < 3
18300  0, /*nb_long*/
18301  #else
18302  0, /*reserved*/
18303  #endif
18304  0, /*nb_float*/
18305  #if PY_MAJOR_VERSION < 3 || CYTHON_COMPILING_IN_PYPY
18306  0, /*nb_oct*/
18307  #endif
18308  #if PY_MAJOR_VERSION < 3 || CYTHON_COMPILING_IN_PYPY
18309  0, /*nb_hex*/
18310  #endif
18311  0, /*nb_inplace_add*/
18312  0, /*nb_inplace_subtract*/
18313  0, /*nb_inplace_multiply*/
18314  #if PY_MAJOR_VERSION < 3 || CYTHON_COMPILING_IN_PYPY
18315  0, /*nb_inplace_divide*/
18316  #endif
18317  0, /*nb_inplace_remainder*/
18318  0, /*nb_inplace_power*/
18319  0, /*nb_inplace_lshift*/
18320  0, /*nb_inplace_rshift*/
18321  __pyx_pw_8PyClical_9index_set_26__iand__, /*nb_inplace_and*/
18322  __pyx_pw_8PyClical_9index_set_22__ixor__, /*nb_inplace_xor*/
18323  __pyx_pw_8PyClical_9index_set_30__ior__, /*nb_inplace_or*/
18324  0, /*nb_floor_divide*/
18325  0, /*nb_true_divide*/
18326  0, /*nb_inplace_floor_divide*/
18327  0, /*nb_inplace_true_divide*/
18328  0, /*nb_index*/
18329  #if PY_VERSION_HEX >= 0x03050000
18330  0, /*nb_matrix_multiply*/
18331  #endif
18332  #if PY_VERSION_HEX >= 0x03050000
18333  0, /*nb_inplace_matrix_multiply*/
18334  #endif
18335  };
18336 
18337  static PySequenceMethods __pyx_tp_as_sequence_index_set = {
18338  0, /*sq_length*/
18339  0, /*sq_concat*/
18340  0, /*sq_repeat*/
18341  __pyx_sq_item_8PyClical_index_set, /*sq_item*/
18342  0, /*sq_slice*/
18343  0, /*sq_ass_item*/
18344  0, /*sq_ass_slice*/
18345  __pyx_pw_8PyClical_9index_set_13__contains__, /*sq_contains*/
18346  0, /*sq_inplace_concat*/
18347  0, /*sq_inplace_repeat*/
18348  };
18349 
18350  static PyMappingMethods __pyx_tp_as_mapping_index_set = {
18351  0, /*mp_length*/
18352  __pyx_pw_8PyClical_9index_set_11__getitem__, /*mp_subscript*/
18353  __pyx_mp_ass_subscript_8PyClical_index_set, /*mp_ass_subscript*/
18354  };
18355 
18356  static PyTypeObject __pyx_type_8PyClical_index_set = {
18357  PyVarObject_HEAD_INIT(0, 0)
18358  "PyClical.index_set", /*tp_name*/
18359  sizeof(struct __pyx_obj_8PyClical_index_set), /*tp_basicsize*/
18360  0, /*tp_itemsize*/
18361  __pyx_tp_dealloc_8PyClical_index_set, /*tp_dealloc*/
18362  0, /*tp_print*/
18363  0, /*tp_getattr*/
18364  0, /*tp_setattr*/
18365  #if PY_MAJOR_VERSION < 3
18366  0, /*tp_compare*/
18367  #endif
18368  #if PY_MAJOR_VERSION >= 3
18369  0, /*tp_as_async*/
18370  #endif
18371  __pyx_pw_8PyClical_9index_set_48__repr__, /*tp_repr*/
18372  &__pyx_tp_as_number_index_set, /*tp_as_number*/
18373  &__pyx_tp_as_sequence_index_set, /*tp_as_sequence*/
18374  &__pyx_tp_as_mapping_index_set, /*tp_as_mapping*/
18375  0, /*tp_hash*/
18376  0, /*tp_call*/
18377  __pyx_pw_8PyClical_9index_set_50__str__, /*tp_str*/
18378  0, /*tp_getattro*/
18379  0, /*tp_setattro*/
18380  0, /*tp_as_buffer*/
18381  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE, /*tp_flags*/
18382  "\n Python class index_set wraps C++ class IndexSet.\n ", /*tp_doc*/
18383  0, /*tp_traverse*/
18384  0, /*tp_clear*/
18385  __pyx_pw_8PyClical_9index_set_7__richcmp__, /*tp_richcompare*/
18386  0, /*tp_weaklistoffset*/
18387  __pyx_pw_8PyClical_9index_set_15__iter__, /*tp_iter*/
18388  0, /*tp_iternext*/
18389  __pyx_methods_8PyClical_index_set, /*tp_methods*/
18390  0, /*tp_members*/
18391  0, /*tp_getset*/
18392  0, /*tp_base*/
18393  0, /*tp_dict*/
18394  0, /*tp_descr_get*/
18395  0, /*tp_descr_set*/
18396  0, /*tp_dictoffset*/
18397  0, /*tp_init*/
18398  0, /*tp_alloc*/
18399  __pyx_tp_new_8PyClical_index_set, /*tp_new*/
18400  0, /*tp_free*/
18401  0, /*tp_is_gc*/
18402  0, /*tp_bases*/
18403  0, /*tp_mro*/
18404  0, /*tp_cache*/
18405  0, /*tp_subclasses*/
18406  0, /*tp_weaklist*/
18407  0, /*tp_del*/
18408  0, /*tp_version_tag*/
18409  #if PY_VERSION_HEX >= 0x030400a1
18410  0, /*tp_finalize*/
18411  #endif
18412  };
18413  static struct __pyx_vtabstruct_8PyClical_clifford __pyx_vtable_8PyClical_clifford;
18414 
18415  static PyObject *__pyx_tp_new_8PyClical_clifford(PyTypeObject *t, PyObject *a, PyObject *k) {
18416  struct __pyx_obj_8PyClical_clifford *p;
18417  PyObject *o;
18418  if (likely((t->tp_flags & Py_TPFLAGS_IS_ABSTRACT) == 0)) {
18419  o = (*t->tp_alloc)(t, 0);
18420  } else {
18421  o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_empty_tuple, 0);
18422  }
18423  if (unlikely(!o)) return 0;
18424  p = ((struct __pyx_obj_8PyClical_clifford *)o);
18425  p->__pyx_vtab = __pyx_vtabptr_8PyClical_clifford;
18426  if (unlikely(__pyx_pw_8PyClical_8clifford_3__cinit__(o, a, k) < 0)) {
18427  Py_DECREF(o); o = 0;
18428  }
18429  return o;
18430  }
18431 
18432  static void __pyx_tp_dealloc_8PyClical_clifford(PyObject *o) {
18433  #if PY_VERSION_HEX >= 0x030400a1
18434  if (unlikely(Py_TYPE(o)->tp_finalize) && (!PyType_IS_GC(Py_TYPE(o)) || !_PyGC_FINALIZED(o))) {
18435  if (PyObject_CallFinalizerFromDealloc(o)) return;
18436  }
18437  #endif
18438  {
18439  PyObject *etype, *eval, *etb;
18440  PyErr_Fetch(&etype, &eval, &etb);
18441  ++Py_REFCNT(o);
18442  __pyx_pw_8PyClical_8clifford_5__dealloc__(o);
18443  --Py_REFCNT(o);
18444  PyErr_Restore(etype, eval, etb);
18445  }
18446  (*Py_TYPE(o)->tp_free)(o);
18447  }
18448  static PyObject *__pyx_sq_item_8PyClical_clifford(PyObject *o, Py_ssize_t i) {
18449  PyObject *r;
18450  PyObject *x = PyInt_FromSsize_t(i); if(!x) return 0;
18451  r = Py_TYPE(o)->tp_as_mapping->mp_subscript(o, x);
18452  Py_DECREF(x);
18453  return r;
18454  }
18455 
18456  static PyMethodDef __pyx_methods_8PyClical_clifford[] = {
18457  {"copy", (PyCFunction)__pyx_pw_8PyClical_8clifford_1copy, METH_NOARGS, __pyx_doc_8PyClical_8clifford_copy},
18458  {"reframe", (PyCFunction)__pyx_pw_8PyClical_8clifford_11reframe, METH_O, __pyx_doc_8PyClical_8clifford_10reframe},
18459  {"inv", (PyCFunction)__pyx_pw_8PyClical_8clifford_49inv, METH_NOARGS, __pyx_doc_8PyClical_8clifford_48inv},
18460  {"pow", (PyCFunction)__pyx_pw_8PyClical_8clifford_57pow, METH_O, __pyx_doc_8PyClical_8clifford_56pow},
18461  {"outer_pow", (PyCFunction)__pyx_pw_8PyClical_8clifford_59outer_pow, METH_O, __pyx_doc_8PyClical_8clifford_58outer_pow},
18462  {"scalar", (PyCFunction)__pyx_pw_8PyClical_8clifford_63scalar, METH_NOARGS, __pyx_doc_8PyClical_8clifford_62scalar},
18463  {"pure", (PyCFunction)__pyx_pw_8PyClical_8clifford_65pure, METH_NOARGS, __pyx_doc_8PyClical_8clifford_64pure},
18464  {"even", (PyCFunction)__pyx_pw_8PyClical_8clifford_67even, METH_NOARGS, __pyx_doc_8PyClical_8clifford_66even},
18465  {"odd", (PyCFunction)__pyx_pw_8PyClical_8clifford_69odd, METH_NOARGS, __pyx_doc_8PyClical_8clifford_68odd},
18466  {"vector_part", (PyCFunction)__pyx_pw_8PyClical_8clifford_71vector_part, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_8clifford_70vector_part},
18467  {"involute", (PyCFunction)__pyx_pw_8PyClical_8clifford_73involute, METH_NOARGS, __pyx_doc_8PyClical_8clifford_72involute},
18468  {"reverse", (PyCFunction)__pyx_pw_8PyClical_8clifford_75reverse, METH_NOARGS, __pyx_doc_8PyClical_8clifford_74reverse},
18469  {"conj", (PyCFunction)__pyx_pw_8PyClical_8clifford_77conj, METH_NOARGS, __pyx_doc_8PyClical_8clifford_76conj},
18470  {"quad", (PyCFunction)__pyx_pw_8PyClical_8clifford_79quad, METH_NOARGS, __pyx_doc_8PyClical_8clifford_78quad},
18471  {"norm", (PyCFunction)__pyx_pw_8PyClical_8clifford_81norm, METH_NOARGS, __pyx_doc_8PyClical_8clifford_80norm},
18472  {"abs", (PyCFunction)__pyx_pw_8PyClical_8clifford_83abs, METH_NOARGS, __pyx_doc_8PyClical_8clifford_82abs},
18473  {"max_abs", (PyCFunction)__pyx_pw_8PyClical_8clifford_85max_abs, METH_NOARGS, __pyx_doc_8PyClical_8clifford_84max_abs},
18474  {"truncated", (PyCFunction)__pyx_pw_8PyClical_8clifford_87truncated, METH_O, __pyx_doc_8PyClical_8clifford_86truncated},
18475  {"isnan", (PyCFunction)__pyx_pw_8PyClical_8clifford_89isnan, METH_NOARGS, __pyx_doc_8PyClical_8clifford_88isnan},
18476  {"frame", (PyCFunction)__pyx_pw_8PyClical_8clifford_91frame, METH_NOARGS, __pyx_doc_8PyClical_8clifford_90frame},
18477  {0, 0, 0, 0}
18478  };
18479 
18480  static PyNumberMethods __pyx_tp_as_number_clifford = {
18481  __pyx_pw_8PyClical_8clifford_21__add__, /*nb_add*/
18482  __pyx_pw_8PyClical_8clifford_25__sub__, /*nb_subtract*/
18483  __pyx_pw_8PyClical_8clifford_29__mul__, /*nb_multiply*/
18484  #if PY_MAJOR_VERSION < 3 || CYTHON_COMPILING_IN_PYPY
18485  __pyx_pw_8PyClical_8clifford_45__div__, /*nb_divide*/
18486  #endif
18487  __pyx_pw_8PyClical_8clifford_33__mod__, /*nb_remainder*/
18488  0, /*nb_divmod*/
18489  __pyx_pw_8PyClical_8clifford_55__pow__, /*nb_power*/
18490  __pyx_pw_8PyClical_8clifford_17__neg__, /*nb_negative*/
18491  __pyx_pw_8PyClical_8clifford_19__pos__, /*nb_positive*/
18492  0, /*nb_absolute*/
18493  0, /*nb_nonzero*/
18494  0, /*nb_invert*/
18495  0, /*nb_lshift*/
18496  0, /*nb_rshift*/
18497  __pyx_pw_8PyClical_8clifford_37__and__, /*nb_and*/
18498  __pyx_pw_8PyClical_8clifford_41__xor__, /*nb_xor*/
18499  __pyx_pw_8PyClical_8clifford_51__or__, /*nb_or*/
18500  #if PY_MAJOR_VERSION < 3 || CYTHON_COMPILING_IN_PYPY
18501  0, /*nb_coerce*/
18502  #endif
18503  0, /*nb_int*/
18504  #if PY_MAJOR_VERSION < 3
18505  0, /*nb_long*/
18506  #else
18507  0, /*reserved*/
18508  #endif
18509  0, /*nb_float*/
18510  #if PY_MAJOR_VERSION < 3 || CYTHON_COMPILING_IN_PYPY
18511  0, /*nb_oct*/
18512  #endif
18513  #if PY_MAJOR_VERSION < 3 || CYTHON_COMPILING_IN_PYPY
18514  0, /*nb_hex*/
18515  #endif
18516  __pyx_pw_8PyClical_8clifford_23__iadd__, /*nb_inplace_add*/
18517  __pyx_pw_8PyClical_8clifford_27__isub__, /*nb_inplace_subtract*/
18518  __pyx_pw_8PyClical_8clifford_31__imul__, /*nb_inplace_multiply*/
18519  #if PY_MAJOR_VERSION < 3 || CYTHON_COMPILING_IN_PYPY
18520  __pyx_pw_8PyClical_8clifford_47__idiv__, /*nb_inplace_divide*/
18521  #endif
18522  __pyx_pw_8PyClical_8clifford_35__imod__, /*nb_inplace_remainder*/
18523  0, /*nb_inplace_power*/
18524  0, /*nb_inplace_lshift*/
18525  0, /*nb_inplace_rshift*/
18526  __pyx_pw_8PyClical_8clifford_39__iand__, /*nb_inplace_and*/
18527  __pyx_pw_8PyClical_8clifford_43__ixor__, /*nb_inplace_xor*/
18528  __pyx_pw_8PyClical_8clifford_53__ior__, /*nb_inplace_or*/
18529  0, /*nb_floor_divide*/
18530  0, /*nb_true_divide*/
18531  0, /*nb_inplace_floor_divide*/
18532  0, /*nb_inplace_true_divide*/
18533  0, /*nb_index*/
18534  #if PY_VERSION_HEX >= 0x03050000
18535  0, /*nb_matrix_multiply*/
18536  #endif
18537  #if PY_VERSION_HEX >= 0x03050000
18538  0, /*nb_inplace_matrix_multiply*/
18539  #endif
18540  };
18541 
18542  static PySequenceMethods __pyx_tp_as_sequence_clifford = {
18543  0, /*sq_length*/
18544  0, /*sq_concat*/
18545  0, /*sq_repeat*/
18546  __pyx_sq_item_8PyClical_clifford, /*sq_item*/
18547  0, /*sq_slice*/
18548  0, /*sq_ass_item*/
18549  0, /*sq_ass_slice*/
18550  __pyx_pw_8PyClical_8clifford_7__contains__, /*sq_contains*/
18551  0, /*sq_inplace_concat*/
18552  0, /*sq_inplace_repeat*/
18553  };
18554 
18555  static PyMappingMethods __pyx_tp_as_mapping_clifford = {
18556  0, /*mp_length*/
18557  __pyx_pw_8PyClical_8clifford_15__getitem__, /*mp_subscript*/
18558  0, /*mp_ass_subscript*/
18559  };
18560 
18561  static PyTypeObject __pyx_type_8PyClical_clifford = {
18562  PyVarObject_HEAD_INIT(0, 0)
18563  "PyClical.clifford", /*tp_name*/
18564  sizeof(struct __pyx_obj_8PyClical_clifford), /*tp_basicsize*/
18565  0, /*tp_itemsize*/
18566  __pyx_tp_dealloc_8PyClical_clifford, /*tp_dealloc*/
18567  0, /*tp_print*/
18568  0, /*tp_getattr*/
18569  0, /*tp_setattr*/
18570  #if PY_MAJOR_VERSION < 3
18571  0, /*tp_compare*/
18572  #endif
18573  #if PY_MAJOR_VERSION >= 3
18574  0, /*tp_as_async*/
18575  #endif
18576  __pyx_pw_8PyClical_8clifford_93__repr__, /*tp_repr*/
18577  &__pyx_tp_as_number_clifford, /*tp_as_number*/
18578  &__pyx_tp_as_sequence_clifford, /*tp_as_sequence*/
18579  &__pyx_tp_as_mapping_clifford, /*tp_as_mapping*/
18580  0, /*tp_hash*/
18581  __pyx_pw_8PyClical_8clifford_61__call__, /*tp_call*/
18582  __pyx_pw_8PyClical_8clifford_95__str__, /*tp_str*/
18583  0, /*tp_getattro*/
18584  0, /*tp_setattro*/
18585  0, /*tp_as_buffer*/
18586  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE, /*tp_flags*/
18587  "\n Python class clifford wraps C++ class Clifford.\n ", /*tp_doc*/
18588  0, /*tp_traverse*/
18589  0, /*tp_clear*/
18590  __pyx_pw_8PyClical_8clifford_13__richcmp__, /*tp_richcompare*/
18591  0, /*tp_weaklistoffset*/
18592  __pyx_pw_8PyClical_8clifford_9__iter__, /*tp_iter*/
18593  0, /*tp_iternext*/
18594  __pyx_methods_8PyClical_clifford, /*tp_methods*/
18595  0, /*tp_members*/
18596  0, /*tp_getset*/
18597  0, /*tp_base*/
18598  0, /*tp_dict*/
18599  0, /*tp_descr_get*/
18600  0, /*tp_descr_set*/
18601  0, /*tp_dictoffset*/
18602  0, /*tp_init*/
18603  0, /*tp_alloc*/
18604  __pyx_tp_new_8PyClical_clifford, /*tp_new*/
18605  0, /*tp_free*/
18606  0, /*tp_is_gc*/
18607  0, /*tp_bases*/
18608  0, /*tp_mro*/
18609  0, /*tp_cache*/
18610  0, /*tp_subclasses*/
18611  0, /*tp_weaklist*/
18612  0, /*tp_del*/
18613  0, /*tp_version_tag*/
18614  #if PY_VERSION_HEX >= 0x030400a1
18615  0, /*tp_finalize*/
18616  #endif
18617  };
18618 
18619  static struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *__pyx_freelist_8PyClical___pyx_scope_struct____iter__[8];
18620  static int __pyx_freecount_8PyClical___pyx_scope_struct____iter__ = 0;
18621 
18622  static PyObject *__pyx_tp_new_8PyClical___pyx_scope_struct____iter__(PyTypeObject *t, CYTHON_UNUSED PyObject *a, CYTHON_UNUSED PyObject *k) {
18623  PyObject *o;
18624  if (CYTHON_COMPILING_IN_CPYTHON && likely((__pyx_freecount_8PyClical___pyx_scope_struct____iter__ > 0) & (t->tp_basicsize == sizeof(struct __pyx_obj_8PyClical___pyx_scope_struct____iter__)))) {
18625  o = (PyObject*)__pyx_freelist_8PyClical___pyx_scope_struct____iter__[--__pyx_freecount_8PyClical___pyx_scope_struct____iter__];
18626  memset(o, 0, sizeof(struct __pyx_obj_8PyClical___pyx_scope_struct____iter__));
18627  (void) PyObject_INIT(o, t);
18628  PyObject_GC_Track(o);
18629  } else {
18630  o = (*t->tp_alloc)(t, 0);
18631  if (unlikely(!o)) return 0;
18632  }
18633  return o;
18634  }
18635 
18636  static void __pyx_tp_dealloc_8PyClical___pyx_scope_struct____iter__(PyObject *o) {
18637  struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *p = (struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *)o;
18638  PyObject_GC_UnTrack(o);
18639  Py_CLEAR(p->__pyx_v_idx);
18640  Py_CLEAR(p->__pyx_v_self);
18641  Py_CLEAR(p->__pyx_t_0);
18642  if (CYTHON_COMPILING_IN_CPYTHON && ((__pyx_freecount_8PyClical___pyx_scope_struct____iter__ < 8) & (Py_TYPE(o)->tp_basicsize == sizeof(struct __pyx_obj_8PyClical___pyx_scope_struct____iter__)))) {
18643  __pyx_freelist_8PyClical___pyx_scope_struct____iter__[__pyx_freecount_8PyClical___pyx_scope_struct____iter__++] = ((struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *)o);
18644  } else {
18645  (*Py_TYPE(o)->tp_free)(o);
18646  }
18647  }
18648 
18649  static int __pyx_tp_traverse_8PyClical___pyx_scope_struct____iter__(PyObject *o, visitproc v, void *a) {
18650  int e;
18651  struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *p = (struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *)o;
18652  if (p->__pyx_v_idx) {
18653  e = (*v)(p->__pyx_v_idx, a); if (e) return e;
18654  }
18655  if (p->__pyx_v_self) {
18656  e = (*v)(((PyObject*)p->__pyx_v_self), a); if (e) return e;
18657  }
18658  if (p->__pyx_t_0) {
18659  e = (*v)(p->__pyx_t_0, a); if (e) return e;
18660  }
18661  return 0;
18662  }
18663 
18664  static int __pyx_tp_clear_8PyClical___pyx_scope_struct____iter__(PyObject *o) {
18665  PyObject* tmp;
18666  struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *p = (struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *)o;
18667  tmp = ((PyObject*)p->__pyx_v_idx);
18668  p->__pyx_v_idx = Py_None; Py_INCREF(Py_None);
18669  Py_XDECREF(tmp);
18670  tmp = ((PyObject*)p->__pyx_v_self);
18671  p->__pyx_v_self = ((struct __pyx_obj_8PyClical_index_set *)Py_None); Py_INCREF(Py_None);
18672  Py_XDECREF(tmp);
18673  tmp = ((PyObject*)p->__pyx_t_0);
18674  p->__pyx_t_0 = Py_None; Py_INCREF(Py_None);
18675  Py_XDECREF(tmp);
18676  return 0;
18677  }
18678 
18679  static PyTypeObject __pyx_type_8PyClical___pyx_scope_struct____iter__ = {
18680  PyVarObject_HEAD_INIT(0, 0)
18681  "PyClical.__pyx_scope_struct____iter__", /*tp_name*/
18682  sizeof(struct __pyx_obj_8PyClical___pyx_scope_struct____iter__), /*tp_basicsize*/
18683  0, /*tp_itemsize*/
18684  __pyx_tp_dealloc_8PyClical___pyx_scope_struct____iter__, /*tp_dealloc*/
18685  0, /*tp_print*/
18686  0, /*tp_getattr*/
18687  0, /*tp_setattr*/
18688  #if PY_MAJOR_VERSION < 3
18689  0, /*tp_compare*/
18690  #endif
18691  #if PY_MAJOR_VERSION >= 3
18692  0, /*tp_as_async*/
18693  #endif
18694  0, /*tp_repr*/
18695  0, /*tp_as_number*/
18696  0, /*tp_as_sequence*/
18697  0, /*tp_as_mapping*/
18698  0, /*tp_hash*/
18699  0, /*tp_call*/
18700  0, /*tp_str*/
18701  0, /*tp_getattro*/
18702  0, /*tp_setattro*/
18703  0, /*tp_as_buffer*/
18704  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
18705  0, /*tp_doc*/
18706  __pyx_tp_traverse_8PyClical___pyx_scope_struct____iter__, /*tp_traverse*/
18707  __pyx_tp_clear_8PyClical___pyx_scope_struct____iter__, /*tp_clear*/
18708  0, /*tp_richcompare*/
18709  0, /*tp_weaklistoffset*/
18710  0, /*tp_iter*/
18711  0, /*tp_iternext*/
18712  0, /*tp_methods*/
18713  0, /*tp_members*/
18714  0, /*tp_getset*/
18715  0, /*tp_base*/
18716  0, /*tp_dict*/
18717  0, /*tp_descr_get*/
18718  0, /*tp_descr_set*/
18719  0, /*tp_dictoffset*/
18720  0, /*tp_init*/
18721  0, /*tp_alloc*/
18722  __pyx_tp_new_8PyClical___pyx_scope_struct____iter__, /*tp_new*/
18723  0, /*tp_free*/
18724  0, /*tp_is_gc*/
18725  0, /*tp_bases*/
18726  0, /*tp_mro*/
18727  0, /*tp_cache*/
18728  0, /*tp_subclasses*/
18729  0, /*tp_weaklist*/
18730  0, /*tp_del*/
18731  0, /*tp_version_tag*/
18732  #if PY_VERSION_HEX >= 0x030400a1
18733  0, /*tp_finalize*/
18734  #endif
18735  };
18736 
18737  static PyMethodDef __pyx_methods[] = {
18738  {"compare", (PyCFunction)__pyx_pw_8PyClical_3compare, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_2compare},
18739  {"min_neg", (PyCFunction)__pyx_pw_8PyClical_5min_neg, METH_O, __pyx_doc_8PyClical_4min_neg},
18740  {"max_pos", (PyCFunction)__pyx_pw_8PyClical_7max_pos, METH_O, __pyx_doc_8PyClical_6max_pos},
18741  {"inv", (PyCFunction)__pyx_pw_8PyClical_11inv, METH_O, __pyx_doc_8PyClical_10inv},
18742  {"scalar", (PyCFunction)__pyx_pw_8PyClical_13scalar, METH_O, __pyx_doc_8PyClical_12scalar},
18743  {"real", (PyCFunction)__pyx_pw_8PyClical_15real, METH_O, __pyx_doc_8PyClical_14real},
18744  {"imag", (PyCFunction)__pyx_pw_8PyClical_17imag, METH_O, __pyx_doc_8PyClical_16imag},
18745  {"pure", (PyCFunction)__pyx_pw_8PyClical_19pure, METH_O, __pyx_doc_8PyClical_18pure},
18746  {"even", (PyCFunction)__pyx_pw_8PyClical_21even, METH_O, __pyx_doc_8PyClical_20even},
18747  {"odd", (PyCFunction)__pyx_pw_8PyClical_23odd, METH_O, __pyx_doc_8PyClical_22odd},
18748  {"involute", (PyCFunction)__pyx_pw_8PyClical_25involute, METH_O, __pyx_doc_8PyClical_24involute},
18749  {"reverse", (PyCFunction)__pyx_pw_8PyClical_27reverse, METH_O, __pyx_doc_8PyClical_26reverse},
18750  {"conj", (PyCFunction)__pyx_pw_8PyClical_29conj, METH_O, __pyx_doc_8PyClical_28conj},
18751  {"quad", (PyCFunction)__pyx_pw_8PyClical_31quad, METH_O, __pyx_doc_8PyClical_30quad},
18752  {"norm", (PyCFunction)__pyx_pw_8PyClical_33norm, METH_O, __pyx_doc_8PyClical_32norm},
18753  {"abs", (PyCFunction)__pyx_pw_8PyClical_35abs, METH_O, __pyx_doc_8PyClical_34abs},
18754  {"max_abs", (PyCFunction)__pyx_pw_8PyClical_37max_abs, METH_O, __pyx_doc_8PyClical_36max_abs},
18755  {"pow", (PyCFunction)__pyx_pw_8PyClical_39pow, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_38pow},
18756  {"outer_pow", (PyCFunction)__pyx_pw_8PyClical_41outer_pow, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_40outer_pow},
18757  {"complexifier", (PyCFunction)__pyx_pw_8PyClical_43complexifier, METH_O, __pyx_doc_8PyClical_42complexifier},
18758  {"sqrt", (PyCFunction)__pyx_pw_8PyClical_45sqrt, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_44sqrt},
18759  {"exp", (PyCFunction)__pyx_pw_8PyClical_47exp, METH_O, __pyx_doc_8PyClical_46exp},
18760  {"log", (PyCFunction)__pyx_pw_8PyClical_49log, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_48log},
18761  {"cos", (PyCFunction)__pyx_pw_8PyClical_51cos, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_50cos},
18762  {"acos", (PyCFunction)__pyx_pw_8PyClical_53acos, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_52acos},
18763  {"cosh", (PyCFunction)__pyx_pw_8PyClical_55cosh, METH_O, __pyx_doc_8PyClical_54cosh},
18764  {"acosh", (PyCFunction)__pyx_pw_8PyClical_57acosh, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_56acosh},
18765  {"sin", (PyCFunction)__pyx_pw_8PyClical_59sin, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_58sin},
18766  {"asin", (PyCFunction)__pyx_pw_8PyClical_61asin, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_60asin},
18767  {"sinh", (PyCFunction)__pyx_pw_8PyClical_63sinh, METH_O, __pyx_doc_8PyClical_62sinh},
18768  {"asinh", (PyCFunction)__pyx_pw_8PyClical_65asinh, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_64asinh},
18769  {"tan", (PyCFunction)__pyx_pw_8PyClical_67tan, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_66tan},
18770  {"atan", (PyCFunction)__pyx_pw_8PyClical_69atan, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_68atan},
18771  {"tanh", (PyCFunction)__pyx_pw_8PyClical_71tanh, METH_O, __pyx_doc_8PyClical_70tanh},
18772  {"atanh", (PyCFunction)__pyx_pw_8PyClical_73atanh, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_72atanh},
18773  {"random_clifford", (PyCFunction)__pyx_pw_8PyClical_75random_clifford, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_74random_clifford},
18774  {"cga3", (PyCFunction)__pyx_pw_8PyClical_77cga3, METH_O, __pyx_doc_8PyClical_76cga3},
18775  {"cga3std", (PyCFunction)__pyx_pw_8PyClical_79cga3std, METH_O, __pyx_doc_8PyClical_78cga3std},
18776  {"agc3", (PyCFunction)__pyx_pw_8PyClical_81agc3, METH_O, __pyx_doc_8PyClical_80agc3},
18777  {0, 0, 0, 0}
18778  };
18779 
18780  #if PY_MAJOR_VERSION >= 3
18781  static struct PyModuleDef __pyx_moduledef = {
18782  #if PY_VERSION_HEX < 0x03020000
18783  { PyObject_HEAD_INIT(NULL) NULL, 0, NULL },
18784  #else
18785  PyModuleDef_HEAD_INIT,
18786  #endif
18787  "PyClical",
18788  0, /* m_doc */
18789  -1, /* m_size */
18790  __pyx_methods /* m_methods */,
18791  NULL, /* m_reload */
18792  NULL, /* m_traverse */
18793  NULL, /* m_clear */
18794  NULL /* m_free */
18795  };
18796  #endif
18797 
18798 static __Pyx_StringTabEntry __pyx_string_tab[] = {
18799  {&__pyx_kp_s_, __pyx_k_, sizeof(__pyx_k_), 0, 0, 1, 0},
18800  {&__pyx_kp_s_0_8_2, __pyx_k_0_8_2, sizeof(__pyx_k_0_8_2), 0, 0, 1, 0},
18801  {&__pyx_kp_u_Abbreviation_for_clifford_index, __pyx_k_Abbreviation_for_clifford_index, sizeof(__pyx_k_Abbreviation_for_clifford_index), 0, 1, 0, 0},
18802  {&__pyx_kp_u_Abbreviation_for_index_set_q_p, __pyx_k_Abbreviation_for_index_set_q_p, sizeof(__pyx_k_Abbreviation_for_index_set_q_p), 0, 1, 0, 0},
18803  {&__pyx_kp_u_Absolute_value_of_multivector_m, __pyx_k_Absolute_value_of_multivector_m, sizeof(__pyx_k_Absolute_value_of_multivector_m), 0, 1, 0, 0},
18804  {&__pyx_kp_u_Absolute_value_square_root_of_n, __pyx_k_Absolute_value_square_root_of_n, sizeof(__pyx_k_Absolute_value_square_root_of_n), 0, 1, 0, 0},
18805  {&__pyx_kp_s_Cannot_initialize_clifford_objec, __pyx_k_Cannot_initialize_clifford_objec, sizeof(__pyx_k_Cannot_initialize_clifford_objec), 0, 0, 1, 0},
18806  {&__pyx_kp_s_Cannot_initialize_index_set_obje, __pyx_k_Cannot_initialize_index_set_obje, sizeof(__pyx_k_Cannot_initialize_index_set_obje), 0, 0, 1, 0},
18807  {&__pyx_kp_s_Cannot_reframe, __pyx_k_Cannot_reframe, sizeof(__pyx_k_Cannot_reframe), 0, 0, 1, 0},
18808  {&__pyx_kp_s_Cannot_take_vector_part_of, __pyx_k_Cannot_take_vector_part_of, sizeof(__pyx_k_Cannot_take_vector_part_of), 0, 0, 1, 0},
18809  {&__pyx_kp_u_Cardinality_Number_of_indices_i, __pyx_k_Cardinality_Number_of_indices_i, sizeof(__pyx_k_Cardinality_Number_of_indices_i), 0, 1, 0, 0},
18810  {&__pyx_kp_u_Check_if_a_multivector_contains, __pyx_k_Check_if_a_multivector_contains, sizeof(__pyx_k_Check_if_a_multivector_contains), 0, 1, 0, 0},
18811  {&__pyx_kp_u_Conjugation_reverse_o_involute, __pyx_k_Conjugation_reverse_o_involute, sizeof(__pyx_k_Conjugation_reverse_o_involute), 0, 1, 0, 0},
18812  {&__pyx_kp_u_Conjugation_reverse_o_involute_2, __pyx_k_Conjugation_reverse_o_involute_2, sizeof(__pyx_k_Conjugation_reverse_o_involute_2), 0, 1, 0, 0},
18813  {&__pyx_kp_u_Contraction_print_clifford_1_cl, __pyx_k_Contraction_print_clifford_1_cl, sizeof(__pyx_k_Contraction_print_clifford_1_cl), 0, 1, 0, 0},
18814  {&__pyx_kp_u_Contraction_x_clifford_1_x_clif, __pyx_k_Contraction_x_clifford_1_x_clif, sizeof(__pyx_k_Contraction_x_clifford_1_x_clif), 0, 1, 0, 0},
18815  {&__pyx_kp_u_Convert_CGA3_null_vector_to_Euc, __pyx_k_Convert_CGA3_null_vector_to_Euc, sizeof(__pyx_k_Convert_CGA3_null_vector_to_Euc), 0, 1, 0, 0},
18816  {&__pyx_kp_u_Convert_CGA3_null_vector_to_sta, __pyx_k_Convert_CGA3_null_vector_to_sta, sizeof(__pyx_k_Convert_CGA3_null_vector_to_sta), 0, 1, 0, 0},
18817  {&__pyx_kp_u_Convert_Euclidean_3D_multivecto, __pyx_k_Convert_Euclidean_3D_multivecto, sizeof(__pyx_k_Convert_Euclidean_3D_multivecto), 0, 1, 0, 0},
18818  {&__pyx_kp_u_Copy_this_clifford_object_x_cli, __pyx_k_Copy_this_clifford_object_x_cli, sizeof(__pyx_k_Copy_this_clifford_object_x_cli), 0, 1, 0, 0},
18819  {&__pyx_kp_u_Copy_this_index_set_object_s_in, __pyx_k_Copy_this_index_set_object_s_in, sizeof(__pyx_k_Copy_this_index_set_object_s_in), 0, 1, 0, 0},
18820  {&__pyx_kp_u_Cosine_of_multivector_with_opti, __pyx_k_Cosine_of_multivector_with_opti, sizeof(__pyx_k_Cosine_of_multivector_with_opti), 0, 1, 0, 0},
18821  {&__pyx_kp_u_Even_part_of_multivector_sum_of, __pyx_k_Even_part_of_multivector_sum_of, sizeof(__pyx_k_Even_part_of_multivector_sum_of), 0, 1, 0, 0},
18822  {&__pyx_kp_u_Even_part_of_multivector_sum_of_2, __pyx_k_Even_part_of_multivector_sum_of_2, sizeof(__pyx_k_Even_part_of_multivector_sum_of_2), 0, 1, 0, 0},
18823  {&__pyx_kp_u_Exponential_of_multivector_x_cl, __pyx_k_Exponential_of_multivector_x_cl, sizeof(__pyx_k_Exponential_of_multivector_x_cl), 0, 1, 0, 0},
18824  {&__pyx_kp_u_Geometric_difference_print_clif, __pyx_k_Geometric_difference_print_clif, sizeof(__pyx_k_Geometric_difference_print_clif), 0, 1, 0, 0},
18825  {&__pyx_kp_u_Geometric_difference_x_clifford, __pyx_k_Geometric_difference_x_clifford, sizeof(__pyx_k_Geometric_difference_x_clifford), 0, 1, 0, 0},
18826  {&__pyx_kp_u_Geometric_multiplicative_invers, __pyx_k_Geometric_multiplicative_invers, sizeof(__pyx_k_Geometric_multiplicative_invers), 0, 1, 0, 0},
18827  {&__pyx_kp_u_Geometric_multiplicative_invers_2, __pyx_k_Geometric_multiplicative_invers_2, sizeof(__pyx_k_Geometric_multiplicative_invers_2), 0, 1, 0, 0},
18828  {&__pyx_kp_u_Geometric_product_print_cliffor, __pyx_k_Geometric_product_print_cliffor, sizeof(__pyx_k_Geometric_product_print_cliffor), 0, 1, 0, 0},
18829  {&__pyx_kp_u_Geometric_product_x_clifford_2, __pyx_k_Geometric_product_x_clifford_2, sizeof(__pyx_k_Geometric_product_x_clifford_2), 0, 1, 0, 0},
18830  {&__pyx_kp_u_Geometric_quotient_print_cliffo, __pyx_k_Geometric_quotient_print_cliffo, sizeof(__pyx_k_Geometric_quotient_print_cliffo), 0, 1, 0, 0},
18831  {&__pyx_kp_u_Geometric_quotient_x_clifford_1, __pyx_k_Geometric_quotient_x_clifford_1, sizeof(__pyx_k_Geometric_quotient_x_clifford_1), 0, 1, 0, 0},
18832  {&__pyx_kp_u_Geometric_sum_print_clifford_1, __pyx_k_Geometric_sum_print_clifford_1, sizeof(__pyx_k_Geometric_sum_print_clifford_1), 0, 1, 0, 0},
18833  {&__pyx_kp_u_Geometric_sum_x_clifford_1_x_cl, __pyx_k_Geometric_sum_x_clifford_1_x_cl, sizeof(__pyx_k_Geometric_sum_x_clifford_1_x_cl), 0, 1, 0, 0},
18834  {&__pyx_kp_u_Get_the_value_of_an_index_set_o, __pyx_k_Get_the_value_of_an_index_set_o, sizeof(__pyx_k_Get_the_value_of_an_index_set_o), 0, 1, 0, 0},
18835  {&__pyx_kp_u_Hyperbolic_cosine_of_multivecto, __pyx_k_Hyperbolic_cosine_of_multivecto, sizeof(__pyx_k_Hyperbolic_cosine_of_multivecto), 0, 1, 0, 0},
18836  {&__pyx_kp_u_Hyperbolic_sine_of_multivector, __pyx_k_Hyperbolic_sine_of_multivector, sizeof(__pyx_k_Hyperbolic_sine_of_multivector), 0, 1, 0, 0},
18837  {&__pyx_kp_u_Hyperbolic_tangent_of_multivect, __pyx_k_Hyperbolic_tangent_of_multivect, sizeof(__pyx_k_Hyperbolic_tangent_of_multivect), 0, 1, 0, 0},
18838  {&__pyx_kp_u_Imaginary_part_deprecated_alway, __pyx_k_Imaginary_part_deprecated_alway, sizeof(__pyx_k_Imaginary_part_deprecated_alway), 0, 1, 0, 0},
18839  {&__pyx_n_s_IndexError, __pyx_k_IndexError, sizeof(__pyx_k_IndexError), 0, 0, 1, 1},
18840  {&__pyx_kp_u_Inner_product_print_clifford_1, __pyx_k_Inner_product_print_clifford_1, sizeof(__pyx_k_Inner_product_print_clifford_1), 0, 1, 0, 0},
18841  {&__pyx_kp_u_Inner_product_x_clifford_1_x_cl, __pyx_k_Inner_product_x_clifford_1_x_cl, sizeof(__pyx_k_Inner_product_x_clifford_1_x_cl), 0, 1, 0, 0},
18842  {&__pyx_kp_u_Integer_power_of_multivector_ob, __pyx_k_Integer_power_of_multivector_ob, sizeof(__pyx_k_Integer_power_of_multivector_ob), 0, 1, 0, 0},
18843  {&__pyx_n_s_Integral, __pyx_k_Integral, sizeof(__pyx_k_Integral), 0, 0, 1, 1},
18844  {&__pyx_kp_u_Inverse_cosine_of_multivector_w, __pyx_k_Inverse_cosine_of_multivector_w, sizeof(__pyx_k_Inverse_cosine_of_multivector_w), 0, 1, 0, 0},
18845  {&__pyx_kp_u_Inverse_hyperbolic_cosine_of_mu, __pyx_k_Inverse_hyperbolic_cosine_of_mu, sizeof(__pyx_k_Inverse_hyperbolic_cosine_of_mu), 0, 1, 0, 0},
18846  {&__pyx_kp_u_Inverse_hyperbolic_sine_of_mult, __pyx_k_Inverse_hyperbolic_sine_of_mult, sizeof(__pyx_k_Inverse_hyperbolic_sine_of_mult), 0, 1, 0, 0},
18847  {&__pyx_kp_u_Inverse_hyperbolic_tangent_of_m, __pyx_k_Inverse_hyperbolic_tangent_of_m, sizeof(__pyx_k_Inverse_hyperbolic_tangent_of_m), 0, 1, 0, 0},
18848  {&__pyx_kp_u_Inverse_sine_of_multivector_wit, __pyx_k_Inverse_sine_of_multivector_wit, sizeof(__pyx_k_Inverse_sine_of_multivector_wit), 0, 1, 0, 0},
18849  {&__pyx_kp_u_Inverse_tangent_of_multivector, __pyx_k_Inverse_tangent_of_multivector, sizeof(__pyx_k_Inverse_tangent_of_multivector), 0, 1, 0, 0},
18850  {&__pyx_kp_u_Iterate_over_the_indices_of_an, __pyx_k_Iterate_over_the_indices_of_an, sizeof(__pyx_k_Iterate_over_the_indices_of_an), 0, 1, 0, 0},
18851  {&__pyx_kp_u_Main_involution_each_i_is_repla, __pyx_k_Main_involution_each_i_is_repla, sizeof(__pyx_k_Main_involution_each_i_is_repla), 0, 1, 0, 0},
18852  {&__pyx_kp_u_Main_involution_each_i_is_repla_2, __pyx_k_Main_involution_each_i_is_repla_2, sizeof(__pyx_k_Main_involution_each_i_is_repla_2), 0, 1, 0, 0},
18853  {&__pyx_kp_u_Maximum_absolute_value_of_coord, __pyx_k_Maximum_absolute_value_of_coord, sizeof(__pyx_k_Maximum_absolute_value_of_coord), 0, 1, 0, 0},
18854  {&__pyx_kp_u_Maximum_member_index_set_1_1_2, __pyx_k_Maximum_member_index_set_1_1_2, sizeof(__pyx_k_Maximum_member_index_set_1_1_2), 0, 1, 0, 0},
18855  {&__pyx_kp_u_Maximum_of_absolute_values_of_c, __pyx_k_Maximum_of_absolute_values_of_c, sizeof(__pyx_k_Maximum_of_absolute_values_of_c), 0, 1, 0, 0},
18856  {&__pyx_kp_u_Maximum_positive_index_or_0_if, __pyx_k_Maximum_positive_index_or_0_if, sizeof(__pyx_k_Maximum_positive_index_or_0_if), 0, 1, 0, 0},
18857  {&__pyx_kp_u_Minimum_member_index_set_1_1_2, __pyx_k_Minimum_member_index_set_1_1_2, sizeof(__pyx_k_Minimum_member_index_set_1_1_2), 0, 1, 0, 0},
18858  {&__pyx_kp_u_Minimum_negative_index_or_0_if, __pyx_k_Minimum_negative_index_or_0_if, sizeof(__pyx_k_Minimum_negative_index_or_0_if), 0, 1, 0, 0},
18859  {&__pyx_kp_u_Natural_logarithm_of_multivecto, __pyx_k_Natural_logarithm_of_multivecto, sizeof(__pyx_k_Natural_logarithm_of_multivecto), 0, 1, 0, 0},
18860  {&__pyx_kp_u_Norm_sum_of_squares_of_coordina, __pyx_k_Norm_sum_of_squares_of_coordina, sizeof(__pyx_k_Norm_sum_of_squares_of_coordina), 0, 1, 0, 0},
18861  {&__pyx_n_s_NotImplemented, __pyx_k_NotImplemented, sizeof(__pyx_k_NotImplemented), 0, 0, 1, 1},
18862  {&__pyx_kp_s_Not_applicable, __pyx_k_Not_applicable, sizeof(__pyx_k_Not_applicable), 0, 0, 1, 0},
18863  {&__pyx_kp_u_Not_applicable_for_a_in_cliffor, __pyx_k_Not_applicable_for_a_in_cliffor, sizeof(__pyx_k_Not_applicable_for_a_in_cliffor), 0, 1, 0, 0},
18864  {&__pyx_kp_u_Number_of_negative_indices_incl, __pyx_k_Number_of_negative_indices_incl, sizeof(__pyx_k_Number_of_negative_indices_incl), 0, 1, 0, 0},
18865  {&__pyx_kp_u_Number_of_positive_indices_incl, __pyx_k_Number_of_positive_indices_incl, sizeof(__pyx_k_Number_of_positive_indices_incl), 0, 1, 0, 0},
18866  {&__pyx_kp_u_Odd_part_of_multivector_sum_of, __pyx_k_Odd_part_of_multivector_sum_of, sizeof(__pyx_k_Odd_part_of_multivector_sum_of), 0, 1, 0, 0},
18867  {&__pyx_kp_u_Odd_part_of_multivector_sum_of_2, __pyx_k_Odd_part_of_multivector_sum_of_2, sizeof(__pyx_k_Odd_part_of_multivector_sum_of_2), 0, 1, 0, 0},
18868  {&__pyx_kp_u_Outer_product_power_of_multivec, __pyx_k_Outer_product_power_of_multivec, sizeof(__pyx_k_Outer_product_power_of_multivec), 0, 1, 0, 0},
18869  {&__pyx_kp_u_Outer_product_power_x_clifford, __pyx_k_Outer_product_power_x_clifford, sizeof(__pyx_k_Outer_product_power_x_clifford), 0, 1, 0, 0},
18870  {&__pyx_kp_u_Outer_product_print_clifford_1, __pyx_k_Outer_product_print_clifford_1, sizeof(__pyx_k_Outer_product_print_clifford_1), 0, 1, 0, 0},
18871  {&__pyx_kp_u_Outer_product_x_clifford_1_x_cl, __pyx_k_Outer_product_x_clifford_1_x_cl, sizeof(__pyx_k_Outer_product_x_clifford_1_x_cl), 0, 1, 0, 0},
18872  {&__pyx_kp_u_Power_self_to_the_m_x_clifford, __pyx_k_Power_self_to_the_m_x_clifford, sizeof(__pyx_k_Power_self_to_the_m_x_clifford), 0, 1, 0, 0},
18873  {&__pyx_kp_u_Power_self_to_the_m_x_clifford_2, __pyx_k_Power_self_to_the_m_x_clifford_2, sizeof(__pyx_k_Power_self_to_the_m_x_clifford_2), 0, 1, 0, 0},
18874  {&__pyx_kp_u_Pure_grade_vector_part_print_cl, __pyx_k_Pure_grade_vector_part_print_cl, sizeof(__pyx_k_Pure_grade_vector_part_print_cl), 0, 1, 0, 0},
18875  {&__pyx_kp_u_Pure_part_print_clifford_1_1_1, __pyx_k_Pure_part_print_clifford_1_1_1, sizeof(__pyx_k_Pure_part_print_clifford_1_1_1), 0, 1, 0, 0},
18876  {&__pyx_kp_u_Pure_part_print_pure_clifford_1, __pyx_k_Pure_part_print_pure_clifford_1, sizeof(__pyx_k_Pure_part_print_pure_clifford_1), 0, 1, 0, 0},
18877  {&__pyx_kp_u_Put_self_into_a_larger_frame_co, __pyx_k_Put_self_into_a_larger_frame_co, sizeof(__pyx_k_Put_self_into_a_larger_frame_co), 0, 1, 0, 0},
18878  {&__pyx_n_s_PyClical, __pyx_k_PyClical, sizeof(__pyx_k_PyClical), 0, 0, 1, 1},
18879  {&__pyx_kp_u_Quadratic_form_rev_x_x_0_print, __pyx_k_Quadratic_form_rev_x_x_0_print, sizeof(__pyx_k_Quadratic_form_rev_x_x_0_print), 0, 1, 0, 0},
18880  {&__pyx_kp_u_Quadratic_form_rev_x_x_0_print_2, __pyx_k_Quadratic_form_rev_x_x_0_print_2, sizeof(__pyx_k_Quadratic_form_rev_x_x_0_print_2), 0, 1, 0, 0},
18881  {&__pyx_kp_u_Random_multivector_within_a_fra, __pyx_k_Random_multivector_within_a_fra, sizeof(__pyx_k_Random_multivector_within_a_fra), 0, 1, 0, 0},
18882  {&__pyx_n_s_Real, __pyx_k_Real, sizeof(__pyx_k_Real), 0, 0, 1, 1},
18883  {&__pyx_kp_u_Real_part_synonym_for_scalar_pa, __pyx_k_Real_part_synonym_for_scalar_pa, sizeof(__pyx_k_Real_part_synonym_for_scalar_pa), 0, 1, 0, 0},
18884  {&__pyx_kp_u_Remove_all_terms_of_self_with_r, __pyx_k_Remove_all_terms_of_self_with_r, sizeof(__pyx_k_Remove_all_terms_of_self_with_r), 0, 1, 0, 0},
18885  {&__pyx_kp_u_Reversion_eg_1_2_2_1_print_reve, __pyx_k_Reversion_eg_1_2_2_1_print_reve, sizeof(__pyx_k_Reversion_eg_1_2_2_1_print_reve), 0, 1, 0, 0},
18886  {&__pyx_kp_u_Reversion_eg_clifford_1_cliffor, __pyx_k_Reversion_eg_clifford_1_cliffor, sizeof(__pyx_k_Reversion_eg_clifford_1_cliffor), 0, 1, 0, 0},
18887  {&__pyx_n_s_RuntimeError, __pyx_k_RuntimeError, sizeof(__pyx_k_RuntimeError), 0, 0, 1, 1},
18888  {&__pyx_kp_u_Scalar_part_clifford_1_1_1_2_sc, __pyx_k_Scalar_part_clifford_1_1_1_2_sc, sizeof(__pyx_k_Scalar_part_clifford_1_1_1_2_sc), 0, 1, 0, 0},
18889  {&__pyx_kp_u_Scalar_part_scalar_clifford_1_1, __pyx_k_Scalar_part_scalar_clifford_1_1, sizeof(__pyx_k_Scalar_part_scalar_clifford_1_1), 0, 1, 0, 0},
18890  {&__pyx_n_s_Sequence, __pyx_k_Sequence, sizeof(__pyx_k_Sequence), 0, 0, 1, 1},
18891  {&__pyx_kp_u_Set_complement_not_print_index, __pyx_k_Set_complement_not_print_index, sizeof(__pyx_k_Set_complement_not_print_index), 0, 1, 0, 0},
18892  {&__pyx_kp_u_Set_intersection_and_print_inde, __pyx_k_Set_intersection_and_print_inde, sizeof(__pyx_k_Set_intersection_and_print_inde), 0, 1, 0, 0},
18893  {&__pyx_kp_u_Set_intersection_and_x_index_se, __pyx_k_Set_intersection_and_x_index_se, sizeof(__pyx_k_Set_intersection_and_x_index_se), 0, 1, 0, 0},
18894  {&__pyx_kp_u_Set_the_value_of_an_index_set_o, __pyx_k_Set_the_value_of_an_index_set_o, sizeof(__pyx_k_Set_the_value_of_an_index_set_o), 0, 1, 0, 0},
18895  {&__pyx_kp_u_Set_union_or_print_index_set_1, __pyx_k_Set_union_or_print_index_set_1, sizeof(__pyx_k_Set_union_or_print_index_set_1), 0, 1, 0, 0},
18896  {&__pyx_kp_u_Set_union_or_x_index_set_1_x_in, __pyx_k_Set_union_or_x_index_set_1_x_in, sizeof(__pyx_k_Set_union_or_x_index_set_1_x_in), 0, 1, 0, 0},
18897  {&__pyx_kp_u_Sign_of_geometric_product_of_tw, __pyx_k_Sign_of_geometric_product_of_tw, sizeof(__pyx_k_Sign_of_geometric_product_of_tw), 0, 1, 0, 0},
18898  {&__pyx_kp_u_Sign_of_geometric_square_of_a_C, __pyx_k_Sign_of_geometric_square_of_a_C, sizeof(__pyx_k_Sign_of_geometric_square_of_a_C), 0, 1, 0, 0},
18899  {&__pyx_kp_u_Sine_of_multivector_with_option, __pyx_k_Sine_of_multivector_with_option, sizeof(__pyx_k_Sine_of_multivector_with_option), 0, 1, 0, 0},
18900  {&__pyx_kp_u_Square_root_of_1_which_commutes, __pyx_k_Square_root_of_1_which_commutes, sizeof(__pyx_k_Square_root_of_1_which_commutes), 0, 1, 0, 0},
18901  {&__pyx_kp_u_Square_root_of_multivector_with, __pyx_k_Square_root_of_multivector_with, sizeof(__pyx_k_Square_root_of_multivector_with), 0, 1, 0, 0},
18902  {&__pyx_kp_u_Subalgebra_generated_by_all_gen, __pyx_k_Subalgebra_generated_by_all_gen, sizeof(__pyx_k_Subalgebra_generated_by_all_gen), 0, 1, 0, 0},
18903  {&__pyx_kp_u_Subscripting_map_from_index_set, __pyx_k_Subscripting_map_from_index_set, sizeof(__pyx_k_Subscripting_map_from_index_set), 0, 1, 0, 0},
18904  {&__pyx_kp_u_Symmetric_set_difference_exclus, __pyx_k_Symmetric_set_difference_exclus, sizeof(__pyx_k_Symmetric_set_difference_exclus), 0, 1, 0, 0},
18905  {&__pyx_kp_u_Symmetric_set_difference_exclus_2, __pyx_k_Symmetric_set_difference_exclus_2, sizeof(__pyx_k_Symmetric_set_difference_exclus_2), 0, 1, 0, 0},
18906  {&__pyx_kp_u_Tangent_of_multivector_with_opt, __pyx_k_Tangent_of_multivector_with_opt, sizeof(__pyx_k_Tangent_of_multivector_with_opt), 0, 1, 0, 0},
18907  {&__pyx_kp_u_Tests_for_functions_that_Doctes, __pyx_k_Tests_for_functions_that_Doctes, sizeof(__pyx_k_Tests_for_functions_that_Doctes), 0, 1, 0, 0},
18908  {&__pyx_kp_u_Tests_for_functions_that_Doctes_2, __pyx_k_Tests_for_functions_that_Doctes_2, sizeof(__pyx_k_Tests_for_functions_that_Doctes_2), 0, 1, 0, 0},
18909  {&__pyx_kp_u_The_informal_string_representat, __pyx_k_The_informal_string_representat, sizeof(__pyx_k_The_informal_string_representat), 0, 1, 0, 0},
18910  {&__pyx_kp_u_The_informal_string_representat_2, __pyx_k_The_informal_string_representat_2, sizeof(__pyx_k_The_informal_string_representat_2), 0, 1, 0, 0},
18911  {&__pyx_kp_u_The_official_string_representat, __pyx_k_The_official_string_representat, sizeof(__pyx_k_The_official_string_representat), 0, 1, 0, 0},
18912  {&__pyx_kp_u_The_official_string_representat_2, __pyx_k_The_official_string_representat_2, sizeof(__pyx_k_The_official_string_representat_2), 0, 1, 0, 0},
18913  {&__pyx_kp_s_This_comparison_operator_is_not, __pyx_k_This_comparison_operator_is_not, sizeof(__pyx_k_This_comparison_operator_is_not), 0, 0, 1, 0},
18914  {&__pyx_kp_u_Transform_left_hand_side_using, __pyx_k_Transform_left_hand_side_using, sizeof(__pyx_k_Transform_left_hand_side_using), 0, 1, 0, 0},
18915  {&__pyx_kp_u_Transform_left_hand_side_using_2, __pyx_k_Transform_left_hand_side_using_2, sizeof(__pyx_k_Transform_left_hand_side_using_2), 0, 1, 0, 0},
18916  {&__pyx_n_s_TypeError, __pyx_k_TypeError, sizeof(__pyx_k_TypeError), 0, 0, 1, 1},
18917  {&__pyx_kp_u_Unary_print_clifford_1_1, __pyx_k_Unary_print_clifford_1_1, sizeof(__pyx_k_Unary_print_clifford_1_1), 0, 1, 0, 0},
18918  {&__pyx_kp_u_Unary_print_clifford_1_1_2, __pyx_k_Unary_print_clifford_1_1_2, sizeof(__pyx_k_Unary_print_clifford_1_1_2), 0, 1, 0, 0},
18919  {&__pyx_n_s_ValueError, __pyx_k_ValueError, sizeof(__pyx_k_ValueError), 0, 0, 1, 1},
18920  {&__pyx_kp_u_Vector_part_of_multivector_as_a, __pyx_k_Vector_part_of_multivector_as_a, sizeof(__pyx_k_Vector_part_of_multivector_as_a), 0, 1, 0, 0},
18921  {&__pyx_kp_s__2, __pyx_k__2, sizeof(__pyx_k__2), 0, 0, 1, 0},
18922  {&__pyx_kp_s__3, __pyx_k__3, sizeof(__pyx_k__3), 0, 0, 1, 0},
18923  {&__pyx_kp_s__4, __pyx_k__4, sizeof(__pyx_k__4), 0, 0, 1, 0},
18924  {&__pyx_kp_s__5, __pyx_k__5, sizeof(__pyx_k__5), 0, 0, 1, 0},
18925  {&__pyx_kp_s__6, __pyx_k__6, sizeof(__pyx_k__6), 0, 0, 1, 0},
18926  {&__pyx_kp_s__7, __pyx_k__7, sizeof(__pyx_k__7), 0, 0, 1, 0},
18927  {&__pyx_kp_u_abs_line_1473, __pyx_k_abs_line_1473, sizeof(__pyx_k_abs_line_1473), 0, 1, 0, 0},
18928  {&__pyx_n_s_acos, __pyx_k_acos, sizeof(__pyx_k_acos), 0, 0, 1, 1},
18929  {&__pyx_kp_u_acos_line_1619, __pyx_k_acos_line_1619, sizeof(__pyx_k_acos_line_1619), 0, 1, 0, 0},
18930  {&__pyx_n_s_acosh, __pyx_k_acosh, sizeof(__pyx_k_acosh), 0, 0, 1, 1},
18931  {&__pyx_kp_u_acosh_line_1656, __pyx_k_acosh_line_1656, sizeof(__pyx_k_acosh_line_1656), 0, 1, 0, 0},
18932  {&__pyx_kp_u_agc3_line_1844, __pyx_k_agc3_line_1844, sizeof(__pyx_k_agc3_line_1844), 0, 1, 0, 0},
18933  {&__pyx_n_s_args, __pyx_k_args, sizeof(__pyx_k_args), 0, 0, 1, 1},
18934  {&__pyx_kp_s_as_frame, __pyx_k_as_frame, sizeof(__pyx_k_as_frame), 0, 0, 1, 0},
18935  {&__pyx_n_s_asin, __pyx_k_asin, sizeof(__pyx_k_asin), 0, 0, 1, 1},
18936  {&__pyx_kp_u_asin_line_1698, __pyx_k_asin_line_1698, sizeof(__pyx_k_asin_line_1698), 0, 1, 0, 0},
18937  {&__pyx_n_s_asinh, __pyx_k_asinh, sizeof(__pyx_k_asinh), 0, 0, 1, 1},
18938  {&__pyx_kp_u_asinh_line_1733, __pyx_k_asinh_line_1733, sizeof(__pyx_k_asinh_line_1733), 0, 1, 0, 0},
18939  {&__pyx_n_s_atan, __pyx_k_atan, sizeof(__pyx_k_atan), 0, 0, 1, 1},
18940  {&__pyx_kp_u_atan_line_1769, __pyx_k_atan_line_1769, sizeof(__pyx_k_atan_line_1769), 0, 1, 0, 0},
18941  {&__pyx_n_s_atanh, __pyx_k_atanh, sizeof(__pyx_k_atanh), 0, 0, 1, 1},
18942  {&__pyx_kp_u_atanh_line_1798, __pyx_k_atanh_line_1798, sizeof(__pyx_k_atanh_line_1798), 0, 1, 0, 0},
18943  {&__pyx_kp_u_cga3_line_1824, __pyx_k_cga3_line_1824, sizeof(__pyx_k_cga3_line_1824), 0, 1, 0, 0},
18944  {&__pyx_kp_u_cga3std_line_1833, __pyx_k_cga3std_line_1833, sizeof(__pyx_k_cga3std_line_1833), 0, 1, 0, 0},
18945  {&__pyx_n_s_cl, __pyx_k_cl, sizeof(__pyx_k_cl), 0, 0, 1, 1},
18946  {&__pyx_kp_u_clifford___add___line_739, __pyx_k_clifford___add___line_739, sizeof(__pyx_k_clifford___add___line_739), 0, 1, 0, 0},
18947  {&__pyx_kp_u_clifford___and___line_835, __pyx_k_clifford___and___line_835, sizeof(__pyx_k_clifford___and___line_835), 0, 1, 0, 0},
18948  {&__pyx_kp_u_clifford___call___line_1019, __pyx_k_clifford___call___line_1019, sizeof(__pyx_k_clifford___call___line_1019), 0, 1, 0, 0},
18949  {&__pyx_kp_u_clifford___div___line_895, __pyx_k_clifford___div___line_895, sizeof(__pyx_k_clifford___div___line_895), 0, 1, 0, 0},
18950  {&__pyx_kp_u_clifford___getitem___line_706, __pyx_k_clifford___getitem___line_706, sizeof(__pyx_k_clifford___getitem___line_706), 0, 1, 0, 0},
18951  {&__pyx_kp_u_clifford___iadd___line_750, __pyx_k_clifford___iadd___line_750, sizeof(__pyx_k_clifford___iadd___line_750), 0, 1, 0, 0},
18952  {&__pyx_kp_u_clifford___iand___line_850, __pyx_k_clifford___iand___line_850, sizeof(__pyx_k_clifford___iand___line_850), 0, 1, 0, 0},
18953  {&__pyx_kp_u_clifford___idiv___line_910, __pyx_k_clifford___idiv___line_910, sizeof(__pyx_k_clifford___idiv___line_910), 0, 1, 0, 0},
18954  {&__pyx_kp_u_clifford___imod___line_820, __pyx_k_clifford___imod___line_820, sizeof(__pyx_k_clifford___imod___line_820), 0, 1, 0, 0},
18955  {&__pyx_kp_u_clifford___imul___line_792, __pyx_k_clifford___imul___line_792, sizeof(__pyx_k_clifford___imul___line_792), 0, 1, 0, 0},
18956  {&__pyx_kp_u_clifford___ior___line_949, __pyx_k_clifford___ior___line_949, sizeof(__pyx_k_clifford___ior___line_949), 0, 1, 0, 0},
18957  {&__pyx_kp_u_clifford___isub___line_770, __pyx_k_clifford___isub___line_770, sizeof(__pyx_k_clifford___isub___line_770), 0, 1, 0, 0},
18958  {&__pyx_kp_u_clifford___iter___line_637, __pyx_k_clifford___iter___line_637, sizeof(__pyx_k_clifford___iter___line_637), 0, 1, 0, 0},
18959  {&__pyx_kp_u_clifford___ixor___line_880, __pyx_k_clifford___ixor___line_880, sizeof(__pyx_k_clifford___ixor___line_880), 0, 1, 0, 0},
18960  {&__pyx_kp_u_clifford___mod___line_805, __pyx_k_clifford___mod___line_805, sizeof(__pyx_k_clifford___mod___line_805), 0, 1, 0, 0},
18961  {&__pyx_kp_u_clifford___mul___line_779, __pyx_k_clifford___mul___line_779, sizeof(__pyx_k_clifford___mul___line_779), 0, 1, 0, 0},
18962  {&__pyx_kp_u_clifford___neg___line_721, __pyx_k_clifford___neg___line_721, sizeof(__pyx_k_clifford___neg___line_721), 0, 1, 0, 0},
18963  {&__pyx_kp_u_clifford___or___line_938, __pyx_k_clifford___or___line_938, sizeof(__pyx_k_clifford___or___line_938), 0, 1, 0, 0},
18964  {&__pyx_kp_u_clifford___pos___line_730, __pyx_k_clifford___pos___line_730, sizeof(__pyx_k_clifford___pos___line_730), 0, 1, 0, 0},
18965  {&__pyx_kp_u_clifford___pow___line_960, __pyx_k_clifford___pow___line_960, sizeof(__pyx_k_clifford___pow___line_960), 0, 1, 0, 0},
18966  {&__pyx_kp_u_clifford___repr___line_1225, __pyx_k_clifford___repr___line_1225, sizeof(__pyx_k_clifford___repr___line_1225), 0, 1, 0, 0},
18967  {&__pyx_kp_u_clifford___str___line_1234, __pyx_k_clifford___str___line_1234, sizeof(__pyx_k_clifford___str___line_1234), 0, 1, 0, 0},
18968  {&__pyx_kp_u_clifford___sub___line_759, __pyx_k_clifford___sub___line_759, sizeof(__pyx_k_clifford___sub___line_759), 0, 1, 0, 0},
18969  {&__pyx_kp_u_clifford___xor___line_865, __pyx_k_clifford___xor___line_865, sizeof(__pyx_k_clifford___xor___line_865), 0, 1, 0, 0},
18970  {&__pyx_kp_u_clifford_abs_line_1174, __pyx_k_clifford_abs_line_1174, sizeof(__pyx_k_clifford_abs_line_1174), 0, 1, 0, 0},
18971  {&__pyx_kp_u_clifford_conj_line_1137, __pyx_k_clifford_conj_line_1137, sizeof(__pyx_k_clifford_conj_line_1137), 0, 1, 0, 0},
18972  {&__pyx_kp_u_clifford_copy_line_554, __pyx_k_clifford_copy_line_554, sizeof(__pyx_k_clifford_copy_line_554), 0, 1, 0, 0},
18973  {&__pyx_kp_u_clifford_even_line_1060, __pyx_k_clifford_even_line_1060, sizeof(__pyx_k_clifford_even_line_1060), 0, 1, 0, 0},
18974  {&__pyx_kp_u_clifford_frame_line_1214, __pyx_k_clifford_frame_line_1214, sizeof(__pyx_k_clifford_frame_line_1214), 0, 1, 0, 0},
18975  {&__pyx_n_s_clifford_hidden_doctests, __pyx_k_clifford_hidden_doctests, sizeof(__pyx_k_clifford_hidden_doctests), 0, 0, 1, 1},
18976  {&__pyx_kp_u_clifford_hidden_doctests_line_12, __pyx_k_clifford_hidden_doctests_line_12, sizeof(__pyx_k_clifford_hidden_doctests_line_12), 0, 1, 0, 0},
18977  {&__pyx_kp_u_clifford_inv_line_925, __pyx_k_clifford_inv_line_925, sizeof(__pyx_k_clifford_inv_line_925), 0, 1, 0, 0},
18978  {&__pyx_kp_u_clifford_involute_line_1106, __pyx_k_clifford_involute_line_1106, sizeof(__pyx_k_clifford_involute_line_1106), 0, 1, 0, 0},
18979  {&__pyx_kp_u_clifford_isnan_line_1205, __pyx_k_clifford_isnan_line_1205, sizeof(__pyx_k_clifford_isnan_line_1205), 0, 1, 0, 0},
18980  {&__pyx_kp_u_clifford_max_abs_line_1183, __pyx_k_clifford_max_abs_line_1183, sizeof(__pyx_k_clifford_max_abs_line_1183), 0, 1, 0, 0},
18981  {&__pyx_kp_u_clifford_norm_line_1163, __pyx_k_clifford_norm_line_1163, sizeof(__pyx_k_clifford_norm_line_1163), 0, 1, 0, 0},
18982  {&__pyx_kp_u_clifford_odd_line_1069, __pyx_k_clifford_odd_line_1069, sizeof(__pyx_k_clifford_odd_line_1069), 0, 1, 0, 0},
18983  {&__pyx_kp_u_clifford_outer_pow_line_1003, __pyx_k_clifford_outer_pow_line_1003, sizeof(__pyx_k_clifford_outer_pow_line_1003), 0, 1, 0, 0},
18984  {&__pyx_kp_u_clifford_pow_line_979, __pyx_k_clifford_pow_line_979, sizeof(__pyx_k_clifford_pow_line_979), 0, 1, 0, 0},
18985  {&__pyx_kp_u_clifford_pure_line_1049, __pyx_k_clifford_pure_line_1049, sizeof(__pyx_k_clifford_pure_line_1049), 0, 1, 0, 0},
18986  {&__pyx_kp_u_clifford_quad_line_1152, __pyx_k_clifford_quad_line_1152, sizeof(__pyx_k_clifford_quad_line_1152), 0, 1, 0, 0},
18987  {&__pyx_kp_u_clifford_reframe_line_648, __pyx_k_clifford_reframe_line_648, sizeof(__pyx_k_clifford_reframe_line_648), 0, 1, 0, 0},
18988  {&__pyx_kp_u_clifford_reverse_line_1122, __pyx_k_clifford_reverse_line_1122, sizeof(__pyx_k_clifford_reverse_line_1122), 0, 1, 0, 0},
18989  {&__pyx_kp_u_clifford_scalar_line_1038, __pyx_k_clifford_scalar_line_1038, sizeof(__pyx_k_clifford_scalar_line_1038), 0, 1, 0, 0},
18990  {&__pyx_kp_u_clifford_truncated_line_1194, __pyx_k_clifford_truncated_line_1194, sizeof(__pyx_k_clifford_truncated_line_1194), 0, 1, 0, 0},
18991  {&__pyx_kp_u_clifford_vector_part_line_1078, __pyx_k_clifford_vector_part_line_1078, sizeof(__pyx_k_clifford_vector_part_line_1078), 0, 1, 0, 0},
18992  {&__pyx_n_s_close, __pyx_k_close, sizeof(__pyx_k_close), 0, 0, 1, 1},
18993  {&__pyx_n_s_collections, __pyx_k_collections, sizeof(__pyx_k_collections), 0, 0, 1, 1},
18994  {&__pyx_kp_u_compare_line_490, __pyx_k_compare_line_490, sizeof(__pyx_k_compare_line_490), 0, 1, 0, 0},
18995  {&__pyx_kp_u_complexifier_line_1527, __pyx_k_complexifier_line_1527, sizeof(__pyx_k_complexifier_line_1527), 0, 1, 0, 0},
18996  {&__pyx_n_s_conj, __pyx_k_conj, sizeof(__pyx_k_conj), 0, 0, 1, 1},
18997  {&__pyx_kp_u_conj_line_1436, __pyx_k_conj_line_1436, sizeof(__pyx_k_conj_line_1436), 0, 1, 0, 0},
18998  {&__pyx_n_s_copy, __pyx_k_copy, sizeof(__pyx_k_copy), 0, 0, 1, 1},
18999  {&__pyx_n_s_cos, __pyx_k_cos, sizeof(__pyx_k_cos), 0, 0, 1, 1},
19000  {&__pyx_kp_u_cos_line_1602, __pyx_k_cos_line_1602, sizeof(__pyx_k_cos_line_1602), 0, 1, 0, 0},
19001  {&__pyx_n_s_cosh, __pyx_k_cosh, sizeof(__pyx_k_cosh), 0, 0, 1, 1},
19002  {&__pyx_kp_u_cosh_line_1640, __pyx_k_cosh_line_1640, sizeof(__pyx_k_cosh_line_1640), 0, 1, 0, 0},
19003  {&__pyx_n_s_doctest, __pyx_k_doctest, sizeof(__pyx_k_doctest), 0, 0, 1, 1},
19004  {&__pyx_n_s_e, __pyx_k_e, sizeof(__pyx_k_e), 0, 0, 1, 1},
19005  {&__pyx_kp_u_e_line_1887, __pyx_k_e_line_1887, sizeof(__pyx_k_e_line_1887), 0, 1, 0, 0},
19006  {&__pyx_n_s_even, __pyx_k_even, sizeof(__pyx_k_even), 0, 0, 1, 1},
19007  {&__pyx_kp_u_even_line_1388, __pyx_k_even_line_1388, sizeof(__pyx_k_even_line_1388), 0, 1, 0, 0},
19008  {&__pyx_n_s_exp, __pyx_k_exp, sizeof(__pyx_k_exp), 0, 0, 1, 1},
19009  {&__pyx_kp_u_exp_line_1565, __pyx_k_exp_line_1565, sizeof(__pyx_k_exp_line_1565), 0, 1, 0, 0},
19010  {&__pyx_n_s_fill, __pyx_k_fill, sizeof(__pyx_k_fill), 0, 0, 1, 1},
19011  {&__pyx_n_s_frm, __pyx_k_frm, sizeof(__pyx_k_frm), 0, 0, 1, 1},
19012  {&__pyx_kp_s_from, __pyx_k_from, sizeof(__pyx_k_from), 0, 0, 1, 0},
19013  {&__pyx_n_s_grade, __pyx_k_grade, sizeof(__pyx_k_grade), 0, 0, 1, 1},
19014  {&__pyx_kp_s_home_abuild_rpmbuild_BUILD_gluc, __pyx_k_home_abuild_rpmbuild_BUILD_gluc, sizeof(__pyx_k_home_abuild_rpmbuild_BUILD_gluc), 0, 0, 1, 0},
19015  {&__pyx_n_s_i, __pyx_k_i, sizeof(__pyx_k_i), 0, 0, 1, 1},
19016  {&__pyx_kp_u_imag_line_1366, __pyx_k_imag_line_1366, sizeof(__pyx_k_imag_line_1366), 0, 1, 0, 0},
19017  {&__pyx_n_s_import, __pyx_k_import, sizeof(__pyx_k_import), 0, 0, 1, 1},
19018  {&__pyx_kp_u_index_set___and___line_269, __pyx_k_index_set___and___line_269, sizeof(__pyx_k_index_set___and___line_269), 0, 1, 0, 0},
19019  {&__pyx_kp_u_index_set___getitem___line_189, __pyx_k_index_set___getitem___line_189, sizeof(__pyx_k_index_set___getitem___line_189), 0, 1, 0, 0},
19020  {&__pyx_kp_u_index_set___iand___line_280, __pyx_k_index_set___iand___line_280, sizeof(__pyx_k_index_set___iand___line_280), 0, 1, 0, 0},
19021  {&__pyx_kp_u_index_set___invert___line_238, __pyx_k_index_set___invert___line_238, sizeof(__pyx_k_index_set___invert___line_238), 0, 1, 0, 0},
19022  {&__pyx_kp_u_index_set___ior___line_302, __pyx_k_index_set___ior___line_302, sizeof(__pyx_k_index_set___ior___line_302), 0, 1, 0, 0},
19023  {&__pyx_n_s_index_set___iter, __pyx_k_index_set___iter, sizeof(__pyx_k_index_set___iter), 0, 0, 1, 1},
19024  {&__pyx_kp_u_index_set___iter___line_227, __pyx_k_index_set___iter___line_227, sizeof(__pyx_k_index_set___iter___line_227), 0, 1, 0, 0},
19025  {&__pyx_kp_u_index_set___ixor___line_258, __pyx_k_index_set___ixor___line_258, sizeof(__pyx_k_index_set___ixor___line_258), 0, 1, 0, 0},
19026  {&__pyx_kp_u_index_set___or___line_291, __pyx_k_index_set___or___line_291, sizeof(__pyx_k_index_set___or___line_291), 0, 1, 0, 0},
19027  {&__pyx_kp_u_index_set___repr___line_382, __pyx_k_index_set___repr___line_382, sizeof(__pyx_k_index_set___repr___line_382), 0, 1, 0, 0},
19028  {&__pyx_kp_u_index_set___setitem___line_177, __pyx_k_index_set___setitem___line_177, sizeof(__pyx_k_index_set___setitem___line_177), 0, 1, 0, 0},
19029  {&__pyx_kp_u_index_set___str___line_393, __pyx_k_index_set___str___line_393, sizeof(__pyx_k_index_set___str___line_393), 0, 1, 0, 0},
19030  {&__pyx_kp_u_index_set___xor___line_247, __pyx_k_index_set___xor___line_247, sizeof(__pyx_k_index_set___xor___line_247), 0, 1, 0, 0},
19031  {&__pyx_kp_u_index_set_copy_line_64, __pyx_k_index_set_copy_line_64, sizeof(__pyx_k_index_set_copy_line_64), 0, 1, 0, 0},
19032  {&__pyx_kp_u_index_set_count_line_313, __pyx_k_index_set_count_line_313, sizeof(__pyx_k_index_set_count_line_313), 0, 1, 0, 0},
19033  {&__pyx_kp_u_index_set_count_neg_line_322, __pyx_k_index_set_count_neg_line_322, sizeof(__pyx_k_index_set_count_neg_line_322), 0, 1, 0, 0},
19034  {&__pyx_kp_u_index_set_count_pos_line_331, __pyx_k_index_set_count_pos_line_331, sizeof(__pyx_k_index_set_count_pos_line_331), 0, 1, 0, 0},
19035  {&__pyx_n_s_index_set_hidden_doctests, __pyx_k_index_set_hidden_doctests, sizeof(__pyx_k_index_set_hidden_doctests), 0, 0, 1, 1},
19036  {&__pyx_kp_u_index_set_hidden_doctests_line_4, __pyx_k_index_set_hidden_doctests_line_4, sizeof(__pyx_k_index_set_hidden_doctests_line_4), 0, 1, 0, 0},
19037  {&__pyx_kp_u_index_set_max_line_349, __pyx_k_index_set_max_line_349, sizeof(__pyx_k_index_set_max_line_349), 0, 1, 0, 0},
19038  {&__pyx_kp_u_index_set_min_line_340, __pyx_k_index_set_min_line_340, sizeof(__pyx_k_index_set_min_line_340), 0, 1, 0, 0},
19039  {&__pyx_kp_u_index_set_sign_of_mult_line_364, __pyx_k_index_set_sign_of_mult_line_364, sizeof(__pyx_k_index_set_sign_of_mult_line_364), 0, 1, 0, 0},
19040  {&__pyx_kp_u_index_set_sign_of_square_line_37, __pyx_k_index_set_sign_of_square_line_37, sizeof(__pyx_k_index_set_sign_of_square_line_37), 0, 1, 0, 0},
19041  {&__pyx_n_s_inv, __pyx_k_inv, sizeof(__pyx_k_inv), 0, 0, 1, 1},
19042  {&__pyx_kp_u_inv_line_1329, __pyx_k_inv_line_1329, sizeof(__pyx_k_inv_line_1329), 0, 1, 0, 0},
19043  {&__pyx_kp_s_invalid, __pyx_k_invalid, sizeof(__pyx_k_invalid), 0, 0, 1, 0},
19044  {&__pyx_kp_s_invalid_string, __pyx_k_invalid_string, sizeof(__pyx_k_invalid_string), 0, 0, 1, 0},
19045  {&__pyx_n_s_involute, __pyx_k_involute, sizeof(__pyx_k_involute), 0, 0, 1, 1},
19046  {&__pyx_kp_u_involute_line_1406, __pyx_k_involute_line_1406, sizeof(__pyx_k_involute_line_1406), 0, 1, 0, 0},
19047  {&__pyx_n_s_ist, __pyx_k_ist, sizeof(__pyx_k_ist), 0, 0, 1, 1},
19048  {&__pyx_n_s_istpq, __pyx_k_istpq, sizeof(__pyx_k_istpq), 0, 0, 1, 1},
19049  {&__pyx_kp_u_istpq_line_1900, __pyx_k_istpq_line_1900, sizeof(__pyx_k_istpq_line_1900), 0, 1, 0, 0},
19050  {&__pyx_n_s_iter, __pyx_k_iter, sizeof(__pyx_k_iter), 0, 0, 1, 1},
19051  {&__pyx_n_s_ixt, __pyx_k_ixt, sizeof(__pyx_k_ixt), 0, 0, 1, 1},
19052  {&__pyx_kp_u_lexicographic_compare_eg_3_4_5, __pyx_k_lexicographic_compare_eg_3_4_5, sizeof(__pyx_k_lexicographic_compare_eg_3_4_5), 0, 1, 0, 0},
19053  {&__pyx_n_s_lhs, __pyx_k_lhs, sizeof(__pyx_k_lhs), 0, 0, 1, 1},
19054  {&__pyx_n_s_log, __pyx_k_log, sizeof(__pyx_k_log), 0, 0, 1, 1},
19055  {&__pyx_kp_u_log_line_1579, __pyx_k_log_line_1579, sizeof(__pyx_k_log_line_1579), 0, 1, 0, 0},
19056  {&__pyx_n_s_m, __pyx_k_m, sizeof(__pyx_k_m), 0, 0, 1, 1},
19057  {&__pyx_n_s_main, __pyx_k_main, sizeof(__pyx_k_main), 0, 0, 1, 1},
19058  {&__pyx_n_s_math, __pyx_k_math, sizeof(__pyx_k_math), 0, 0, 1, 1},
19059  {&__pyx_n_s_max, __pyx_k_max, sizeof(__pyx_k_max), 0, 0, 1, 1},
19060  {&__pyx_kp_u_max_abs_line_1482, __pyx_k_max_abs_line_1482, sizeof(__pyx_k_max_abs_line_1482), 0, 1, 0, 0},
19061  {&__pyx_kp_u_max_pos_line_511, __pyx_k_max_pos_line_511, sizeof(__pyx_k_max_pos_line_511), 0, 1, 0, 0},
19062  {&__pyx_n_s_min, __pyx_k_min, sizeof(__pyx_k_min), 0, 0, 1, 1},
19063  {&__pyx_kp_u_min_neg_line_502, __pyx_k_min_neg_line_502, sizeof(__pyx_k_min_neg_line_502), 0, 1, 0, 0},
19064  {&__pyx_n_s_name, __pyx_k_name, sizeof(__pyx_k_name), 0, 0, 1, 1},
19065  {&__pyx_n_s_nbar3, __pyx_k_nbar3, sizeof(__pyx_k_nbar3), 0, 0, 1, 1},
19066  {&__pyx_n_s_ninf3, __pyx_k_ninf3, sizeof(__pyx_k_ninf3), 0, 0, 1, 1},
19067  {&__pyx_n_s_norm, __pyx_k_norm, sizeof(__pyx_k_norm), 0, 0, 1, 1},
19068  {&__pyx_kp_u_norm_line_1462, __pyx_k_norm_line_1462, sizeof(__pyx_k_norm_line_1462), 0, 1, 0, 0},
19069  {&__pyx_kp_u_norm_sum_of_squares_of_coordina, __pyx_k_norm_sum_of_squares_of_coordina, sizeof(__pyx_k_norm_sum_of_squares_of_coordina), 0, 1, 0, 0},
19070  {&__pyx_n_s_numbers, __pyx_k_numbers, sizeof(__pyx_k_numbers), 0, 0, 1, 1},
19071  {&__pyx_n_s_obj, __pyx_k_obj, sizeof(__pyx_k_obj), 0, 0, 1, 1},
19072  {&__pyx_n_s_odd, __pyx_k_odd, sizeof(__pyx_k_odd), 0, 0, 1, 1},
19073  {&__pyx_kp_u_odd_line_1397, __pyx_k_odd_line_1397, sizeof(__pyx_k_odd_line_1397), 0, 1, 0, 0},
19074  {&__pyx_n_s_other, __pyx_k_other, sizeof(__pyx_k_other), 0, 0, 1, 1},
19075  {&__pyx_n_s_outer_pow, __pyx_k_outer_pow, sizeof(__pyx_k_outer_pow), 0, 0, 1, 1},
19076  {&__pyx_kp_u_outer_pow_line_1518, __pyx_k_outer_pow_line_1518, sizeof(__pyx_k_outer_pow_line_1518), 0, 1, 0, 0},
19077  {&__pyx_n_s_p, __pyx_k_p, sizeof(__pyx_k_p), 0, 0, 1, 1},
19078  {&__pyx_n_s_pi, __pyx_k_pi, sizeof(__pyx_k_pi), 0, 0, 1, 1},
19079  {&__pyx_n_s_pow, __pyx_k_pow, sizeof(__pyx_k_pow), 0, 0, 1, 1},
19080  {&__pyx_kp_u_pow_line_1494, __pyx_k_pow_line_1494, sizeof(__pyx_k_pow_line_1494), 0, 1, 0, 0},
19081  {&__pyx_n_s_pure, __pyx_k_pure, sizeof(__pyx_k_pure), 0, 0, 1, 1},
19082  {&__pyx_kp_u_pure_line_1377, __pyx_k_pure_line_1377, sizeof(__pyx_k_pure_line_1377), 0, 1, 0, 0},
19083  {&__pyx_n_s_pyx_vtable, __pyx_k_pyx_vtable, sizeof(__pyx_k_pyx_vtable), 0, 0, 1, 1},
19084  {&__pyx_n_s_q, __pyx_k_q, sizeof(__pyx_k_q), 0, 0, 1, 1},
19085  {&__pyx_n_s_quad, __pyx_k_quad, sizeof(__pyx_k_quad), 0, 0, 1, 1},
19086  {&__pyx_kp_u_quad_line_1451, __pyx_k_quad_line_1451, sizeof(__pyx_k_quad_line_1451), 0, 1, 0, 0},
19087  {&__pyx_kp_u_random_clifford_line_1815, __pyx_k_random_clifford_line_1815, sizeof(__pyx_k_random_clifford_line_1815), 0, 1, 0, 0},
19088  {&__pyx_n_s_range, __pyx_k_range, sizeof(__pyx_k_range), 0, 0, 1, 1},
19089  {&__pyx_kp_u_real_line_1355, __pyx_k_real_line_1355, sizeof(__pyx_k_real_line_1355), 0, 1, 0, 0},
19090  {&__pyx_n_s_reverse, __pyx_k_reverse, sizeof(__pyx_k_reverse), 0, 0, 1, 1},
19091  {&__pyx_kp_u_reverse_line_1421, __pyx_k_reverse_line_1421, sizeof(__pyx_k_reverse_line_1421), 0, 1, 0, 0},
19092  {&__pyx_n_s_rhs, __pyx_k_rhs, sizeof(__pyx_k_rhs), 0, 0, 1, 1},
19093  {&__pyx_n_s_scalar, __pyx_k_scalar, sizeof(__pyx_k_scalar), 0, 0, 1, 1},
19094  {&__pyx_kp_u_scalar_line_1344, __pyx_k_scalar_line_1344, sizeof(__pyx_k_scalar_line_1344), 0, 1, 0, 0},
19095  {&__pyx_n_s_send, __pyx_k_send, sizeof(__pyx_k_send), 0, 0, 1, 1},
19096  {&__pyx_n_s_sin, __pyx_k_sin, sizeof(__pyx_k_sin), 0, 0, 1, 1},
19097  {&__pyx_kp_u_sin_line_1679, __pyx_k_sin_line_1679, sizeof(__pyx_k_sin_line_1679), 0, 1, 0, 0},
19098  {&__pyx_n_s_sinh, __pyx_k_sinh, sizeof(__pyx_k_sinh), 0, 0, 1, 1},
19099  {&__pyx_kp_u_sinh_line_1719, __pyx_k_sinh_line_1719, sizeof(__pyx_k_sinh_line_1719), 0, 1, 0, 0},
19100  {&__pyx_n_s_sqrt, __pyx_k_sqrt, sizeof(__pyx_k_sqrt), 0, 0, 1, 1},
19101  {&__pyx_kp_u_sqrt_line_1542, __pyx_k_sqrt_line_1542, sizeof(__pyx_k_sqrt_line_1542), 0, 1, 0, 0},
19102  {&__pyx_n_s_tan, __pyx_k_tan, sizeof(__pyx_k_tan), 0, 0, 1, 1},
19103  {&__pyx_kp_u_tan_line_1752, __pyx_k_tan_line_1752, sizeof(__pyx_k_tan_line_1752), 0, 1, 0, 0},
19104  {&__pyx_n_s_tanh, __pyx_k_tanh, sizeof(__pyx_k_tanh), 0, 0, 1, 1},
19105  {&__pyx_kp_u_tanh_line_1786, __pyx_k_tanh_line_1786, sizeof(__pyx_k_tanh_line_1786), 0, 1, 0, 0},
19106  {&__pyx_n_s_tau, __pyx_k_tau, sizeof(__pyx_k_tau), 0, 0, 1, 1},
19107  {&__pyx_n_s_test, __pyx_k_test, sizeof(__pyx_k_test), 0, 0, 1, 1},
19108  {&__pyx_n_s_test_2, __pyx_k_test_2, sizeof(__pyx_k_test_2), 0, 0, 1, 1},
19109  {&__pyx_n_s_testmod, __pyx_k_testmod, sizeof(__pyx_k_testmod), 0, 0, 1, 1},
19110  {&__pyx_n_s_throw, __pyx_k_throw, sizeof(__pyx_k_throw), 0, 0, 1, 1},
19111  {&__pyx_kp_s_to_frame, __pyx_k_to_frame, sizeof(__pyx_k_to_frame), 0, 0, 1, 0},
19112  {&__pyx_kp_s_using, __pyx_k_using, sizeof(__pyx_k_using), 0, 0, 1, 0},
19113  {&__pyx_kp_s_using_invalid, __pyx_k_using_invalid, sizeof(__pyx_k_using_invalid), 0, 0, 1, 0},
19114  {&__pyx_kp_s_value, __pyx_k_value, sizeof(__pyx_k_value), 0, 0, 1, 0},
19115  {&__pyx_n_s_version, __pyx_k_version, sizeof(__pyx_k_version), 0, 0, 1, 1},
19116  {&__pyx_n_s_xrange, __pyx_k_xrange, sizeof(__pyx_k_xrange), 0, 0, 1, 1},
19117  {0, 0, 0, 0, 0, 0, 0}
19118 };
19119 static int __Pyx_InitCachedBuiltins(void) {
19120  __pyx_builtin_IndexError = __Pyx_GetBuiltinName(__pyx_n_s_IndexError); if (!__pyx_builtin_IndexError) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 102; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19121  __pyx_builtin_RuntimeError = __Pyx_GetBuiltinName(__pyx_n_s_RuntimeError); if (!__pyx_builtin_RuntimeError) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 104; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19122  __pyx_builtin_TypeError = __Pyx_GetBuiltinName(__pyx_n_s_TypeError); if (!__pyx_builtin_TypeError) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 104; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19123  __pyx_builtin_ValueError = __Pyx_GetBuiltinName(__pyx_n_s_ValueError); if (!__pyx_builtin_ValueError) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 105; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19124  __pyx_builtin_NotImplemented = __Pyx_GetBuiltinName(__pyx_n_s_NotImplemented); if (!__pyx_builtin_NotImplemented) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 157; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19125  __pyx_builtin_range = __Pyx_GetBuiltinName(__pyx_n_s_range); if (!__pyx_builtin_range) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 234; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19126  #if PY_MAJOR_VERSION >= 3
19127  __pyx_builtin_xrange = __Pyx_GetBuiltinName(__pyx_n_s_range); if (!__pyx_builtin_xrange) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1098; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19128  #else
19129  __pyx_builtin_xrange = __Pyx_GetBuiltinName(__pyx_n_s_xrange); if (!__pyx_builtin_xrange) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1098; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19130  #endif
19131  return 0;
19132  __pyx_L1_error:;
19133  return -1;
19134 }
19135 
19136 static int __Pyx_InitCachedConstants(void) {
19137  __Pyx_RefNannyDeclarations
19138  __Pyx_RefNannySetupContext("__Pyx_InitCachedConstants", 0);
19139 
19140  /* "PyClical.pyx":635
19141  * TypeError: Not applicable.
19142  * """
19143  * raise TypeError("Not applicable.") # <<<<<<<<<<<<<<
19144  *
19145  * def __iter__(self):
19146  */
19147  __pyx_tuple__8 = PyTuple_Pack(1, __pyx_kp_s_Not_applicable); if (unlikely(!__pyx_tuple__8)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 635; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19148  __Pyx_GOTREF(__pyx_tuple__8);
19149  __Pyx_GIVEREF(__pyx_tuple__8);
19150 
19151  /* "PyClical.pyx":646
19152  * TypeError: Not applicable.
19153  * """
19154  * raise TypeError("Not applicable.") # <<<<<<<<<<<<<<
19155  *
19156  * def reframe(self, ixt):
19157  */
19158  __pyx_tuple__9 = PyTuple_Pack(1, __pyx_kp_s_Not_applicable); if (unlikely(!__pyx_tuple__9)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 646; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19159  __Pyx_GOTREF(__pyx_tuple__9);
19160  __Pyx_GIVEREF(__pyx_tuple__9);
19161 
19162  /* "PyClical.pyx":404
19163  * return index_set_to_str( self.unwrap() ).c_str()
19164  *
19165  * def index_set_hidden_doctests(): # <<<<<<<<<<<<<<
19166  * """
19167  * Tests for functions that Doctest cannot see.
19168  */
19169  __pyx_codeobj__10 = (PyObject*)__Pyx_PyCode_New(0, 0, 0, 0, 0, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_home_abuild_rpmbuild_BUILD_gluc, __pyx_n_s_index_set_hidden_doctests, 404, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__10)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 404; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19170 
19171  /* "PyClical.pyx":1243
19172  * return clifford_to_str( self.unwrap() ).c_str()
19173  *
19174  * def clifford_hidden_doctests(): # <<<<<<<<<<<<<<
19175  * """
19176  * Tests for functions that Doctest cannot see.
19177  */
19178  __pyx_codeobj__11 = (PyObject*)__Pyx_PyCode_New(0, 0, 0, 0, 0, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_home_abuild_rpmbuild_BUILD_gluc, __pyx_n_s_clifford_hidden_doctests, 1243, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__11)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1243; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19179 
19180  /* "PyClical.pyx":1856
19181  *
19182  * # Some abbreviations.
19183  * tau = atan(clifford(1.0)) * 8.0 # <<<<<<<<<<<<<<
19184  * pi = tau / 2.0
19185  *
19186  */
19187  __pyx_tuple__12 = PyTuple_Pack(1, __pyx_float_1_0); if (unlikely(!__pyx_tuple__12)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1856; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19188  __Pyx_GOTREF(__pyx_tuple__12);
19189  __Pyx_GIVEREF(__pyx_tuple__12);
19190 
19191  /* "PyClical.pyx":1887
19192  * """
19193  *
19194  * def e(obj): # <<<<<<<<<<<<<<
19195  * """
19196  * Abbreviation for clifford(index_set(obj)).
19197  */
19198  __pyx_tuple__13 = PyTuple_Pack(1, __pyx_n_s_obj); if (unlikely(!__pyx_tuple__13)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1887; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19199  __Pyx_GOTREF(__pyx_tuple__13);
19200  __Pyx_GIVEREF(__pyx_tuple__13);
19201  __pyx_codeobj__14 = (PyObject*)__Pyx_PyCode_New(1, 0, 1, 0, 0, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__13, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_home_abuild_rpmbuild_BUILD_gluc, __pyx_n_s_e, 1887, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__14)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1887; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19202 
19203  /* "PyClical.pyx":1900
19204  * return clifford(index_set(obj))
19205  *
19206  * def istpq(p, q): # <<<<<<<<<<<<<<
19207  * """
19208  * Abbreviation for index_set({-q,...p}).
19209  */
19210  __pyx_tuple__15 = PyTuple_Pack(2, __pyx_n_s_p, __pyx_n_s_q); if (unlikely(!__pyx_tuple__15)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1900; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19211  __Pyx_GOTREF(__pyx_tuple__15);
19212  __Pyx_GIVEREF(__pyx_tuple__15);
19213  __pyx_codeobj__16 = (PyObject*)__Pyx_PyCode_New(2, 0, 2, 0, 0, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__15, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_home_abuild_rpmbuild_BUILD_gluc, __pyx_n_s_istpq, 1900, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__16)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1900; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19214 
19215  /* "PyClical.pyx":1909
19216  * return index_set(set(range(-q,p+1)))
19217  *
19218  * ninf3 = e(4) + e(-1) # Null infinity point in 3D Conformal Geometric Algebra [DL]. # <<<<<<<<<<<<<<
19219  * nbar3 = e(4) - e(-1) # Null bar point in 3D Conformal Geometric Algebra [DL].
19220  *
19221  */
19222  __pyx_tuple__17 = PyTuple_Pack(1, __pyx_int_4); if (unlikely(!__pyx_tuple__17)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1909; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19223  __Pyx_GOTREF(__pyx_tuple__17);
19224  __Pyx_GIVEREF(__pyx_tuple__17);
19225  __pyx_tuple__18 = PyTuple_Pack(1, __pyx_int_neg_1); if (unlikely(!__pyx_tuple__18)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1909; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19226  __Pyx_GOTREF(__pyx_tuple__18);
19227  __Pyx_GIVEREF(__pyx_tuple__18);
19228 
19229  /* "PyClical.pyx":1910
19230  *
19231  * ninf3 = e(4) + e(-1) # Null infinity point in 3D Conformal Geometric Algebra [DL].
19232  * nbar3 = e(4) - e(-1) # Null bar point in 3D Conformal Geometric Algebra [DL]. # <<<<<<<<<<<<<<
19233  *
19234  * # Doctest interface.
19235  */
19236  __pyx_tuple__19 = PyTuple_Pack(1, __pyx_int_4); if (unlikely(!__pyx_tuple__19)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1910; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19237  __Pyx_GOTREF(__pyx_tuple__19);
19238  __Pyx_GIVEREF(__pyx_tuple__19);
19239  __pyx_tuple__20 = PyTuple_Pack(1, __pyx_int_neg_1); if (unlikely(!__pyx_tuple__20)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1910; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19240  __Pyx_GOTREF(__pyx_tuple__20);
19241  __Pyx_GIVEREF(__pyx_tuple__20);
19242 
19243  /* "PyClical.pyx":1913
19244  *
19245  * # Doctest interface.
19246  * def _test(): # <<<<<<<<<<<<<<
19247  * import PyClical, doctest
19248  * return doctest.testmod(PyClical)
19249  */
19250  __pyx_tuple__21 = PyTuple_Pack(2, __pyx_n_s_PyClical, __pyx_n_s_doctest); if (unlikely(!__pyx_tuple__21)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1913; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19251  __Pyx_GOTREF(__pyx_tuple__21);
19252  __Pyx_GIVEREF(__pyx_tuple__21);
19253  __pyx_codeobj__22 = (PyObject*)__Pyx_PyCode_New(0, 0, 2, 0, 0, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__21, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_home_abuild_rpmbuild_BUILD_gluc, __pyx_n_s_test, 1913, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__22)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1913; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19254  __Pyx_RefNannyFinishContext();
19255  return 0;
19256  __pyx_L1_error:;
19257  __Pyx_RefNannyFinishContext();
19258  return -1;
19259 }
19260 
19261 static int __Pyx_InitGlobals(void) {
19262  if (__Pyx_InitStrings(__pyx_string_tab) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;};
19263  __pyx_float_0_0 = PyFloat_FromDouble(0.0); if (unlikely(!__pyx_float_0_0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19264  __pyx_float_1_0 = PyFloat_FromDouble(1.0); if (unlikely(!__pyx_float_1_0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19265  __pyx_float_2_0 = PyFloat_FromDouble(2.0); if (unlikely(!__pyx_float_2_0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19266  __pyx_float_8_0 = PyFloat_FromDouble(8.0); if (unlikely(!__pyx_float_8_0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19267  __pyx_int_0 = PyInt_FromLong(0); if (unlikely(!__pyx_int_0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19268  __pyx_int_1 = PyInt_FromLong(1); if (unlikely(!__pyx_int_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19269  __pyx_int_4 = PyInt_FromLong(4); if (unlikely(!__pyx_int_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19270  __pyx_int_neg_1 = PyInt_FromLong(-1); if (unlikely(!__pyx_int_neg_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19271  return 0;
19272  __pyx_L1_error:;
19273  return -1;
19274 }
19275 
19276 #if PY_MAJOR_VERSION < 3
19277 PyMODINIT_FUNC initPyClical(void); /*proto*/
19278 PyMODINIT_FUNC initPyClical(void)
19279 #else
19280 PyMODINIT_FUNC PyInit_PyClical(void); /*proto*/
19281 PyMODINIT_FUNC PyInit_PyClical(void)
19282 #endif
19283 {
19284  PyObject *__pyx_t_1 = NULL;
19285  PyObject *__pyx_t_2 = NULL;
19286  PyObject *__pyx_t_3 = NULL;
19287  int __pyx_t_4;
19288  int __pyx_lineno = 0;
19289  const char *__pyx_filename = NULL;
19290  int __pyx_clineno = 0;
19291  __Pyx_RefNannyDeclarations
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19293  __Pyx_RefNanny = __Pyx_RefNannyImportAPI("refnanny");
19294  if (!__Pyx_RefNanny) {
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19296  __Pyx_RefNanny = __Pyx_RefNannyImportAPI("Cython.Runtime.refnanny");
19297  if (!__Pyx_RefNanny)
19298  Py_FatalError("failed to import 'refnanny' module");
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19303  __pyx_empty_tuple = PyTuple_New(0); if (unlikely(!__pyx_empty_tuple)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19304  __pyx_empty_bytes = PyBytes_FromStringAndSize("", 0); if (unlikely(!__pyx_empty_bytes)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19305  #ifdef __Pyx_CyFunction_USED
19306  if (__pyx_CyFunction_init() < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19307  #endif
19308  #ifdef __Pyx_FusedFunction_USED
19309  if (__pyx_FusedFunction_init() < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19310  #endif
19311  #ifdef __Pyx_Coroutine_USED
19312  if (__pyx_Coroutine_init() < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19313  #endif
19314  #ifdef __Pyx_Generator_USED
19315  if (__pyx_Generator_init() < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19316  #endif
19317  #ifdef __Pyx_StopAsyncIteration_USED
19318  if (__pyx_StopAsyncIteration_init() < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19319  #endif
19320  /*--- Library function declarations ---*/
19321  /*--- Threads initialization code ---*/
19322  #if defined(__PYX_FORCE_INIT_THREADS) && __PYX_FORCE_INIT_THREADS
19323  #ifdef WITH_THREAD /* Python build with threading support? */
19324  PyEval_InitThreads();
19325  #endif
19326  #endif
19327  /*--- Module creation code ---*/
19328  #if PY_MAJOR_VERSION < 3
19329  __pyx_m = Py_InitModule4("PyClical", __pyx_methods, 0, 0, PYTHON_API_VERSION); Py_XINCREF(__pyx_m);
19330  #else
19331  __pyx_m = PyModule_Create(&__pyx_moduledef);
19332  #endif
19333  if (unlikely(!__pyx_m)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19334  __pyx_d = PyModule_GetDict(__pyx_m); if (unlikely(!__pyx_d)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19335  Py_INCREF(__pyx_d);
19336  __pyx_b = PyImport_AddModule(__Pyx_BUILTIN_MODULE_NAME); if (unlikely(!__pyx_b)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19337  #if CYTHON_COMPILING_IN_PYPY
19338  Py_INCREF(__pyx_b);
19339  #endif
19340  if (PyObject_SetAttrString(__pyx_m, "__builtins__", __pyx_b) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;};
19341  /*--- Initialize various global constants etc. ---*/
19342  if (__Pyx_InitGlobals() < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19343  #if PY_MAJOR_VERSION < 3 && (__PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT)
19344  if (__Pyx_init_sys_getdefaultencoding_params() < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19345  #endif
19346  if (__pyx_module_is_main_PyClical) {
19347  if (PyObject_SetAttrString(__pyx_m, "__name__", __pyx_n_s_main) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19348  }
19349  #if PY_MAJOR_VERSION >= 3
19350  {
19351  PyObject *modules = PyImport_GetModuleDict(); if (unlikely(!modules)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19352  if (!PyDict_GetItemString(modules, "PyClical")) {
19353  if (unlikely(PyDict_SetItemString(modules, "PyClical", __pyx_m) < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19354  }
19355  }
19356  #endif
19357  /*--- Builtin init code ---*/
19358  if (__Pyx_InitCachedBuiltins() < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19359  /*--- Constants init code ---*/
19360  if (__Pyx_InitCachedConstants() < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19361  /*--- Global init code ---*/
19362  /*--- Variable export code ---*/
19363  /*--- Function export code ---*/
19364  /*--- Type init code ---*/
19365  __pyx_vtabptr_8PyClical_index_set = &__pyx_vtable_8PyClical_index_set;
19366  __pyx_vtable_8PyClical_index_set.wrap = (PyObject *(*)(struct __pyx_obj_8PyClical_index_set *, IndexSet))__pyx_f_8PyClical_9index_set_wrap;
19367  __pyx_vtable_8PyClical_index_set.unwrap = (IndexSet (*)(struct __pyx_obj_8PyClical_index_set *))__pyx_f_8PyClical_9index_set_unwrap;
19368  __pyx_vtable_8PyClical_index_set.copy = (PyObject *(*)(struct __pyx_obj_8PyClical_index_set *, int __pyx_skip_dispatch))__pyx_f_8PyClical_9index_set_copy;
19369  if (PyType_Ready(&__pyx_type_8PyClical_index_set) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 45; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19370  __pyx_type_8PyClical_index_set.tp_print = 0;
19371  #if CYTHON_COMPILING_IN_CPYTHON
19372  {
19373  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__setitem__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 45; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19374  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19375  __pyx_wrapperbase_8PyClical_9index_set_8__setitem__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19376  __pyx_wrapperbase_8PyClical_9index_set_8__setitem__.doc = __pyx_doc_8PyClical_9index_set_8__setitem__;
19377  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_8__setitem__;
19378  }
19379  }
19380  #endif
19381  #if CYTHON_COMPILING_IN_CPYTHON
19382  {
19383  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__getitem__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 45; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19384  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19385  __pyx_wrapperbase_8PyClical_9index_set_10__getitem__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19386  __pyx_wrapperbase_8PyClical_9index_set_10__getitem__.doc = __pyx_doc_8PyClical_9index_set_10__getitem__;
19387  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_10__getitem__;
19388  }
19389  }
19390  #endif
19391  #if CYTHON_COMPILING_IN_CPYTHON
19392  {
19393  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__contains__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 45; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19394  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19395  __pyx_wrapperbase_8PyClical_9index_set_12__contains__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19396  __pyx_wrapperbase_8PyClical_9index_set_12__contains__.doc = __pyx_doc_8PyClical_9index_set_12__contains__;
19397  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_12__contains__;
19398  }
19399  }
19400  #endif
19401  #if CYTHON_COMPILING_IN_CPYTHON
19402  {
19403  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__iter__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 45; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19404  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19405  __pyx_wrapperbase_8PyClical_9index_set_14__iter__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19406  __pyx_wrapperbase_8PyClical_9index_set_14__iter__.doc = __pyx_doc_8PyClical_9index_set_14__iter__;
19407  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_14__iter__;
19408  }
19409  }
19410  #endif
19411  #if CYTHON_COMPILING_IN_CPYTHON
19412  {
19413  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__invert__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 45; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19414  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19415  __pyx_wrapperbase_8PyClical_9index_set_17__invert__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19416  __pyx_wrapperbase_8PyClical_9index_set_17__invert__.doc = __pyx_doc_8PyClical_9index_set_17__invert__;
19417  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_17__invert__;
19418  }
19419  }
19420  #endif
19421  #if CYTHON_COMPILING_IN_CPYTHON
19422  {
19423  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__xor__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 45; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19424  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19425  __pyx_wrapperbase_8PyClical_9index_set_19__xor__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19426  __pyx_wrapperbase_8PyClical_9index_set_19__xor__.doc = __pyx_doc_8PyClical_9index_set_19__xor__;
19427  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_19__xor__;
19428  }
19429  }
19430  #endif
19431  #if CYTHON_COMPILING_IN_CPYTHON
19432  {
19433  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__ixor__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 45; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19434  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19435  __pyx_wrapperbase_8PyClical_9index_set_21__ixor__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19436  __pyx_wrapperbase_8PyClical_9index_set_21__ixor__.doc = __pyx_doc_8PyClical_9index_set_21__ixor__;
19437  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_21__ixor__;
19438  }
19439  }
19440  #endif
19441  #if CYTHON_COMPILING_IN_CPYTHON
19442  {
19443  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__and__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 45; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19444  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19445  __pyx_wrapperbase_8PyClical_9index_set_23__and__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19446  __pyx_wrapperbase_8PyClical_9index_set_23__and__.doc = __pyx_doc_8PyClical_9index_set_23__and__;
19447  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_23__and__;
19448  }
19449  }
19450  #endif
19451  #if CYTHON_COMPILING_IN_CPYTHON
19452  {
19453  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__iand__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 45; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19454  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19455  __pyx_wrapperbase_8PyClical_9index_set_25__iand__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19456  __pyx_wrapperbase_8PyClical_9index_set_25__iand__.doc = __pyx_doc_8PyClical_9index_set_25__iand__;
19457  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_25__iand__;
19458  }
19459  }
19460  #endif
19461  #if CYTHON_COMPILING_IN_CPYTHON
19462  {
19463  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__or__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 45; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19464  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19465  __pyx_wrapperbase_8PyClical_9index_set_27__or__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19466  __pyx_wrapperbase_8PyClical_9index_set_27__or__.doc = __pyx_doc_8PyClical_9index_set_27__or__;
19467  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_27__or__;
19468  }
19469  }
19470  #endif
19471  #if CYTHON_COMPILING_IN_CPYTHON
19472  {
19473  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__ior__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 45; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19474  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19475  __pyx_wrapperbase_8PyClical_9index_set_29__ior__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19476  __pyx_wrapperbase_8PyClical_9index_set_29__ior__.doc = __pyx_doc_8PyClical_9index_set_29__ior__;
19477  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_29__ior__;
19478  }
19479  }
19480  #endif
19481  #if CYTHON_COMPILING_IN_CPYTHON
19482  {
19483  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__repr__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 45; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19484  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19485  __pyx_wrapperbase_8PyClical_9index_set_47__repr__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19486  __pyx_wrapperbase_8PyClical_9index_set_47__repr__.doc = __pyx_doc_8PyClical_9index_set_47__repr__;
19487  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_47__repr__;
19488  }
19489  }
19490  #endif
19491  #if CYTHON_COMPILING_IN_CPYTHON
19492  {
19493  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__str__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 45; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19494  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19495  __pyx_wrapperbase_8PyClical_9index_set_49__str__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19496  __pyx_wrapperbase_8PyClical_9index_set_49__str__.doc = __pyx_doc_8PyClical_9index_set_49__str__;
19497  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_49__str__;
19498  }
19499  }
19500  #endif
19501  if (__Pyx_SetVtable(__pyx_type_8PyClical_index_set.tp_dict, __pyx_vtabptr_8PyClical_index_set) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 45; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19502  if (PyObject_SetAttrString(__pyx_m, "index_set", (PyObject *)&__pyx_type_8PyClical_index_set) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 45; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19503  __pyx_ptype_8PyClical_index_set = &__pyx_type_8PyClical_index_set;
19504  __pyx_vtabptr_8PyClical_clifford = &__pyx_vtable_8PyClical_clifford;
19505  __pyx_vtable_8PyClical_clifford.wrap = (PyObject *(*)(struct __pyx_obj_8PyClical_clifford *, Clifford))__pyx_f_8PyClical_8clifford_wrap;
19506  __pyx_vtable_8PyClical_clifford.unwrap = (Clifford (*)(struct __pyx_obj_8PyClical_clifford *))__pyx_f_8PyClical_8clifford_unwrap;
19507  __pyx_vtable_8PyClical_clifford.copy = (PyObject *(*)(struct __pyx_obj_8PyClical_clifford *, int __pyx_skip_dispatch))__pyx_f_8PyClical_8clifford_copy;
19508  if (PyType_Ready(&__pyx_type_8PyClical_clifford) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19509  __pyx_type_8PyClical_clifford.tp_print = 0;
19510  #if CYTHON_COMPILING_IN_CPYTHON
19511  {
19512  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__contains__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19513  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19514  __pyx_wrapperbase_8PyClical_8clifford_6__contains__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19515  __pyx_wrapperbase_8PyClical_8clifford_6__contains__.doc = __pyx_doc_8PyClical_8clifford_6__contains__;
19516  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_6__contains__;
19517  }
19518  }
19519  #endif
19520  #if CYTHON_COMPILING_IN_CPYTHON
19521  {
19522  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__iter__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19523  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19524  __pyx_wrapperbase_8PyClical_8clifford_8__iter__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19525  __pyx_wrapperbase_8PyClical_8clifford_8__iter__.doc = __pyx_doc_8PyClical_8clifford_8__iter__;
19526  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_8__iter__;
19527  }
19528  }
19529  #endif
19530  #if CYTHON_COMPILING_IN_CPYTHON
19531  {
19532  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__getitem__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19533  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19534  __pyx_wrapperbase_8PyClical_8clifford_14__getitem__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19535  __pyx_wrapperbase_8PyClical_8clifford_14__getitem__.doc = __pyx_doc_8PyClical_8clifford_14__getitem__;
19536  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_14__getitem__;
19537  }
19538  }
19539  #endif
19540  #if CYTHON_COMPILING_IN_CPYTHON
19541  {
19542  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__neg__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19543  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19544  __pyx_wrapperbase_8PyClical_8clifford_16__neg__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19545  __pyx_wrapperbase_8PyClical_8clifford_16__neg__.doc = __pyx_doc_8PyClical_8clifford_16__neg__;
19546  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_16__neg__;
19547  }
19548  }
19549  #endif
19550  #if CYTHON_COMPILING_IN_CPYTHON
19551  {
19552  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__pos__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19553  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19554  __pyx_wrapperbase_8PyClical_8clifford_18__pos__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19555  __pyx_wrapperbase_8PyClical_8clifford_18__pos__.doc = __pyx_doc_8PyClical_8clifford_18__pos__;
19556  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_18__pos__;
19557  }
19558  }
19559  #endif
19560  #if CYTHON_COMPILING_IN_CPYTHON
19561  {
19562  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__add__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19563  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19564  __pyx_wrapperbase_8PyClical_8clifford_20__add__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19565  __pyx_wrapperbase_8PyClical_8clifford_20__add__.doc = __pyx_doc_8PyClical_8clifford_20__add__;
19566  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_20__add__;
19567  }
19568  }
19569  #endif
19570  #if CYTHON_COMPILING_IN_CPYTHON
19571  {
19572  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__iadd__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19573  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19574  __pyx_wrapperbase_8PyClical_8clifford_22__iadd__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19575  __pyx_wrapperbase_8PyClical_8clifford_22__iadd__.doc = __pyx_doc_8PyClical_8clifford_22__iadd__;
19576  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_22__iadd__;
19577  }
19578  }
19579  #endif
19580  #if CYTHON_COMPILING_IN_CPYTHON
19581  {
19582  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__sub__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19583  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19584  __pyx_wrapperbase_8PyClical_8clifford_24__sub__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19585  __pyx_wrapperbase_8PyClical_8clifford_24__sub__.doc = __pyx_doc_8PyClical_8clifford_24__sub__;
19586  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_24__sub__;
19587  }
19588  }
19589  #endif
19590  #if CYTHON_COMPILING_IN_CPYTHON
19591  {
19592  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__isub__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19593  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19594  __pyx_wrapperbase_8PyClical_8clifford_26__isub__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19595  __pyx_wrapperbase_8PyClical_8clifford_26__isub__.doc = __pyx_doc_8PyClical_8clifford_26__isub__;
19596  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_26__isub__;
19597  }
19598  }
19599  #endif
19600  #if CYTHON_COMPILING_IN_CPYTHON
19601  {
19602  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__mul__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19603  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19604  __pyx_wrapperbase_8PyClical_8clifford_28__mul__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19605  __pyx_wrapperbase_8PyClical_8clifford_28__mul__.doc = __pyx_doc_8PyClical_8clifford_28__mul__;
19606  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_28__mul__;
19607  }
19608  }
19609  #endif
19610  #if CYTHON_COMPILING_IN_CPYTHON
19611  {
19612  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__imul__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19613  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19614  __pyx_wrapperbase_8PyClical_8clifford_30__imul__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19615  __pyx_wrapperbase_8PyClical_8clifford_30__imul__.doc = __pyx_doc_8PyClical_8clifford_30__imul__;
19616  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_30__imul__;
19617  }
19618  }
19619  #endif
19620  #if CYTHON_COMPILING_IN_CPYTHON
19621  {
19622  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__mod__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19623  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19624  __pyx_wrapperbase_8PyClical_8clifford_32__mod__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19625  __pyx_wrapperbase_8PyClical_8clifford_32__mod__.doc = __pyx_doc_8PyClical_8clifford_32__mod__;
19626  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_32__mod__;
19627  }
19628  }
19629  #endif
19630  #if CYTHON_COMPILING_IN_CPYTHON
19631  {
19632  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__imod__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19633  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19634  __pyx_wrapperbase_8PyClical_8clifford_34__imod__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19635  __pyx_wrapperbase_8PyClical_8clifford_34__imod__.doc = __pyx_doc_8PyClical_8clifford_34__imod__;
19636  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_34__imod__;
19637  }
19638  }
19639  #endif
19640  #if CYTHON_COMPILING_IN_CPYTHON
19641  {
19642  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__and__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19643  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19644  __pyx_wrapperbase_8PyClical_8clifford_36__and__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19645  __pyx_wrapperbase_8PyClical_8clifford_36__and__.doc = __pyx_doc_8PyClical_8clifford_36__and__;
19646  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_36__and__;
19647  }
19648  }
19649  #endif
19650  #if CYTHON_COMPILING_IN_CPYTHON
19651  {
19652  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__iand__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19653  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19654  __pyx_wrapperbase_8PyClical_8clifford_38__iand__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19655  __pyx_wrapperbase_8PyClical_8clifford_38__iand__.doc = __pyx_doc_8PyClical_8clifford_38__iand__;
19656  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_38__iand__;
19657  }
19658  }
19659  #endif
19660  #if CYTHON_COMPILING_IN_CPYTHON
19661  {
19662  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__xor__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19663  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19664  __pyx_wrapperbase_8PyClical_8clifford_40__xor__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19665  __pyx_wrapperbase_8PyClical_8clifford_40__xor__.doc = __pyx_doc_8PyClical_8clifford_40__xor__;
19666  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_40__xor__;
19667  }
19668  }
19669  #endif
19670  #if CYTHON_COMPILING_IN_CPYTHON
19671  {
19672  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__ixor__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19673  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19674  __pyx_wrapperbase_8PyClical_8clifford_42__ixor__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19675  __pyx_wrapperbase_8PyClical_8clifford_42__ixor__.doc = __pyx_doc_8PyClical_8clifford_42__ixor__;
19676  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_42__ixor__;
19677  }
19678  }
19679  #endif
19680  #if PY_MAJOR_VERSION < 3 || CYTHON_COMPILING_IN_PYPY
19681  #if CYTHON_COMPILING_IN_CPYTHON
19682  {
19683  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__div__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19684  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19685  __pyx_wrapperbase_8PyClical_8clifford_44__div__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19686  __pyx_wrapperbase_8PyClical_8clifford_44__div__.doc = __pyx_doc_8PyClical_8clifford_44__div__;
19687  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_44__div__;
19688  }
19689  }
19690  #endif
19691  #endif
19692  #if PY_MAJOR_VERSION < 3 || CYTHON_COMPILING_IN_PYPY
19693  #if CYTHON_COMPILING_IN_CPYTHON
19694  {
19695  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__idiv__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19696  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19697  __pyx_wrapperbase_8PyClical_8clifford_46__idiv__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19698  __pyx_wrapperbase_8PyClical_8clifford_46__idiv__.doc = __pyx_doc_8PyClical_8clifford_46__idiv__;
19699  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_46__idiv__;
19700  }
19701  }
19702  #endif
19703  #endif
19704  #if CYTHON_COMPILING_IN_CPYTHON
19705  {
19706  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__or__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19707  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19708  __pyx_wrapperbase_8PyClical_8clifford_50__or__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19709  __pyx_wrapperbase_8PyClical_8clifford_50__or__.doc = __pyx_doc_8PyClical_8clifford_50__or__;
19710  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_50__or__;
19711  }
19712  }
19713  #endif
19714  #if CYTHON_COMPILING_IN_CPYTHON
19715  {
19716  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__ior__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19717  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19718  __pyx_wrapperbase_8PyClical_8clifford_52__ior__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19719  __pyx_wrapperbase_8PyClical_8clifford_52__ior__.doc = __pyx_doc_8PyClical_8clifford_52__ior__;
19720  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_52__ior__;
19721  }
19722  }
19723  #endif
19724  #if CYTHON_COMPILING_IN_CPYTHON
19725  {
19726  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__pow__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19727  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19728  __pyx_wrapperbase_8PyClical_8clifford_54__pow__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19729  __pyx_wrapperbase_8PyClical_8clifford_54__pow__.doc = __pyx_doc_8PyClical_8clifford_54__pow__;
19730  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_54__pow__;
19731  }
19732  }
19733  #endif
19734  #if CYTHON_COMPILING_IN_CPYTHON
19735  {
19736  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__call__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19737  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19738  __pyx_wrapperbase_8PyClical_8clifford_60__call__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19739  __pyx_wrapperbase_8PyClical_8clifford_60__call__.doc = __pyx_doc_8PyClical_8clifford_60__call__;
19740  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_60__call__;
19741  }
19742  }
19743  #endif
19744  #if CYTHON_COMPILING_IN_CPYTHON
19745  {
19746  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__repr__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19747  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19748  __pyx_wrapperbase_8PyClical_8clifford_92__repr__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19749  __pyx_wrapperbase_8PyClical_8clifford_92__repr__.doc = __pyx_doc_8PyClical_8clifford_92__repr__;
19750  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_92__repr__;
19751  }
19752  }
19753  #endif
19754  #if CYTHON_COMPILING_IN_CPYTHON
19755  {
19756  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__str__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19757  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19758  __pyx_wrapperbase_8PyClical_8clifford_94__str__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19759  __pyx_wrapperbase_8PyClical_8clifford_94__str__.doc = __pyx_doc_8PyClical_8clifford_94__str__;
19760  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_94__str__;
19761  }
19762  }
19763  #endif
19764  if (__Pyx_SetVtable(__pyx_type_8PyClical_clifford.tp_dict, __pyx_vtabptr_8PyClical_clifford) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19765  if (PyObject_SetAttrString(__pyx_m, "clifford", (PyObject *)&__pyx_type_8PyClical_clifford) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 535; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19766  __pyx_ptype_8PyClical_clifford = &__pyx_type_8PyClical_clifford;
19767  if (PyType_Ready(&__pyx_type_8PyClical___pyx_scope_struct____iter__) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 227; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19768  __pyx_type_8PyClical___pyx_scope_struct____iter__.tp_print = 0;
19769  __pyx_ptype_8PyClical___pyx_scope_struct____iter__ = &__pyx_type_8PyClical___pyx_scope_struct____iter__;
19770  /*--- Type import code ---*/
19771  /*--- Variable import code ---*/
19772  /*--- Function import code ---*/
19773  /*--- Execution code ---*/
19774  #if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
19775  if (__Pyx_patch_abc() < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19776  #endif
19777 
19778  /* "PyClical.pyx":28
19779  * # C. Doran and A. Lasenby, "Geometric algebra for physicists", Cambridge, 2003.
19780  *
19781  * import math # <<<<<<<<<<<<<<
19782  * import numbers
19783  * import collections
19784  */
19785  __pyx_t_1 = __Pyx_Import(__pyx_n_s_math, 0, -1); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 28; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19786  __Pyx_GOTREF(__pyx_t_1);
19787  if (PyDict_SetItem(__pyx_d, __pyx_n_s_math, __pyx_t_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 28; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19788  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19789 
19790  /* "PyClical.pyx":29
19791  *
19792  * import math
19793  * import numbers # <<<<<<<<<<<<<<
19794  * import collections
19795  *
19796  */
19797  __pyx_t_1 = __Pyx_Import(__pyx_n_s_numbers, 0, -1); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 29; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19798  __Pyx_GOTREF(__pyx_t_1);
19799  if (PyDict_SetItem(__pyx_d, __pyx_n_s_numbers, __pyx_t_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 29; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19800  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19801 
19802  /* "PyClical.pyx":30
19803  * import math
19804  * import numbers
19805  * import collections # <<<<<<<<<<<<<<
19806  *
19807  * __version__ = "0.8.2"
19808  */
19809  __pyx_t_1 = __Pyx_Import(__pyx_n_s_collections, 0, -1); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 30; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19810  __Pyx_GOTREF(__pyx_t_1);
19811  if (PyDict_SetItem(__pyx_d, __pyx_n_s_collections, __pyx_t_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 30; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19812  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19813 
19814  /* "PyClical.pyx":32
19815  * import collections
19816  *
19817  * __version__ = "0.8.2" # <<<<<<<<<<<<<<
19818  *
19819  * from PyClical cimport *
19820  */
19821  if (PyDict_SetItem(__pyx_d, __pyx_n_s_version, __pyx_kp_s_0_8_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 32; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19822 
19823  /* "PyClical.pyx":404
19824  * return index_set_to_str( self.unwrap() ).c_str()
19825  *
19826  * def index_set_hidden_doctests(): # <<<<<<<<<<<<<<
19827  * """
19828  * Tests for functions that Doctest cannot see.
19829  */
19830  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_8PyClical_1index_set_hidden_doctests, NULL, __pyx_n_s_PyClical); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 404; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19831  __Pyx_GOTREF(__pyx_t_1);
19832  if (PyDict_SetItem(__pyx_d, __pyx_n_s_index_set_hidden_doctests, __pyx_t_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 404; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19833  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19834 
19835  /* "PyClical.pyx":1243
19836  * return clifford_to_str( self.unwrap() ).c_str()
19837  *
19838  * def clifford_hidden_doctests(): # <<<<<<<<<<<<<<
19839  * """
19840  * Tests for functions that Doctest cannot see.
19841  */
19842  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_8PyClical_9clifford_hidden_doctests, NULL, __pyx_n_s_PyClical); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1243; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19843  __Pyx_GOTREF(__pyx_t_1);
19844  if (PyDict_SetItem(__pyx_d, __pyx_n_s_clifford_hidden_doctests, __pyx_t_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1243; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19845  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19846 
19847  /* "PyClical.pyx":1856
19848  *
19849  * # Some abbreviations.
19850  * tau = atan(clifford(1.0)) * 8.0 # <<<<<<<<<<<<<<
19851  * pi = tau / 2.0
19852  *
19853  */
19854  __pyx_t_1 = __Pyx_PyObject_Call(((PyObject *)__pyx_ptype_8PyClical_clifford), __pyx_tuple__12, NULL); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1856; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19855  __Pyx_GOTREF(__pyx_t_1);
19856  __pyx_t_2 = __pyx_f_8PyClical_atan(__pyx_t_1, 0, NULL); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1856; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19857  __Pyx_GOTREF(__pyx_t_2);
19858  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
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19860  __Pyx_GOTREF(__pyx_t_1);
19861  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
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19863  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19864 
19865  /* "PyClical.pyx":1857
19866  * # Some abbreviations.
19867  * tau = atan(clifford(1.0)) * 8.0
19868  * pi = tau / 2.0 # <<<<<<<<<<<<<<
19869  *
19870  * cl = clifford
19871  */
19872  __pyx_t_1 = __Pyx_GetModuleGlobalName(__pyx_n_s_tau); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1857; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19873  __Pyx_GOTREF(__pyx_t_1);
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19875  __Pyx_GOTREF(__pyx_t_2);
19876  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
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19878  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
19879 
19880  /* "PyClical.pyx":1859
19881  * pi = tau / 2.0
19882  *
19883  * cl = clifford # <<<<<<<<<<<<<<
19884  * """
19885  * Abbreviation for clifford.
19886  */
19887  if (PyDict_SetItem(__pyx_d, __pyx_n_s_cl, ((PyObject *)__pyx_ptype_8PyClical_clifford)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1859; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19888 
19889  /* "PyClical.pyx":1879
19890  * """
19891  *
19892  * ist = index_set # <<<<<<<<<<<<<<
19893  * """
19894  * Abbreviation for index_set.
19895  */
19896  if (PyDict_SetItem(__pyx_d, __pyx_n_s_ist, ((PyObject *)__pyx_ptype_8PyClical_index_set)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1879; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19897 
19898  /* "PyClical.pyx":1887
19899  * """
19900  *
19901  * def e(obj): # <<<<<<<<<<<<<<
19902  * """
19903  * Abbreviation for clifford(index_set(obj)).
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19906  __Pyx_GOTREF(__pyx_t_2);
19907  if (PyDict_SetItem(__pyx_d, __pyx_n_s_e, __pyx_t_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1887; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19908  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
19909 
19910  /* "PyClical.pyx":1900
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19913  * def istpq(p, q): # <<<<<<<<<<<<<<
19914  * """
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19916  */
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19918  __Pyx_GOTREF(__pyx_t_2);
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19920  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
19921 
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19923  * return index_set(set(range(-q,p+1)))
19924  *
19925  * ninf3 = e(4) + e(-1) # Null infinity point in 3D Conformal Geometric Algebra [DL]. # <<<<<<<<<<<<<<
19926  * nbar3 = e(4) - e(-1) # Null bar point in 3D Conformal Geometric Algebra [DL].
19927  *
19928  */
19929  __pyx_t_2 = __Pyx_GetModuleGlobalName(__pyx_n_s_e); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1909; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19930  __Pyx_GOTREF(__pyx_t_2);
19931  __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_2, __pyx_tuple__17, NULL); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1909; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19932  __Pyx_GOTREF(__pyx_t_1);
19933  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
19934  __pyx_t_2 = __Pyx_GetModuleGlobalName(__pyx_n_s_e); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1909; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19935  __Pyx_GOTREF(__pyx_t_2);
19936  __pyx_t_3 = __Pyx_PyObject_Call(__pyx_t_2, __pyx_tuple__18, NULL); if (unlikely(!__pyx_t_3)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1909; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19937  __Pyx_GOTREF(__pyx_t_3);
19938  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
19939  __pyx_t_2 = PyNumber_Add(__pyx_t_1, __pyx_t_3); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1909; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19940  __Pyx_GOTREF(__pyx_t_2);
19941  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19942  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
19943  if (PyDict_SetItem(__pyx_d, __pyx_n_s_ninf3, __pyx_t_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1909; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19944  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
19945 
19946  /* "PyClical.pyx":1910
19947  *
19948  * ninf3 = e(4) + e(-1) # Null infinity point in 3D Conformal Geometric Algebra [DL].
19949  * nbar3 = e(4) - e(-1) # Null bar point in 3D Conformal Geometric Algebra [DL]. # <<<<<<<<<<<<<<
19950  *
19951  * # Doctest interface.
19952  */
19953  __pyx_t_2 = __Pyx_GetModuleGlobalName(__pyx_n_s_e); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1910; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19954  __Pyx_GOTREF(__pyx_t_2);
19955  __pyx_t_3 = __Pyx_PyObject_Call(__pyx_t_2, __pyx_tuple__19, NULL); if (unlikely(!__pyx_t_3)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1910; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19956  __Pyx_GOTREF(__pyx_t_3);
19957  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
19958  __pyx_t_2 = __Pyx_GetModuleGlobalName(__pyx_n_s_e); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1910; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19959  __Pyx_GOTREF(__pyx_t_2);
19960  __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_2, __pyx_tuple__20, NULL); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1910; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19961  __Pyx_GOTREF(__pyx_t_1);
19962  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
19963  __pyx_t_2 = PyNumber_Subtract(__pyx_t_3, __pyx_t_1); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1910; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19964  __Pyx_GOTREF(__pyx_t_2);
19965  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
19966  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19967  if (PyDict_SetItem(__pyx_d, __pyx_n_s_nbar3, __pyx_t_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1910; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19968  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
19969 
19970  /* "PyClical.pyx":1913
19971  *
19972  * # Doctest interface.
19973  * def _test(): # <<<<<<<<<<<<<<
19974  * import PyClical, doctest
19975  * return doctest.testmod(PyClical)
19976  */
19977  __pyx_t_2 = PyCFunction_NewEx(&__pyx_mdef_8PyClical_87_test, NULL, __pyx_n_s_PyClical); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1913; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19978  __Pyx_GOTREF(__pyx_t_2);
19979  if (PyDict_SetItem(__pyx_d, __pyx_n_s_test, __pyx_t_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1913; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19980  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
19981 
19982  /* "PyClical.pyx":1917
19983  * return doctest.testmod(PyClical)
19984  *
19985  * if __name__ == "__main__": # <<<<<<<<<<<<<<
19986  * _test()
19987  */
19988  __pyx_t_2 = __Pyx_GetModuleGlobalName(__pyx_n_s_name); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1917; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19989  __Pyx_GOTREF(__pyx_t_2);
19990  __pyx_t_4 = (__Pyx_PyString_Equals(__pyx_t_2, __pyx_n_s_main, Py_EQ)); if (unlikely(__pyx_t_4 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1917; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
19991  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
19992  if (__pyx_t_4) {
19993 
19994  /* "PyClical.pyx":1918
19995  *
19996  * if __name__ == "__main__":
19997  * _test() # <<<<<<<<<<<<<<
19998  */
19999  __pyx_t_1 = __Pyx_GetModuleGlobalName(__pyx_n_s_test); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1918; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20000  __Pyx_GOTREF(__pyx_t_1);
20001  __pyx_t_3 = NULL;
20002  if (CYTHON_COMPILING_IN_CPYTHON && unlikely(PyMethod_Check(__pyx_t_1))) {
20003  __pyx_t_3 = PyMethod_GET_SELF(__pyx_t_1);
20004  if (likely(__pyx_t_3)) {
20005  PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_1);
20006  __Pyx_INCREF(__pyx_t_3);
20007  __Pyx_INCREF(function);
20008  __Pyx_DECREF_SET(__pyx_t_1, function);
20009  }
20010  }
20011  if (__pyx_t_3) {
20012  __pyx_t_2 = __Pyx_PyObject_CallOneArg(__pyx_t_1, __pyx_t_3); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1918; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20013  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
20014  } else {
20015  __pyx_t_2 = __Pyx_PyObject_CallNoArg(__pyx_t_1); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1918; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20016  }
20017  __Pyx_GOTREF(__pyx_t_2);
20018  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
20019  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
20020 
20021  /* "PyClical.pyx":1917
20022  * return doctest.testmod(PyClical)
20023  *
20024  * if __name__ == "__main__": # <<<<<<<<<<<<<<
20025  * _test()
20026  */
20027  }
20028 
20029  /* "PyClical.pyx":1
20030  * # -*- coding: utf-8 -*- # <<<<<<<<<<<<<<
20031  * # distutils: language = c++
20032  * #
20033  */
20034  __pyx_t_2 = PyDict_New(); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20035  __Pyx_GOTREF(__pyx_t_2);
20036  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set_copy_line_64, __pyx_kp_u_Copy_this_index_set_object_s_in) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20037  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set___setitem___line_177, __pyx_kp_u_Set_the_value_of_an_index_set_o) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20038  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set___getitem___line_189, __pyx_kp_u_Get_the_value_of_an_index_set_o) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20039  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set___iter___line_227, __pyx_kp_u_Iterate_over_the_indices_of_an) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20040  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set___invert___line_238, __pyx_kp_u_Set_complement_not_print_index) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20041  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set___xor___line_247, __pyx_kp_u_Symmetric_set_difference_exclus) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20042  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set___ixor___line_258, __pyx_kp_u_Symmetric_set_difference_exclus_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20043  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set___and___line_269, __pyx_kp_u_Set_intersection_and_print_inde) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20044  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set___iand___line_280, __pyx_kp_u_Set_intersection_and_x_index_se) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20045  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set___or___line_291, __pyx_kp_u_Set_union_or_print_index_set_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20046  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set___ior___line_302, __pyx_kp_u_Set_union_or_x_index_set_1_x_in) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20047  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set_count_line_313, __pyx_kp_u_Cardinality_Number_of_indices_i) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20048  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set_count_neg_line_322, __pyx_kp_u_Number_of_negative_indices_incl) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20049  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set_count_pos_line_331, __pyx_kp_u_Number_of_positive_indices_incl) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20050  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set_min_line_340, __pyx_kp_u_Minimum_member_index_set_1_1_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20051  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set_max_line_349, __pyx_kp_u_Maximum_member_index_set_1_1_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20052  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set_sign_of_mult_line_364, __pyx_kp_u_Sign_of_geometric_product_of_tw) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20053  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set_sign_of_square_line_37, __pyx_kp_u_Sign_of_geometric_square_of_a_C) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20054  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set___repr___line_382, __pyx_kp_u_The_official_string_representat) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20055  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set___str___line_393, __pyx_kp_u_The_informal_string_representat) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20056  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_index_set_hidden_doctests_line_4, __pyx_kp_u_Tests_for_functions_that_Doctes) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20057  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_compare_line_490, __pyx_kp_u_lexicographic_compare_eg_3_4_5) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20058  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_min_neg_line_502, __pyx_kp_u_Minimum_negative_index_or_0_if) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20059  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_max_pos_line_511, __pyx_kp_u_Maximum_positive_index_or_0_if) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20060  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_copy_line_554, __pyx_kp_u_Copy_this_clifford_object_x_cli) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20061  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___iter___line_637, __pyx_kp_u_Not_applicable_for_a_in_cliffor) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20062  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_reframe_line_648, __pyx_kp_u_Put_self_into_a_larger_frame_co) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20063  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___getitem___line_706, __pyx_kp_u_Subscripting_map_from_index_set) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20064  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___neg___line_721, __pyx_kp_u_Unary_print_clifford_1_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20065  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___pos___line_730, __pyx_kp_u_Unary_print_clifford_1_1_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20066  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___add___line_739, __pyx_kp_u_Geometric_sum_print_clifford_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20067  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___iadd___line_750, __pyx_kp_u_Geometric_sum_x_clifford_1_x_cl) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20068  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___sub___line_759, __pyx_kp_u_Geometric_difference_print_clif) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20069  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___isub___line_770, __pyx_kp_u_Geometric_difference_x_clifford) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20070  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___mul___line_779, __pyx_kp_u_Geometric_product_print_cliffor) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20071  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___imul___line_792, __pyx_kp_u_Geometric_product_x_clifford_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20072  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___mod___line_805, __pyx_kp_u_Contraction_print_clifford_1_cl) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20073  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___imod___line_820, __pyx_kp_u_Contraction_x_clifford_1_x_clif) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20074  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___and___line_835, __pyx_kp_u_Inner_product_print_clifford_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20075  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___iand___line_850, __pyx_kp_u_Inner_product_x_clifford_1_x_cl) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20076  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___xor___line_865, __pyx_kp_u_Outer_product_print_clifford_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20077  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___ixor___line_880, __pyx_kp_u_Outer_product_x_clifford_1_x_cl) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20078  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___div___line_895, __pyx_kp_u_Geometric_quotient_print_cliffo) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20079  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___idiv___line_910, __pyx_kp_u_Geometric_quotient_x_clifford_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20080  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_inv_line_925, __pyx_kp_u_Geometric_multiplicative_invers) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20081  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___or___line_938, __pyx_kp_u_Transform_left_hand_side_using) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20082  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___ior___line_949, __pyx_kp_u_Transform_left_hand_side_using_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20083  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___pow___line_960, __pyx_kp_u_Power_self_to_the_m_x_clifford) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20084  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_pow_line_979, __pyx_kp_u_Power_self_to_the_m_x_clifford_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20085  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_outer_pow_line_1003, __pyx_kp_u_Outer_product_power_x_clifford) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20086  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___call___line_1019, __pyx_kp_u_Pure_grade_vector_part_print_cl) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20087  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_scalar_line_1038, __pyx_kp_u_Scalar_part_clifford_1_1_1_2_sc) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20088  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_pure_line_1049, __pyx_kp_u_Pure_part_print_clifford_1_1_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20089  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_even_line_1060, __pyx_kp_u_Even_part_of_multivector_sum_of) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20090  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_odd_line_1069, __pyx_kp_u_Odd_part_of_multivector_sum_of) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20091  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_vector_part_line_1078, __pyx_kp_u_Vector_part_of_multivector_as_a) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20092  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_involute_line_1106, __pyx_kp_u_Main_involution_each_i_is_repla) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20093  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_reverse_line_1122, __pyx_kp_u_Reversion_eg_clifford_1_cliffor) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20094  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_conj_line_1137, __pyx_kp_u_Conjugation_reverse_o_involute) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20095  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_quad_line_1152, __pyx_kp_u_Quadratic_form_rev_x_x_0_print) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20096  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_norm_line_1163, __pyx_kp_u_Norm_sum_of_squares_of_coordina) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20097  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_abs_line_1174, __pyx_kp_u_Absolute_value_square_root_of_n) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20098  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_max_abs_line_1183, __pyx_kp_u_Maximum_of_absolute_values_of_c) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20099  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_truncated_line_1194, __pyx_kp_u_Remove_all_terms_of_self_with_r) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20100  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_isnan_line_1205, __pyx_kp_u_Check_if_a_multivector_contains) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20101  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_frame_line_1214, __pyx_kp_u_Subalgebra_generated_by_all_gen) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20102  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___repr___line_1225, __pyx_kp_u_The_official_string_representat_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20103  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford___str___line_1234, __pyx_kp_u_The_informal_string_representat_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20104  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_clifford_hidden_doctests_line_12, __pyx_kp_u_Tests_for_functions_that_Doctes_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20105  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_inv_line_1329, __pyx_kp_u_Geometric_multiplicative_invers_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20106  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_scalar_line_1344, __pyx_kp_u_Scalar_part_scalar_clifford_1_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20107  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_real_line_1355, __pyx_kp_u_Real_part_synonym_for_scalar_pa) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20108  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_imag_line_1366, __pyx_kp_u_Imaginary_part_deprecated_alway) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20109  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_pure_line_1377, __pyx_kp_u_Pure_part_print_pure_clifford_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20110  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_even_line_1388, __pyx_kp_u_Even_part_of_multivector_sum_of_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20111  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_odd_line_1397, __pyx_kp_u_Odd_part_of_multivector_sum_of_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20112  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_involute_line_1406, __pyx_kp_u_Main_involution_each_i_is_repla_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20113  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_reverse_line_1421, __pyx_kp_u_Reversion_eg_1_2_2_1_print_reve) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20114  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_conj_line_1436, __pyx_kp_u_Conjugation_reverse_o_involute_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20115  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_quad_line_1451, __pyx_kp_u_Quadratic_form_rev_x_x_0_print_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20116  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_norm_line_1462, __pyx_kp_u_norm_sum_of_squares_of_coordina) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20117  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_abs_line_1473, __pyx_kp_u_Absolute_value_of_multivector_m) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20118  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_max_abs_line_1482, __pyx_kp_u_Maximum_absolute_value_of_coord) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20119  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_pow_line_1494, __pyx_kp_u_Integer_power_of_multivector_ob) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20120  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_outer_pow_line_1518, __pyx_kp_u_Outer_product_power_of_multivec) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20121  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_complexifier_line_1527, __pyx_kp_u_Square_root_of_1_which_commutes) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20122  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_sqrt_line_1542, __pyx_kp_u_Square_root_of_multivector_with) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20123  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_exp_line_1565, __pyx_kp_u_Exponential_of_multivector_x_cl) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20124  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_log_line_1579, __pyx_kp_u_Natural_logarithm_of_multivecto) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20125  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_cos_line_1602, __pyx_kp_u_Cosine_of_multivector_with_opti) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20126  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_acos_line_1619, __pyx_kp_u_Inverse_cosine_of_multivector_w) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20127  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_cosh_line_1640, __pyx_kp_u_Hyperbolic_cosine_of_multivecto) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20128  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_acosh_line_1656, __pyx_kp_u_Inverse_hyperbolic_cosine_of_mu) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20129  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_sin_line_1679, __pyx_kp_u_Sine_of_multivector_with_option) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20130  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_asin_line_1698, __pyx_kp_u_Inverse_sine_of_multivector_wit) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20131  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_sinh_line_1719, __pyx_kp_u_Hyperbolic_sine_of_multivector) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20132  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_asinh_line_1733, __pyx_kp_u_Inverse_hyperbolic_sine_of_mult) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20133  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_tan_line_1752, __pyx_kp_u_Tangent_of_multivector_with_opt) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20134  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_atan_line_1769, __pyx_kp_u_Inverse_tangent_of_multivector) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20135  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_tanh_line_1786, __pyx_kp_u_Hyperbolic_tangent_of_multivect) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20136  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_atanh_line_1798, __pyx_kp_u_Inverse_hyperbolic_tangent_of_m) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20137  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_random_clifford_line_1815, __pyx_kp_u_Random_multivector_within_a_fra) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20138  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_cga3_line_1824, __pyx_kp_u_Convert_Euclidean_3D_multivecto) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20139  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_cga3std_line_1833, __pyx_kp_u_Convert_CGA3_null_vector_to_sta) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20140  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_agc3_line_1844, __pyx_kp_u_Convert_CGA3_null_vector_to_Euc) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20141  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_e_line_1887, __pyx_kp_u_Abbreviation_for_clifford_index) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20142  if (PyDict_SetItem(__pyx_t_2, __pyx_kp_u_istpq_line_1900, __pyx_kp_u_Abbreviation_for_index_set_q_p) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20143  if (PyDict_SetItem(__pyx_d, __pyx_n_s_test_2, __pyx_t_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
20144  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
20145 
20146  /*--- Wrapped vars code ---*/
20147 
20148  goto __pyx_L0;
20149  __pyx_L1_error:;
20150  __Pyx_XDECREF(__pyx_t_1);
20151  __Pyx_XDECREF(__pyx_t_2);
20152  __Pyx_XDECREF(__pyx_t_3);
20153  if (__pyx_m) {
20154  if (__pyx_d) {
20155  __Pyx_AddTraceback("init PyClical", __pyx_clineno, __pyx_lineno, __pyx_filename);
20156  }
20157  Py_DECREF(__pyx_m); __pyx_m = 0;
20158  } else if (!PyErr_Occurred()) {
20159  PyErr_SetString(PyExc_ImportError, "init PyClical");
20160  }
20161  __pyx_L0:;
20162  __Pyx_RefNannyFinishContext();
20163  #if PY_MAJOR_VERSION < 3
20164  return;
20165  #else
20166  return __pyx_m;
20167  #endif
20168 }
20169 
20170 /* --- Runtime support code --- */
20171 #if CYTHON_REFNANNY
20172 static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname) {
20173  PyObject *m = NULL, *p = NULL;
20174  void *r = NULL;
20175  m = PyImport_ImportModule((char *)modname);
20176  if (!m) goto end;
20177  p = PyObject_GetAttrString(m, (char *)"RefNannyAPI");
20178  if (!p) goto end;
20179  r = PyLong_AsVoidPtr(p);
20180 end:
20181  Py_XDECREF(p);
20182  Py_XDECREF(m);
20183  return (__Pyx_RefNannyAPIStruct *)r;
20184 }
20185 #endif
20186 
20187 static PyObject *__Pyx_GetBuiltinName(PyObject *name) {
20188  PyObject* result = __Pyx_PyObject_GetAttrStr(__pyx_b, name);
20189  if (unlikely(!result)) {
20190  PyErr_Format(PyExc_NameError,
20191 #if PY_MAJOR_VERSION >= 3
20192  "name '%U' is not defined", name);
20193 #else
20194  "name '%.200s' is not defined", PyString_AS_STRING(name));
20195 #endif
20196  }
20197  return result;
20198 }
20199 
20200 #if CYTHON_COMPILING_IN_CPYTHON
20201 static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) {
20202  PyObject *result;
20203  ternaryfunc call = func->ob_type->tp_call;
20204  if (unlikely(!call))
20205  return PyObject_Call(func, arg, kw);
20206  if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
20207  return NULL;
20208  result = (*call)(func, arg, kw);
20209  Py_LeaveRecursiveCall();
20210  if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
20211  PyErr_SetString(
20212  PyExc_SystemError,
20213  "NULL result without error in PyObject_Call");
20214  }
20215  return result;
20216 }
20217 #endif
20218 
20219 static CYTHON_INLINE void __Pyx_ErrRestore(PyObject *type, PyObject *value, PyObject *tb) {
20220 #if CYTHON_COMPILING_IN_CPYTHON
20221  PyObject *tmp_type, *tmp_value, *tmp_tb;
20222  PyThreadState *tstate = PyThreadState_GET();
20223  tmp_type = tstate->curexc_type;
20224  tmp_value = tstate->curexc_value;
20225  tmp_tb = tstate->curexc_traceback;
20226  tstate->curexc_type = type;
20227  tstate->curexc_value = value;
20228  tstate->curexc_traceback = tb;
20229  Py_XDECREF(tmp_type);
20230  Py_XDECREF(tmp_value);
20231  Py_XDECREF(tmp_tb);
20232 #else
20233  PyErr_Restore(type, value, tb);
20234 #endif
20235 }
20236 static CYTHON_INLINE void __Pyx_ErrFetch(PyObject **type, PyObject **value, PyObject **tb) {
20237 #if CYTHON_COMPILING_IN_CPYTHON
20238  PyThreadState *tstate = PyThreadState_GET();
20239  *type = tstate->curexc_type;
20240  *value = tstate->curexc_value;
20241  *tb = tstate->curexc_traceback;
20242  tstate->curexc_type = 0;
20243  tstate->curexc_value = 0;
20244  tstate->curexc_traceback = 0;
20245 #else
20246  PyErr_Fetch(type, value, tb);
20247 #endif
20248 }
20249 
20250 static void __Pyx_WriteUnraisable(const char *name, CYTHON_UNUSED int clineno,
20251  CYTHON_UNUSED int lineno, CYTHON_UNUSED const char *filename,
20252  int full_traceback, CYTHON_UNUSED int nogil) {
20253  PyObject *old_exc, *old_val, *old_tb;
20254  PyObject *ctx;
20255 #ifdef WITH_THREAD
20256  PyGILState_STATE state;
20257  if (nogil)
20258  state = PyGILState_Ensure();
20259 #endif
20260  __Pyx_ErrFetch(&old_exc, &old_val, &old_tb);
20261  if (full_traceback) {
20262  Py_XINCREF(old_exc);
20263  Py_XINCREF(old_val);
20264  Py_XINCREF(old_tb);
20265  __Pyx_ErrRestore(old_exc, old_val, old_tb);
20266  PyErr_PrintEx(1);
20267  }
20268  #if PY_MAJOR_VERSION < 3
20269  ctx = PyString_FromString(name);
20270  #else
20271  ctx = PyUnicode_FromString(name);
20272  #endif
20273  __Pyx_ErrRestore(old_exc, old_val, old_tb);
20274  if (!ctx) {
20275  PyErr_WriteUnraisable(Py_None);
20276  } else {
20277  PyErr_WriteUnraisable(ctx);
20278  Py_DECREF(ctx);
20279  }
20280 #ifdef WITH_THREAD
20281  if (nogil)
20282  PyGILState_Release(state);
20283 #endif
20284 }
20285 
20286 #if CYTHON_COMPILING_IN_CPYTHON
20287 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) {
20288  PyObject *self, *result;
20289  PyCFunction cfunc;
20290  cfunc = PyCFunction_GET_FUNCTION(func);
20291  self = PyCFunction_GET_SELF(func);
20292  if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
20293  return NULL;
20294  result = cfunc(self, arg);
20295  Py_LeaveRecursiveCall();
20296  if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
20297  PyErr_SetString(
20298  PyExc_SystemError,
20299  "NULL result without error in PyObject_Call");
20300  }
20301  return result;
20302 }
20303 #endif
20304 
20305 #if CYTHON_COMPILING_IN_CPYTHON
20306 static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) {
20307  PyObject *result;
20308  PyObject *args = PyTuple_New(1);
20309  if (unlikely(!args)) return NULL;
20310  Py_INCREF(arg);
20311  PyTuple_SET_ITEM(args, 0, arg);
20312  result = __Pyx_PyObject_Call(func, args, NULL);
20313  Py_DECREF(args);
20314  return result;
20315 }
20316 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
20317 #ifdef __Pyx_CyFunction_USED
20318  if (likely(PyCFunction_Check(func) || PyObject_TypeCheck(func, __pyx_CyFunctionType))) {
20319 #else
20320  if (likely(PyCFunction_Check(func))) {
20321 #endif
20322  if (likely(PyCFunction_GET_FLAGS(func) & METH_O)) {
20323  return __Pyx_PyObject_CallMethO(func, arg);
20324  }
20325  }
20326  return __Pyx__PyObject_CallOneArg(func, arg);
20327 }
20328 #else
20329 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
20330  PyObject *result;
20331  PyObject *args = PyTuple_Pack(1, arg);
20332  if (unlikely(!args)) return NULL;
20333  result = __Pyx_PyObject_Call(func, args, NULL);
20334  Py_DECREF(args);
20335  return result;
20336 }
20337 #endif
20338 
20339 #if CYTHON_COMPILING_IN_CPYTHON
20340 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func) {
20341 #ifdef __Pyx_CyFunction_USED
20342  if (likely(PyCFunction_Check(func) || PyObject_TypeCheck(func, __pyx_CyFunctionType))) {
20343 #else
20344  if (likely(PyCFunction_Check(func))) {
20345 #endif
20346  if (likely(PyCFunction_GET_FLAGS(func) & METH_NOARGS)) {
20347  return __Pyx_PyObject_CallMethO(func, NULL);
20348  }
20349  }
20350  return __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL);
20351 }
20352 #endif
20353 
20354 static void __Pyx_RaiseDoubleKeywordsError(
20355  const char* func_name,
20356  PyObject* kw_name)
20357 {
20358  PyErr_Format(PyExc_TypeError,
20359  #if PY_MAJOR_VERSION >= 3
20360  "%s() got multiple values for keyword argument '%U'", func_name, kw_name);
20361  #else
20362  "%s() got multiple values for keyword argument '%s'", func_name,
20363  PyString_AsString(kw_name));
20364  #endif
20365 }
20366 
20367 static int __Pyx_ParseOptionalKeywords(
20368  PyObject *kwds,
20369  PyObject **argnames[],
20370  PyObject *kwds2,
20371  PyObject *values[],
20372  Py_ssize_t num_pos_args,
20373  const char* function_name)
20374 {
20375  PyObject *key = 0, *value = 0;
20376  Py_ssize_t pos = 0;
20377  PyObject*** name;
20378  PyObject*** first_kw_arg = argnames + num_pos_args;
20379  while (PyDict_Next(kwds, &pos, &key, &value)) {
20380  name = first_kw_arg;
20381  while (*name && (**name != key)) name++;
20382  if (*name) {
20383  values[name-argnames] = value;
20384  continue;
20385  }
20386  name = first_kw_arg;
20387  #if PY_MAJOR_VERSION < 3
20388  if (likely(PyString_CheckExact(key)) || likely(PyString_Check(key))) {
20389  while (*name) {
20390  if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key))
20391  && _PyString_Eq(**name, key)) {
20392  values[name-argnames] = value;
20393  break;
20394  }
20395  name++;
20396  }
20397  if (*name) continue;
20398  else {
20399  PyObject*** argname = argnames;
20400  while (argname != first_kw_arg) {
20401  if ((**argname == key) || (
20402  (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key))
20403  && _PyString_Eq(**argname, key))) {
20404  goto arg_passed_twice;
20405  }
20406  argname++;
20407  }
20408  }
20409  } else
20410  #endif
20411  if (likely(PyUnicode_Check(key))) {
20412  while (*name) {
20413  int cmp = (**name == key) ? 0 :
20414  #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
20415  (PyUnicode_GET_SIZE(**name) != PyUnicode_GET_SIZE(key)) ? 1 :
20416  #endif
20417  PyUnicode_Compare(**name, key);
20418  if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
20419  if (cmp == 0) {
20420  values[name-argnames] = value;
20421  break;
20422  }
20423  name++;
20424  }
20425  if (*name) continue;
20426  else {
20427  PyObject*** argname = argnames;
20428  while (argname != first_kw_arg) {
20429  int cmp = (**argname == key) ? 0 :
20430  #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
20431  (PyUnicode_GET_SIZE(**argname) != PyUnicode_GET_SIZE(key)) ? 1 :
20432  #endif
20433  PyUnicode_Compare(**argname, key);
20434  if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
20435  if (cmp == 0) goto arg_passed_twice;
20436  argname++;
20437  }
20438  }
20439  } else
20440  goto invalid_keyword_type;
20441  if (kwds2) {
20442  if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
20443  } else {
20444  goto invalid_keyword;
20445  }
20446  }
20447  return 0;
20448 arg_passed_twice:
20449  __Pyx_RaiseDoubleKeywordsError(function_name, key);
20450  goto bad;
20451 invalid_keyword_type:
20452  PyErr_Format(PyExc_TypeError,
20453  "%.200s() keywords must be strings", function_name);
20454  goto bad;
20455 invalid_keyword:
20456  PyErr_Format(PyExc_TypeError,
20457  #if PY_MAJOR_VERSION < 3
20458  "%.200s() got an unexpected keyword argument '%.200s'",
20459  function_name, PyString_AsString(key));
20460  #else
20461  "%s() got an unexpected keyword argument '%U'",
20462  function_name, key);
20463  #endif
20464 bad:
20465  return -1;
20466 }
20467 
20468 static void __Pyx_RaiseArgtupleInvalid(
20469  const char* func_name,
20470  int exact,
20471  Py_ssize_t num_min,
20472  Py_ssize_t num_max,
20473  Py_ssize_t num_found)
20474 {
20475  Py_ssize_t num_expected;
20476  const char *more_or_less;
20477  if (num_found < num_min) {
20478  num_expected = num_min;
20479  more_or_less = "at least";
20480  } else {
20481  num_expected = num_max;
20482  more_or_less = "at most";
20483  }
20484  if (exact) {
20485  more_or_less = "exactly";
20486  }
20487  PyErr_Format(PyExc_TypeError,
20488  "%.200s() takes %.8s %" CYTHON_FORMAT_SSIZE_T "d positional argument%.1s (%" CYTHON_FORMAT_SSIZE_T "d given)",
20489  func_name, more_or_less, num_expected,
20490  (num_expected == 1) ? "" : "s", num_found);
20491 }
20492 
20493 static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name) {
20494  PyObject *result;
20495 #if CYTHON_COMPILING_IN_CPYTHON
20496  result = PyDict_GetItem(__pyx_d, name);
20497  if (likely(result)) {
20498  Py_INCREF(result);
20499  } else {
20500 #else
20501  result = PyObject_GetItem(__pyx_d, name);
20502  if (!result) {
20503  PyErr_Clear();
20504 #endif
20505  result = __Pyx_GetBuiltinName(name);
20506  }
20507  return result;
20508 }
20509 
20510 static CYTHON_INLINE void __Pyx_ExceptionSave(PyObject **type, PyObject **value, PyObject **tb) {
20511 #if CYTHON_COMPILING_IN_CPYTHON
20512  PyThreadState *tstate = PyThreadState_GET();
20513  *type = tstate->exc_type;
20514  *value = tstate->exc_value;
20515  *tb = tstate->exc_traceback;
20516  Py_XINCREF(*type);
20517  Py_XINCREF(*value);
20518  Py_XINCREF(*tb);
20519 #else
20520  PyErr_GetExcInfo(type, value, tb);
20521 #endif
20522 }
20523 static void __Pyx_ExceptionReset(PyObject *type, PyObject *value, PyObject *tb) {
20524 #if CYTHON_COMPILING_IN_CPYTHON
20525  PyObject *tmp_type, *tmp_value, *tmp_tb;
20526  PyThreadState *tstate = PyThreadState_GET();
20527  tmp_type = tstate->exc_type;
20528  tmp_value = tstate->exc_value;
20529  tmp_tb = tstate->exc_traceback;
20530  tstate->exc_type = type;
20531  tstate->exc_value = value;
20532  tstate->exc_traceback = tb;
20533  Py_XDECREF(tmp_type);
20534  Py_XDECREF(tmp_value);
20535  Py_XDECREF(tmp_tb);
20536 #else
20537  PyErr_SetExcInfo(type, value, tb);
20538 #endif
20539 }
20540 
20541 static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb) {
20542  PyObject *local_type, *local_value, *local_tb;
20543 #if CYTHON_COMPILING_IN_CPYTHON
20544  PyObject *tmp_type, *tmp_value, *tmp_tb;
20545  PyThreadState *tstate = PyThreadState_GET();
20546  local_type = tstate->curexc_type;
20547  local_value = tstate->curexc_value;
20548  local_tb = tstate->curexc_traceback;
20549  tstate->curexc_type = 0;
20550  tstate->curexc_value = 0;
20551  tstate->curexc_traceback = 0;
20552 #else
20553  PyErr_Fetch(&local_type, &local_value, &local_tb);
20554 #endif
20555  PyErr_NormalizeException(&local_type, &local_value, &local_tb);
20556 #if CYTHON_COMPILING_IN_CPYTHON
20557  if (unlikely(tstate->curexc_type))
20558 #else
20559  if (unlikely(PyErr_Occurred()))
20560 #endif
20561  goto bad;
20562  #if PY_MAJOR_VERSION >= 3
20563  if (local_tb) {
20564  if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0))
20565  goto bad;
20566  }
20567  #endif
20568  Py_XINCREF(local_tb);
20569  Py_XINCREF(local_type);
20570  Py_XINCREF(local_value);
20571  *type = local_type;
20572  *value = local_value;
20573  *tb = local_tb;
20574 #if CYTHON_COMPILING_IN_CPYTHON
20575  tmp_type = tstate->exc_type;
20576  tmp_value = tstate->exc_value;
20577  tmp_tb = tstate->exc_traceback;
20578  tstate->exc_type = local_type;
20579  tstate->exc_value = local_value;
20580  tstate->exc_traceback = local_tb;
20581  Py_XDECREF(tmp_type);
20582  Py_XDECREF(tmp_value);
20583  Py_XDECREF(tmp_tb);
20584 #else
20585  PyErr_SetExcInfo(local_type, local_value, local_tb);
20586 #endif
20587  return 0;
20588 bad:
20589  *type = 0;
20590  *value = 0;
20591  *tb = 0;
20592  Py_XDECREF(local_type);
20593  Py_XDECREF(local_value);
20594  Py_XDECREF(local_tb);
20595  return -1;
20596 }
20597 
20598 #if PY_MAJOR_VERSION < 3
20599 static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb,
20600  CYTHON_UNUSED PyObject *cause) {
20601  Py_XINCREF(type);
20602  if (!value || value == Py_None)
20603  value = NULL;
20604  else
20605  Py_INCREF(value);
20606  if (!tb || tb == Py_None)
20607  tb = NULL;
20608  else {
20609  Py_INCREF(tb);
20610  if (!PyTraceBack_Check(tb)) {
20611  PyErr_SetString(PyExc_TypeError,
20612  "raise: arg 3 must be a traceback or None");
20613  goto raise_error;
20614  }
20615  }
20616  if (PyType_Check(type)) {
20617 #if CYTHON_COMPILING_IN_PYPY
20618  if (!value) {
20619  Py_INCREF(Py_None);
20620  value = Py_None;
20621  }
20622 #endif
20623  PyErr_NormalizeException(&type, &value, &tb);
20624  } else {
20625  if (value) {
20626  PyErr_SetString(PyExc_TypeError,
20627  "instance exception may not have a separate value");
20628  goto raise_error;
20629  }
20630  value = type;
20631  type = (PyObject*) Py_TYPE(type);
20632  Py_INCREF(type);
20633  if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) {
20634  PyErr_SetString(PyExc_TypeError,
20635  "raise: exception class must be a subclass of BaseException");
20636  goto raise_error;
20637  }
20638  }
20639  __Pyx_ErrRestore(type, value, tb);
20640  return;
20641 raise_error:
20642  Py_XDECREF(value);
20643  Py_XDECREF(type);
20644  Py_XDECREF(tb);
20645  return;
20646 }
20647 #else
20648 static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) {
20649  PyObject* owned_instance = NULL;
20650  if (tb == Py_None) {
20651  tb = 0;
20652  } else if (tb && !PyTraceBack_Check(tb)) {
20653  PyErr_SetString(PyExc_TypeError,
20654  "raise: arg 3 must be a traceback or None");
20655  goto bad;
20656  }
20657  if (value == Py_None)
20658  value = 0;
20659  if (PyExceptionInstance_Check(type)) {
20660  if (value) {
20661  PyErr_SetString(PyExc_TypeError,
20662  "instance exception may not have a separate value");
20663  goto bad;
20664  }
20665  value = type;
20666  type = (PyObject*) Py_TYPE(value);
20667  } else if (PyExceptionClass_Check(type)) {
20668  PyObject *instance_class = NULL;
20669  if (value && PyExceptionInstance_Check(value)) {
20670  instance_class = (PyObject*) Py_TYPE(value);
20671  if (instance_class != type) {
20672  int is_subclass = PyObject_IsSubclass(instance_class, type);
20673  if (!is_subclass) {
20674  instance_class = NULL;
20675  } else if (unlikely(is_subclass == -1)) {
20676  goto bad;
20677  } else {
20678  type = instance_class;
20679  }
20680  }
20681  }
20682  if (!instance_class) {
20683  PyObject *args;
20684  if (!value)
20685  args = PyTuple_New(0);
20686  else if (PyTuple_Check(value)) {
20687  Py_INCREF(value);
20688  args = value;
20689  } else
20690  args = PyTuple_Pack(1, value);
20691  if (!args)
20692  goto bad;
20693  owned_instance = PyObject_Call(type, args, NULL);
20694  Py_DECREF(args);
20695  if (!owned_instance)
20696  goto bad;
20697  value = owned_instance;
20698  if (!PyExceptionInstance_Check(value)) {
20699  PyErr_Format(PyExc_TypeError,
20700  "calling %R should have returned an instance of "
20701  "BaseException, not %R",
20702  type, Py_TYPE(value));
20703  goto bad;
20704  }
20705  }
20706  } else {
20707  PyErr_SetString(PyExc_TypeError,
20708  "raise: exception class must be a subclass of BaseException");
20709  goto bad;
20710  }
20711 #if PY_VERSION_HEX >= 0x03030000
20712  if (cause) {
20713 #else
20714  if (cause && cause != Py_None) {
20715 #endif
20716  PyObject *fixed_cause;
20717  if (cause == Py_None) {
20718  fixed_cause = NULL;
20719  } else if (PyExceptionClass_Check(cause)) {
20720  fixed_cause = PyObject_CallObject(cause, NULL);
20721  if (fixed_cause == NULL)
20722  goto bad;
20723  } else if (PyExceptionInstance_Check(cause)) {
20724  fixed_cause = cause;
20725  Py_INCREF(fixed_cause);
20726  } else {
20727  PyErr_SetString(PyExc_TypeError,
20728  "exception causes must derive from "
20729  "BaseException");
20730  goto bad;
20731  }
20732  PyException_SetCause(value, fixed_cause);
20733  }
20734  PyErr_SetObject(type, value);
20735  if (tb) {
20736 #if CYTHON_COMPILING_IN_PYPY
20737  PyObject *tmp_type, *tmp_value, *tmp_tb;
20738  PyErr_Fetch(&tmp_type, &tmp_value, &tmp_tb);
20739  Py_INCREF(tb);
20740  PyErr_Restore(tmp_type, tmp_value, tb);
20741  Py_XDECREF(tmp_tb);
20742 #else
20743  PyThreadState *tstate = PyThreadState_GET();
20744  PyObject* tmp_tb = tstate->curexc_traceback;
20745  if (tb != tmp_tb) {
20746  Py_INCREF(tb);
20747  tstate->curexc_traceback = tb;
20748  Py_XDECREF(tmp_tb);
20749  }
20750 #endif
20751  }
20752 bad:
20753  Py_XDECREF(owned_instance);
20754  return;
20755 }
20756 #endif
20757 
20758 #if CYTHON_USE_PYLONG_INTERNALS
20759  #include "longintrepr.h"
20760 #endif
20761 
20762 #if CYTHON_COMPILING_IN_CPYTHON
20763 static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, CYTHON_UNUSED long intval, CYTHON_UNUSED int inplace) {
20764  #if PY_MAJOR_VERSION < 3
20765  if (likely(PyInt_CheckExact(op1))) {
20766  const long b = intval;
20767  long x;
20768  long a = PyInt_AS_LONG(op1);
20769  x = (long)((unsigned long)a + b);
20770  if (likely((x^a) >= 0 || (x^b) >= 0))
20771  return PyInt_FromLong(x);
20772  return PyLong_Type.tp_as_number->nb_add(op1, op2);
20773  }
20774  #endif
20775  #if CYTHON_USE_PYLONG_INTERNALS && PY_MAJOR_VERSION >= 3
20776  if (likely(PyLong_CheckExact(op1))) {
20777  const long b = intval;
20778  long a, x;
20779  const PY_LONG_LONG llb = intval;
20780  PY_LONG_LONG lla, llx;
20781  const digit* digits = ((PyLongObject*)op1)->ob_digit;
20782  const Py_ssize_t size = Py_SIZE(op1);
20783  if (likely(__Pyx_sst_abs(size) <= 1)) {
20784  a = likely(size) ? digits[0] : 0;
20785  if (size == -1) a = -a;
20786  } else {
20787  switch (size) {
20788  case -2:
20789  if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
20790  a = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
20791  break;
20792  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
20793  lla = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
20794  goto long_long;
20795  }
20796  case 2:
20797  if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
20798  a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
20799  break;
20800  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
20801  lla = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
20802  goto long_long;
20803  }
20804  case -3:
20805  if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
20806  a = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
20807  break;
20808  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
20809  lla = -(PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
20810  goto long_long;
20811  }
20812  case 3:
20813  if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
20814  a = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
20815  break;
20816  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
20817  lla = (PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
20818  goto long_long;
20819  }
20820  case -4:
20821  if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
20822  a = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
20823  break;
20824  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
20825  lla = -(PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
20826  goto long_long;
20827  }
20828  case 4:
20829  if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
20830  a = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
20831  break;
20832  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
20833  lla = (PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
20834  goto long_long;
20835  }
20836  default: return PyLong_Type.tp_as_number->nb_add(op1, op2);
20837  }
20838  }
20839  x = a + b;
20840  return PyLong_FromLong(x);
20841  long_long:
20842  llx = lla + llb;
20843  return PyLong_FromLongLong(llx);
20844  }
20845  #endif
20846  if (PyFloat_CheckExact(op1)) {
20847  const long b = intval;
20848  double a = PyFloat_AS_DOUBLE(op1);
20849  double result;
20850  PyFPE_START_PROTECT("add", return NULL)
20851  result = ((double)a) + (double)b;
20852  PyFPE_END_PROTECT(result)
20853  return PyFloat_FromDouble(result);
20854  }
20855  return (inplace ? PyNumber_InPlaceAdd : PyNumber_Add)(op1, op2);
20856 }
20857 #endif
20858 
20859 static CYTHON_INLINE int __Pyx_SetItemInt_Generic(PyObject *o, PyObject *j, PyObject *v) {
20860  int r;
20861  if (!j) return -1;
20862  r = PyObject_SetItem(o, j, v);
20863  Py_DECREF(j);
20864  return r;
20865 }
20866 static CYTHON_INLINE int __Pyx_SetItemInt_Fast(PyObject *o, Py_ssize_t i, PyObject *v, int is_list,
20867  CYTHON_NCP_UNUSED int wraparound, CYTHON_NCP_UNUSED int boundscheck) {
20868 #if CYTHON_COMPILING_IN_CPYTHON
20869  if (is_list || PyList_CheckExact(o)) {
20870  Py_ssize_t n = (!wraparound) ? i : ((likely(i >= 0)) ? i : i + PyList_GET_SIZE(o));
20871  if ((!boundscheck) || likely((n >= 0) & (n < PyList_GET_SIZE(o)))) {
20872  PyObject* old = PyList_GET_ITEM(o, n);
20873  Py_INCREF(v);
20874  PyList_SET_ITEM(o, n, v);
20875  Py_DECREF(old);
20876  return 1;
20877  }
20878  } else {
20879  PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;
20880  if (likely(m && m->sq_ass_item)) {
20881  if (wraparound && unlikely(i < 0) && likely(m->sq_length)) {
20882  Py_ssize_t l = m->sq_length(o);
20883  if (likely(l >= 0)) {
20884  i += l;
20885  } else {
20886  if (PyErr_ExceptionMatches(PyExc_OverflowError))
20887  PyErr_Clear();
20888  else
20889  return -1;
20890  }
20891  }
20892  return m->sq_ass_item(o, i, v);
20893  }
20894  }
20895 #else
20896 #if CYTHON_COMPILING_IN_PYPY
20897  if (is_list || (PySequence_Check(o) && !PyDict_Check(o))) {
20898 #else
20899  if (is_list || PySequence_Check(o)) {
20900 #endif
20901  return PySequence_SetItem(o, i, v);
20902  }
20903 #endif
20904  return __Pyx_SetItemInt_Generic(o, PyInt_FromSsize_t(i), v);
20905 }
20906 
20907 static void __Pyx_RaiseArgumentTypeInvalid(const char* name, PyObject *obj, PyTypeObject *type) {
20908  PyErr_Format(PyExc_TypeError,
20909  "Argument '%.200s' has incorrect type (expected %.200s, got %.200s)",
20910  name, type->tp_name, Py_TYPE(obj)->tp_name);
20911 }
20912 static CYTHON_INLINE int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed,
20913  const char *name, int exact)
20914 {
20915  if (unlikely(!type)) {
20916  PyErr_SetString(PyExc_SystemError, "Missing type object");
20917  return 0;
20918  }
20919  if (none_allowed && obj == Py_None) return 1;
20920  else if (exact) {
20921  if (likely(Py_TYPE(obj) == type)) return 1;
20922  #if PY_MAJOR_VERSION == 2
20923  else if ((type == &PyBaseString_Type) && likely(__Pyx_PyBaseString_CheckExact(obj))) return 1;
20924  #endif
20925  }
20926  else {
20927  if (likely(PyObject_TypeCheck(obj, type))) return 1;
20928  }
20929  __Pyx_RaiseArgumentTypeInvalid(name, obj, type);
20930  return 0;
20931 }
20932 
20933 static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) {
20934  PyObject *empty_list = 0;
20935  PyObject *module = 0;
20936  PyObject *global_dict = 0;
20937  PyObject *empty_dict = 0;
20938  PyObject *list;
20939  #if PY_VERSION_HEX < 0x03030000
20940  PyObject *py_import;
20941  py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import);
20942  if (!py_import)
20943  goto bad;
20944  #endif
20945  if (from_list)
20946  list = from_list;
20947  else {
20948  empty_list = PyList_New(0);
20949  if (!empty_list)
20950  goto bad;
20951  list = empty_list;
20952  }
20953  global_dict = PyModule_GetDict(__pyx_m);
20954  if (!global_dict)
20955  goto bad;
20956  empty_dict = PyDict_New();
20957  if (!empty_dict)
20958  goto bad;
20959  {
20960  #if PY_MAJOR_VERSION >= 3
20961  if (level == -1) {
20962  if (strchr(__Pyx_MODULE_NAME, '.')) {
20963  #if PY_VERSION_HEX < 0x03030000
20964  PyObject *py_level = PyInt_FromLong(1);
20965  if (!py_level)
20966  goto bad;
20967  module = PyObject_CallFunctionObjArgs(py_import,
20968  name, global_dict, empty_dict, list, py_level, NULL);
20969  Py_DECREF(py_level);
20970  #else
20971  module = PyImport_ImportModuleLevelObject(
20972  name, global_dict, empty_dict, list, 1);
20973  #endif
20974  if (!module) {
20975  if (!PyErr_ExceptionMatches(PyExc_ImportError))
20976  goto bad;
20977  PyErr_Clear();
20978  }
20979  }
20980  level = 0;
20981  }
20982  #endif
20983  if (!module) {
20984  #if PY_VERSION_HEX < 0x03030000
20985  PyObject *py_level = PyInt_FromLong(level);
20986  if (!py_level)
20987  goto bad;
20988  module = PyObject_CallFunctionObjArgs(py_import,
20989  name, global_dict, empty_dict, list, py_level, NULL);
20990  Py_DECREF(py_level);
20991  #else
20992  module = PyImport_ImportModuleLevelObject(
20993  name, global_dict, empty_dict, list, level);
20994  #endif
20995  }
20996  }
20997 bad:
20998  #if PY_VERSION_HEX < 0x03030000
20999  Py_XDECREF(py_import);
21000  #endif
21001  Py_XDECREF(empty_list);
21002  Py_XDECREF(empty_dict);
21003  return module;
21004 }
21005 
21006 static int __Pyx_SetVtable(PyObject *dict, void *vtable) {
21007 #if PY_VERSION_HEX >= 0x02070000
21008  PyObject *ob = PyCapsule_New(vtable, 0, 0);
21009 #else
21010  PyObject *ob = PyCObject_FromVoidPtr(vtable, 0);
21011 #endif
21012  if (!ob)
21013  goto bad;
21014  if (PyDict_SetItem(dict, __pyx_n_s_pyx_vtable, ob) < 0)
21015  goto bad;
21016  Py_DECREF(ob);
21017  return 0;
21018 bad:
21019  Py_XDECREF(ob);
21020  return -1;
21021 }
21022 
21023 #if CYTHON_COMPILING_IN_CPYTHON
21024 static PyObject* __Pyx_PyFloat_DivideObjC(PyObject *op1, PyObject *op2, double floatval, CYTHON_UNUSED int inplace) {
21025  const double b = floatval;
21026  double a, result;
21027  if (likely(PyFloat_CheckExact(op1))) {
21028  a = PyFloat_AS_DOUBLE(op1);
21029  } else
21030  #if PY_MAJOR_VERSION < 3
21031  if (likely(PyInt_CheckExact(op1))) {
21032  a = (double) PyInt_AS_LONG(op1);
21033  } else
21034  #endif
21035  if (likely(PyLong_CheckExact(op1))) {
21036  #if CYTHON_USE_PYLONG_INTERNALS && PY_MAJOR_VERSION >= 3
21037  const digit* digits = ((PyLongObject*)op1)->ob_digit;
21038  const Py_ssize_t size = Py_SIZE(op1);
21039  switch (size) {
21040  case 0: a = 0.0; break;
21041  case -1: a = -(double) digits[0]; break;
21042  case 1: a = (double) digits[0]; break;
21043  case -2:
21044  case 2:
21045  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (1 * PyLong_SHIFT < 53))) {
21046  a = (double) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21047  if ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53) || (a < (double) (1L<<53))) {
21048  if (size == -2)
21049  a = -a;
21050  break;
21051  }
21052  }
21053  case -3:
21054  case 3:
21055  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53))) {
21056  a = (double) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21057  if ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53) || (a < (double) (1L<<53))) {
21058  if (size == -3)
21059  a = -a;
21060  break;
21061  }
21062  }
21063  case -4:
21064  case 4:
21065  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53))) {
21066  a = (double) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21067  if ((8 * sizeof(unsigned long) < 53) || (4 * PyLong_SHIFT < 53) || (a < (double) (1L<<53))) {
21068  if (size == -4)
21069  a = -a;
21070  break;
21071  }
21072  }
21073  default:
21074  #else
21075  {
21076  #endif
21077  a = PyLong_AsDouble(op1);
21078  if (unlikely(a == -1.0 && PyErr_Occurred())) return NULL;
21079  }
21080  } else {
21081  return (inplace ? __Pyx_PyNumber_InPlaceDivide(op1, op2) : __Pyx_PyNumber_Divide(op1, op2));
21082  }
21083  PyFPE_START_PROTECT("divide", return NULL)
21084  result = a / b;
21085  PyFPE_END_PROTECT(result)
21086  return PyFloat_FromDouble(result);
21087 }
21088 #endif
21089 
21090 static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals) {
21091 #if CYTHON_COMPILING_IN_PYPY
21092  return PyObject_RichCompareBool(s1, s2, equals);
21093 #else
21094  if (s1 == s2) {
21095  return (equals == Py_EQ);
21096  } else if (PyBytes_CheckExact(s1) & PyBytes_CheckExact(s2)) {
21097  const char *ps1, *ps2;
21098  Py_ssize_t length = PyBytes_GET_SIZE(s1);
21099  if (length != PyBytes_GET_SIZE(s2))
21100  return (equals == Py_NE);
21101  ps1 = PyBytes_AS_STRING(s1);
21102  ps2 = PyBytes_AS_STRING(s2);
21103  if (ps1[0] != ps2[0]) {
21104  return (equals == Py_NE);
21105  } else if (length == 1) {
21106  return (equals == Py_EQ);
21107  } else {
21108  int result = memcmp(ps1, ps2, (size_t)length);
21109  return (equals == Py_EQ) ? (result == 0) : (result != 0);
21110  }
21111  } else if ((s1 == Py_None) & PyBytes_CheckExact(s2)) {
21112  return (equals == Py_NE);
21113  } else if ((s2 == Py_None) & PyBytes_CheckExact(s1)) {
21114  return (equals == Py_NE);
21115  } else {
21116  int result;
21117  PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
21118  if (!py_result)
21119  return -1;
21120  result = __Pyx_PyObject_IsTrue(py_result);
21121  Py_DECREF(py_result);
21122  return result;
21123  }
21124 #endif
21125 }
21126 
21127 static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals) {
21128 #if CYTHON_COMPILING_IN_PYPY
21129  return PyObject_RichCompareBool(s1, s2, equals);
21130 #else
21131 #if PY_MAJOR_VERSION < 3
21132  PyObject* owned_ref = NULL;
21133 #endif
21134  int s1_is_unicode, s2_is_unicode;
21135  if (s1 == s2) {
21136  goto return_eq;
21137  }
21138  s1_is_unicode = PyUnicode_CheckExact(s1);
21139  s2_is_unicode = PyUnicode_CheckExact(s2);
21140 #if PY_MAJOR_VERSION < 3
21141  if ((s1_is_unicode & (!s2_is_unicode)) && PyString_CheckExact(s2)) {
21142  owned_ref = PyUnicode_FromObject(s2);
21143  if (unlikely(!owned_ref))
21144  return -1;
21145  s2 = owned_ref;
21146  s2_is_unicode = 1;
21147  } else if ((s2_is_unicode & (!s1_is_unicode)) && PyString_CheckExact(s1)) {
21148  owned_ref = PyUnicode_FromObject(s1);
21149  if (unlikely(!owned_ref))
21150  return -1;
21151  s1 = owned_ref;
21152  s1_is_unicode = 1;
21153  } else if (((!s2_is_unicode) & (!s1_is_unicode))) {
21154  return __Pyx_PyBytes_Equals(s1, s2, equals);
21155  }
21156 #endif
21157  if (s1_is_unicode & s2_is_unicode) {
21158  Py_ssize_t length;
21159  int kind;
21160  void *data1, *data2;
21161  if (unlikely(__Pyx_PyUnicode_READY(s1) < 0) || unlikely(__Pyx_PyUnicode_READY(s2) < 0))
21162  return -1;
21163  length = __Pyx_PyUnicode_GET_LENGTH(s1);
21164  if (length != __Pyx_PyUnicode_GET_LENGTH(s2)) {
21165  goto return_ne;
21166  }
21167  kind = __Pyx_PyUnicode_KIND(s1);
21168  if (kind != __Pyx_PyUnicode_KIND(s2)) {
21169  goto return_ne;
21170  }
21171  data1 = __Pyx_PyUnicode_DATA(s1);
21172  data2 = __Pyx_PyUnicode_DATA(s2);
21173  if (__Pyx_PyUnicode_READ(kind, data1, 0) != __Pyx_PyUnicode_READ(kind, data2, 0)) {
21174  goto return_ne;
21175  } else if (length == 1) {
21176  goto return_eq;
21177  } else {
21178  int result = memcmp(data1, data2, (size_t)(length * kind));
21179  #if PY_MAJOR_VERSION < 3
21180  Py_XDECREF(owned_ref);
21181  #endif
21182  return (equals == Py_EQ) ? (result == 0) : (result != 0);
21183  }
21184  } else if ((s1 == Py_None) & s2_is_unicode) {
21185  goto return_ne;
21186  } else if ((s2 == Py_None) & s1_is_unicode) {
21187  goto return_ne;
21188  } else {
21189  int result;
21190  PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
21191  if (!py_result)
21192  return -1;
21193  result = __Pyx_PyObject_IsTrue(py_result);
21194  Py_DECREF(py_result);
21195  return result;
21196  }
21197 return_eq:
21198  #if PY_MAJOR_VERSION < 3
21199  Py_XDECREF(owned_ref);
21200  #endif
21201  return (equals == Py_EQ);
21202 return_ne:
21203  #if PY_MAJOR_VERSION < 3
21204  Py_XDECREF(owned_ref);
21205  #endif
21206  return (equals == Py_NE);
21207 #endif
21208 }
21209 
21210 static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) {
21211  int start = 0, mid = 0, end = count - 1;
21212  if (end >= 0 && code_line > entries[end].code_line) {
21213  return count;
21214  }
21215  while (start < end) {
21216  mid = start + (end - start) / 2;
21217  if (code_line < entries[mid].code_line) {
21218  end = mid;
21219  } else if (code_line > entries[mid].code_line) {
21220  start = mid + 1;
21221  } else {
21222  return mid;
21223  }
21224  }
21225  if (code_line <= entries[mid].code_line) {
21226  return mid;
21227  } else {
21228  return mid + 1;
21229  }
21230 }
21231 static PyCodeObject *__pyx_find_code_object(int code_line) {
21232  PyCodeObject* code_object;
21233  int pos;
21234  if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) {
21235  return NULL;
21236  }
21237  pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
21238  if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) {
21239  return NULL;
21240  }
21241  code_object = __pyx_code_cache.entries[pos].code_object;
21242  Py_INCREF(code_object);
21243  return code_object;
21244 }
21245 static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) {
21246  int pos, i;
21247  __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries;
21248  if (unlikely(!code_line)) {
21249  return;
21250  }
21251  if (unlikely(!entries)) {
21252  entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));
21253  if (likely(entries)) {
21254  __pyx_code_cache.entries = entries;
21255  __pyx_code_cache.max_count = 64;
21256  __pyx_code_cache.count = 1;
21257  entries[0].code_line = code_line;
21258  entries[0].code_object = code_object;
21259  Py_INCREF(code_object);
21260  }
21261  return;
21262  }
21263  pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
21264  if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) {
21265  PyCodeObject* tmp = entries[pos].code_object;
21266  entries[pos].code_object = code_object;
21267  Py_DECREF(tmp);
21268  return;
21269  }
21270  if (__pyx_code_cache.count == __pyx_code_cache.max_count) {
21271  int new_max = __pyx_code_cache.max_count + 64;
21272  entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(
21273  __pyx_code_cache.entries, (size_t)new_max*sizeof(__Pyx_CodeObjectCacheEntry));
21274  if (unlikely(!entries)) {
21275  return;
21276  }
21277  __pyx_code_cache.entries = entries;
21278  __pyx_code_cache.max_count = new_max;
21279  }
21280  for (i=__pyx_code_cache.count; i>pos; i--) {
21281  entries[i] = entries[i-1];
21282  }
21283  entries[pos].code_line = code_line;
21284  entries[pos].code_object = code_object;
21285  __pyx_code_cache.count++;
21286  Py_INCREF(code_object);
21287 }
21288 
21289 #include "compile.h"
21290 #include "frameobject.h"
21291 #include "traceback.h"
21292 static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(
21293  const char *funcname, int c_line,
21294  int py_line, const char *filename) {
21295  PyCodeObject *py_code = 0;
21296  PyObject *py_srcfile = 0;
21297  PyObject *py_funcname = 0;
21298  #if PY_MAJOR_VERSION < 3
21299  py_srcfile = PyString_FromString(filename);
21300  #else
21301  py_srcfile = PyUnicode_FromString(filename);
21302  #endif
21303  if (!py_srcfile) goto bad;
21304  if (c_line) {
21305  #if PY_MAJOR_VERSION < 3
21306  py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
21307  #else
21308  py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
21309  #endif
21310  }
21311  else {
21312  #if PY_MAJOR_VERSION < 3
21313  py_funcname = PyString_FromString(funcname);
21314  #else
21315  py_funcname = PyUnicode_FromString(funcname);
21316  #endif
21317  }
21318  if (!py_funcname) goto bad;
21319  py_code = __Pyx_PyCode_New(
21320  0,
21321  0,
21322  0,
21323  0,
21324  0,
21325  __pyx_empty_bytes, /*PyObject *code,*/
21326  __pyx_empty_tuple, /*PyObject *consts,*/
21327  __pyx_empty_tuple, /*PyObject *names,*/
21328  __pyx_empty_tuple, /*PyObject *varnames,*/
21329  __pyx_empty_tuple, /*PyObject *freevars,*/
21330  __pyx_empty_tuple, /*PyObject *cellvars,*/
21331  py_srcfile, /*PyObject *filename,*/
21332  py_funcname, /*PyObject *name,*/
21333  py_line,
21334  __pyx_empty_bytes /*PyObject *lnotab*/
21335  );
21336  Py_DECREF(py_srcfile);
21337  Py_DECREF(py_funcname);
21338  return py_code;
21339 bad:
21340  Py_XDECREF(py_srcfile);
21341  Py_XDECREF(py_funcname);
21342  return NULL;
21343 }
21344 static void __Pyx_AddTraceback(const char *funcname, int c_line,
21345  int py_line, const char *filename) {
21346  PyCodeObject *py_code = 0;
21347  PyFrameObject *py_frame = 0;
21348  py_code = __pyx_find_code_object(c_line ? c_line : py_line);
21349  if (!py_code) {
21350  py_code = __Pyx_CreateCodeObjectForTraceback(
21351  funcname, c_line, py_line, filename);
21352  if (!py_code) goto bad;
21353  __pyx_insert_code_object(c_line ? c_line : py_line, py_code);
21354  }
21355  py_frame = PyFrame_New(
21356  PyThreadState_GET(), /*PyThreadState *tstate,*/
21357  py_code, /*PyCodeObject *code,*/
21358  __pyx_d, /*PyObject *globals,*/
21359  0 /*PyObject *locals*/
21360  );
21361  if (!py_frame) goto bad;
21362  py_frame->f_lineno = py_line;
21363  PyTraceBack_Here(py_frame);
21364 bad:
21365  Py_XDECREF(py_code);
21366  Py_XDECREF(py_frame);
21367 }
21368 
21369 #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\
21370  __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0)
21371 #define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\
21372  __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1)
21373 #define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\
21374  {\
21375  func_type value = func_value;\
21376  if (sizeof(target_type) < sizeof(func_type)) {\
21377  if (unlikely(value != (func_type) (target_type) value)) {\
21378  func_type zero = 0;\
21379  if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\
21380  return (target_type) -1;\
21381  if (is_unsigned && unlikely(value < zero))\
21382  goto raise_neg_overflow;\
21383  else\
21384  goto raise_overflow;\
21385  }\
21386  }\
21387  return (target_type) value;\
21388  }
21389 
21390 static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
21391  const int neg_one = (int) -1, const_zero = (int) 0;
21392  const int is_unsigned = neg_one > const_zero;
21393 #if PY_MAJOR_VERSION < 3
21394  if (likely(PyInt_Check(x))) {
21395  if (sizeof(int) < sizeof(long)) {
21396  __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x))
21397  } else {
21398  long val = PyInt_AS_LONG(x);
21399  if (is_unsigned && unlikely(val < 0)) {
21400  goto raise_neg_overflow;
21401  }
21402  return (int) val;
21403  }
21404  } else
21405 #endif
21406  if (likely(PyLong_Check(x))) {
21407  if (is_unsigned) {
21408 #if CYTHON_USE_PYLONG_INTERNALS
21409  const digit* digits = ((PyLongObject*)x)->ob_digit;
21410  switch (Py_SIZE(x)) {
21411  case 0: return (int) 0;
21412  case 1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0])
21413  case 2:
21414  if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
21415  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
21416  __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
21417  } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) {
21418  return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
21419  }
21420  }
21421  break;
21422  case 3:
21423  if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
21424  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
21425  __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
21426  } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) {
21427  return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
21428  }
21429  }
21430  break;
21431  case 4:
21432  if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
21433  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
21434  __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
21435  } else if (8 * sizeof(int) >= 4 * PyLong_SHIFT) {
21436  return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
21437  }
21438  }
21439  break;
21440  }
21441 #endif
21442 #if CYTHON_COMPILING_IN_CPYTHON
21443  if (unlikely(Py_SIZE(x) < 0)) {
21444  goto raise_neg_overflow;
21445  }
21446 #else
21447  {
21448  int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
21449  if (unlikely(result < 0))
21450  return (int) -1;
21451  if (unlikely(result == 1))
21452  goto raise_neg_overflow;
21453  }
21454 #endif
21455  if (sizeof(int) <= sizeof(unsigned long)) {
21456  __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x))
21457  } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
21458  __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
21459  }
21460  } else {
21461 #if CYTHON_USE_PYLONG_INTERNALS
21462  const digit* digits = ((PyLongObject*)x)->ob_digit;
21463  switch (Py_SIZE(x)) {
21464  case 0: return (int) 0;
21465  case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, -(sdigit) digits[0])
21466  case 1: __PYX_VERIFY_RETURN_INT(int, digit, +digits[0])
21467  case -2:
21468  if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) {
21469  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
21470  __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
21471  } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
21472  return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
21473  }
21474  }
21475  break;
21476  case 2:
21477  if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
21478  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
21479  __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
21480  } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
21481  return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
21482  }
21483  }
21484  break;
21485  case -3:
21486  if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
21487  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
21488  __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
21489  } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
21490  return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
21491  }
21492  }
21493  break;
21494  case 3:
21495  if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
21496  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
21497  __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
21498  } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
21499  return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
21500  }
21501  }
21502  break;
21503  case -4:
21504  if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
21505  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
21506  __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
21507  } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
21508  return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
21509  }
21510  }
21511  break;
21512  case 4:
21513  if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
21514  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
21515  __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
21516  } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
21517  return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
21518  }
21519  }
21520  break;
21521  }
21522 #endif
21523  if (sizeof(int) <= sizeof(long)) {
21524  __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x))
21525  } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
21526  __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x))
21527  }
21528  }
21529  {
21530 #if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
21531  PyErr_SetString(PyExc_RuntimeError,
21532  "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
21533 #else
21534  int val;
21535  PyObject *v = __Pyx_PyNumber_Int(x);
21536  #if PY_MAJOR_VERSION < 3
21537  if (likely(v) && !PyLong_Check(v)) {
21538  PyObject *tmp = v;
21539  v = PyNumber_Long(tmp);
21540  Py_DECREF(tmp);
21541  }
21542  #endif
21543  if (likely(v)) {
21544  int one = 1; int is_little = (int)*(unsigned char *)&one;
21545  unsigned char *bytes = (unsigned char *)&val;
21546  int ret = _PyLong_AsByteArray((PyLongObject *)v,
21547  bytes, sizeof(val),
21548  is_little, !is_unsigned);
21549  Py_DECREF(v);
21550  if (likely(!ret))
21551  return val;
21552  }
21553 #endif
21554  return (int) -1;
21555  }
21556  } else {
21557  int val;
21558  PyObject *tmp = __Pyx_PyNumber_Int(x);
21559  if (!tmp) return (int) -1;
21560  val = __Pyx_PyInt_As_int(tmp);
21561  Py_DECREF(tmp);
21562  return val;
21563  }
21564 raise_overflow:
21565  PyErr_SetString(PyExc_OverflowError,
21566  "value too large to convert to int");
21567  return (int) -1;
21568 raise_neg_overflow:
21569  PyErr_SetString(PyExc_OverflowError,
21570  "can't convert negative value to int");
21571  return (int) -1;
21572 }
21573 
21574 static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) {
21575  const int neg_one = (int) -1, const_zero = (int) 0;
21576  const int is_unsigned = neg_one > const_zero;
21577  if (is_unsigned) {
21578  if (sizeof(int) < sizeof(long)) {
21579  return PyInt_FromLong((long) value);
21580  } else if (sizeof(int) <= sizeof(unsigned long)) {
21581  return PyLong_FromUnsignedLong((unsigned long) value);
21582  } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
21583  return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
21584  }
21585  } else {
21586  if (sizeof(int) <= sizeof(long)) {
21587  return PyInt_FromLong((long) value);
21588  } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
21589  return PyLong_FromLongLong((PY_LONG_LONG) value);
21590  }
21591  }
21592  {
21593  int one = 1; int little = (int)*(unsigned char *)&one;
21594  unsigned char *bytes = (unsigned char *)&value;
21595  return _PyLong_FromByteArray(bytes, sizeof(int),
21596  little, !is_unsigned);
21597  }
21598 }
21599 
21600 static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {
21601  const long neg_one = (long) -1, const_zero = (long) 0;
21602  const int is_unsigned = neg_one > const_zero;
21603  if (is_unsigned) {
21604  if (sizeof(long) < sizeof(long)) {
21605  return PyInt_FromLong((long) value);
21606  } else if (sizeof(long) <= sizeof(unsigned long)) {
21607  return PyLong_FromUnsignedLong((unsigned long) value);
21608  } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
21609  return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
21610  }
21611  } else {
21612  if (sizeof(long) <= sizeof(long)) {
21613  return PyInt_FromLong((long) value);
21614  } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
21615  return PyLong_FromLongLong((PY_LONG_LONG) value);
21616  }
21617  }
21618  {
21619  int one = 1; int little = (int)*(unsigned char *)&one;
21620  unsigned char *bytes = (unsigned char *)&value;
21621  return _PyLong_FromByteArray(bytes, sizeof(long),
21622  little, !is_unsigned);
21623  }
21624 }
21625 
21626 static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
21627  const long neg_one = (long) -1, const_zero = (long) 0;
21628  const int is_unsigned = neg_one > const_zero;
21629 #if PY_MAJOR_VERSION < 3
21630  if (likely(PyInt_Check(x))) {
21631  if (sizeof(long) < sizeof(long)) {
21632  __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x))
21633  } else {
21634  long val = PyInt_AS_LONG(x);
21635  if (is_unsigned && unlikely(val < 0)) {
21636  goto raise_neg_overflow;
21637  }
21638  return (long) val;
21639  }
21640  } else
21641 #endif
21642  if (likely(PyLong_Check(x))) {
21643  if (is_unsigned) {
21644 #if CYTHON_USE_PYLONG_INTERNALS
21645  const digit* digits = ((PyLongObject*)x)->ob_digit;
21646  switch (Py_SIZE(x)) {
21647  case 0: return (long) 0;
21648  case 1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0])
21649  case 2:
21650  if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
21651  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
21652  __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
21653  } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) {
21654  return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
21655  }
21656  }
21657  break;
21658  case 3:
21659  if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
21660  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
21661  __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
21662  } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) {
21663  return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
21664  }
21665  }
21666  break;
21667  case 4:
21668  if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
21669  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
21670  __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
21671  } else if (8 * sizeof(long) >= 4 * PyLong_SHIFT) {
21672  return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
21673  }
21674  }
21675  break;
21676  }
21677 #endif
21678 #if CYTHON_COMPILING_IN_CPYTHON
21679  if (unlikely(Py_SIZE(x) < 0)) {
21680  goto raise_neg_overflow;
21681  }
21682 #else
21683  {
21684  int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
21685  if (unlikely(result < 0))
21686  return (long) -1;
21687  if (unlikely(result == 1))
21688  goto raise_neg_overflow;
21689  }
21690 #endif
21691  if (sizeof(long) <= sizeof(unsigned long)) {
21692  __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x))
21693  } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
21694  __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
21695  }
21696  } else {
21697 #if CYTHON_USE_PYLONG_INTERNALS
21698  const digit* digits = ((PyLongObject*)x)->ob_digit;
21699  switch (Py_SIZE(x)) {
21700  case 0: return (long) 0;
21701  case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, -(sdigit) digits[0])
21702  case 1: __PYX_VERIFY_RETURN_INT(long, digit, +digits[0])
21703  case -2:
21704  if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) {
21705  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
21706  __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
21707  } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
21708  return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
21709  }
21710  }
21711  break;
21712  case 2:
21713  if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
21714  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
21715  __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
21716  } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
21717  return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
21718  }
21719  }
21720  break;
21721  case -3:
21722  if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
21723  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
21724  __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
21725  } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
21726  return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
21727  }
21728  }
21729  break;
21730  case 3:
21731  if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
21732  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
21733  __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
21734  } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
21735  return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
21736  }
21737  }
21738  break;
21739  case -4:
21740  if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
21741  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
21742  __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
21743  } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
21744  return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
21745  }
21746  }
21747  break;
21748  case 4:
21749  if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
21750  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
21751  __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
21752  } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
21753  return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
21754  }
21755  }
21756  break;
21757  }
21758 #endif
21759  if (sizeof(long) <= sizeof(long)) {
21760  __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x))
21761  } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
21762  __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x))
21763  }
21764  }
21765  {
21766 #if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
21767  PyErr_SetString(PyExc_RuntimeError,
21768  "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
21769 #else
21770  long val;
21771  PyObject *v = __Pyx_PyNumber_Int(x);
21772  #if PY_MAJOR_VERSION < 3
21773  if (likely(v) && !PyLong_Check(v)) {
21774  PyObject *tmp = v;
21775  v = PyNumber_Long(tmp);
21776  Py_DECREF(tmp);
21777  }
21778  #endif
21779  if (likely(v)) {
21780  int one = 1; int is_little = (int)*(unsigned char *)&one;
21781  unsigned char *bytes = (unsigned char *)&val;
21782  int ret = _PyLong_AsByteArray((PyLongObject *)v,
21783  bytes, sizeof(val),
21784  is_little, !is_unsigned);
21785  Py_DECREF(v);
21786  if (likely(!ret))
21787  return val;
21788  }
21789 #endif
21790  return (long) -1;
21791  }
21792  } else {
21793  long val;
21794  PyObject *tmp = __Pyx_PyNumber_Int(x);
21795  if (!tmp) return (long) -1;
21796  val = __Pyx_PyInt_As_long(tmp);
21797  Py_DECREF(tmp);
21798  return val;
21799  }
21800 raise_overflow:
21801  PyErr_SetString(PyExc_OverflowError,
21802  "value too large to convert to long");
21803  return (long) -1;
21804 raise_neg_overflow:
21805  PyErr_SetString(PyExc_OverflowError,
21806  "can't convert negative value to long");
21807  return (long) -1;
21808 }
21809 
21810 static PyTypeObject* __Pyx_FetchCommonType(PyTypeObject* type) {
21811  PyObject* fake_module;
21812  PyTypeObject* cached_type = NULL;
21813  fake_module = PyImport_AddModule((char*) "_cython_" CYTHON_ABI);
21814  if (!fake_module) return NULL;
21815  Py_INCREF(fake_module);
21816  cached_type = (PyTypeObject*) PyObject_GetAttrString(fake_module, type->tp_name);
21817  if (cached_type) {
21818  if (!PyType_Check((PyObject*)cached_type)) {
21819  PyErr_Format(PyExc_TypeError,
21820  "Shared Cython type %.200s is not a type object",
21821  type->tp_name);
21822  goto bad;
21823  }
21824  if (cached_type->tp_basicsize != type->tp_basicsize) {
21825  PyErr_Format(PyExc_TypeError,
21826  "Shared Cython type %.200s has the wrong size, try recompiling",
21827  type->tp_name);
21828  goto bad;
21829  }
21830  } else {
21831  if (!PyErr_ExceptionMatches(PyExc_AttributeError)) goto bad;
21832  PyErr_Clear();
21833  if (PyType_Ready(type) < 0) goto bad;
21834  if (PyObject_SetAttrString(fake_module, type->tp_name, (PyObject*) type) < 0)
21835  goto bad;
21836  Py_INCREF(type);
21837  cached_type = type;
21838  }
21839 done:
21840  Py_DECREF(fake_module);
21841  return cached_type;
21842 bad:
21843  Py_XDECREF(cached_type);
21844  cached_type = NULL;
21845  goto done;
21846 }
21847 
21848 static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb) {
21849  PyObject *tmp_type, *tmp_value, *tmp_tb;
21850 #if CYTHON_COMPILING_IN_CPYTHON
21851  PyThreadState *tstate = PyThreadState_GET();
21852  tmp_type = tstate->exc_type;
21853  tmp_value = tstate->exc_value;
21854  tmp_tb = tstate->exc_traceback;
21855  tstate->exc_type = *type;
21856  tstate->exc_value = *value;
21857  tstate->exc_traceback = *tb;
21858 #else
21859  PyErr_GetExcInfo(&tmp_type, &tmp_value, &tmp_tb);
21860  PyErr_SetExcInfo(*type, *value, *tb);
21861 #endif
21862  *type = tmp_type;
21863  *value = tmp_value;
21864  *tb = tmp_tb;
21865 }
21866 
21867 static PyObject* __Pyx_PyObject_CallMethod1(PyObject* obj, PyObject* method_name, PyObject* arg) {
21868  PyObject *method, *result = NULL;
21869  method = __Pyx_PyObject_GetAttrStr(obj, method_name);
21870  if (unlikely(!method)) goto bad;
21871 #if CYTHON_COMPILING_IN_CPYTHON
21872  if (likely(PyMethod_Check(method))) {
21873  PyObject *self = PyMethod_GET_SELF(method);
21874  if (likely(self)) {
21875  PyObject *args;
21876  PyObject *function = PyMethod_GET_FUNCTION(method);
21877  args = PyTuple_New(2);
21878  if (unlikely(!args)) goto bad;
21879  Py_INCREF(self);
21880  PyTuple_SET_ITEM(args, 0, self);
21881  Py_INCREF(arg);
21882  PyTuple_SET_ITEM(args, 1, arg);
21883  Py_INCREF(function);
21884  Py_DECREF(method); method = NULL;
21885  result = __Pyx_PyObject_Call(function, args, NULL);
21886  Py_DECREF(args);
21887  Py_DECREF(function);
21888  return result;
21889  }
21890  }
21891 #endif
21892  result = __Pyx_PyObject_CallOneArg(method, arg);
21893 bad:
21894  Py_XDECREF(method);
21895  return result;
21896 }
21897 
21898 #include <structmember.h>
21899 #include <frameobject.h>
21900 static PyObject *__Pyx_Coroutine_Send(PyObject *self, PyObject *value);
21901 static PyObject *__Pyx_Coroutine_Close(PyObject *self);
21902 static PyObject *__Pyx_Coroutine_Throw(PyObject *gen, PyObject *args);
21903 #define __Pyx_Coroutine_Undelegate(gen) Py_CLEAR((gen)->yieldfrom)
21904 #if 1 || PY_VERSION_HEX < 0x030300B0
21905 static int __Pyx_PyGen_FetchStopIterationValue(PyObject **pvalue) {
21906  PyObject *et, *ev, *tb;
21907  PyObject *value = NULL;
21908  __Pyx_ErrFetch(&et, &ev, &tb);
21909  if (!et) {
21910  Py_XDECREF(tb);
21911  Py_XDECREF(ev);
21912  Py_INCREF(Py_None);
21913  *pvalue = Py_None;
21914  return 0;
21915  }
21916  if (likely(et == PyExc_StopIteration)) {
21917 #if PY_VERSION_HEX >= 0x030300A0
21918  if (ev && Py_TYPE(ev) == (PyTypeObject*)PyExc_StopIteration) {
21919  value = ((PyStopIterationObject *)ev)->value;
21920  Py_INCREF(value);
21921  Py_DECREF(ev);
21922  Py_XDECREF(tb);
21923  Py_DECREF(et);
21924  *pvalue = value;
21925  return 0;
21926  }
21927 #endif
21928  if (!ev || !PyObject_TypeCheck(ev, (PyTypeObject*)PyExc_StopIteration)) {
21929  if (!ev) {
21930  Py_INCREF(Py_None);
21931  ev = Py_None;
21932  } else if (PyTuple_Check(ev)) {
21933  if (PyTuple_GET_SIZE(ev) >= 1) {
21934  PyObject *value;
21935 #if CYTHON_COMPILING_IN_CPYTHON
21936  value = PySequence_ITEM(ev, 0);
21937 #else
21938  value = PyTuple_GET_ITEM(ev, 0);
21939  Py_INCREF(value);
21940 #endif
21941  Py_DECREF(ev);
21942  ev = value;
21943  } else {
21944  Py_INCREF(Py_None);
21945  Py_DECREF(ev);
21946  ev = Py_None;
21947  }
21948  }
21949  Py_XDECREF(tb);
21950  Py_DECREF(et);
21951  *pvalue = ev;
21952  return 0;
21953  }
21954  } else if (!PyErr_GivenExceptionMatches(et, PyExc_StopIteration)) {
21955  __Pyx_ErrRestore(et, ev, tb);
21956  return -1;
21957  }
21958  PyErr_NormalizeException(&et, &ev, &tb);
21959  if (unlikely(!PyObject_TypeCheck(ev, (PyTypeObject*)PyExc_StopIteration))) {
21960  __Pyx_ErrRestore(et, ev, tb);
21961  return -1;
21962  }
21963  Py_XDECREF(tb);
21964  Py_DECREF(et);
21965 #if PY_VERSION_HEX >= 0x030300A0
21966  value = ((PyStopIterationObject *)ev)->value;
21967  Py_INCREF(value);
21968  Py_DECREF(ev);
21969 #else
21970  {
21971  PyObject* args = __Pyx_PyObject_GetAttrStr(ev, __pyx_n_s_args);
21972  Py_DECREF(ev);
21973  if (likely(args)) {
21974  value = PySequence_GetItem(args, 0);
21975  Py_DECREF(args);
21976  }
21977  if (unlikely(!value)) {
21978  __Pyx_ErrRestore(NULL, NULL, NULL);
21979  Py_INCREF(Py_None);
21980  value = Py_None;
21981  }
21982  }
21983 #endif
21984  *pvalue = value;
21985  return 0;
21986 }
21987 #endif
21988 static CYTHON_INLINE
21989 void __Pyx_Coroutine_ExceptionClear(__pyx_CoroutineObject *self) {
21990  PyObject *exc_type = self->exc_type;
21991  PyObject *exc_value = self->exc_value;
21992  PyObject *exc_traceback = self->exc_traceback;
21993  self->exc_type = NULL;
21994  self->exc_value = NULL;
21995  self->exc_traceback = NULL;
21996  Py_XDECREF(exc_type);
21997  Py_XDECREF(exc_value);
21998  Py_XDECREF(exc_traceback);
21999 }
22000 static CYTHON_INLINE
22001 int __Pyx_Coroutine_CheckRunning(__pyx_CoroutineObject *gen) {
22002  if (unlikely(gen->is_running)) {
22003  PyErr_SetString(PyExc_ValueError,
22004  "generator already executing");
22005  return 1;
22006  }
22007  return 0;
22008 }
22009 static CYTHON_INLINE
22010 PyObject *__Pyx_Coroutine_SendEx(__pyx_CoroutineObject *self, PyObject *value) {
22011  PyObject *retval;
22012  assert(!self->is_running);
22013  if (unlikely(self->resume_label == 0)) {
22014  if (unlikely(value && value != Py_None)) {
22015  PyErr_SetString(PyExc_TypeError,
22016  "can't send non-None value to a "
22017  "just-started generator");
22018  return NULL;
22019  }
22020  }
22021  if (unlikely(self->resume_label == -1)) {
22022  PyErr_SetNone(PyExc_StopIteration);
22023  return NULL;
22024  }
22025  if (value) {
22026 #if CYTHON_COMPILING_IN_PYPY
22027 #else
22028  if (self->exc_traceback) {
22029  PyThreadState *tstate = PyThreadState_GET();
22030  PyTracebackObject *tb = (PyTracebackObject *) self->exc_traceback;
22031  PyFrameObject *f = tb->tb_frame;
22032  Py_XINCREF(tstate->frame);
22033  assert(f->f_back == NULL);
22034  f->f_back = tstate->frame;
22035  }
22036 #endif
22037  __Pyx_ExceptionSwap(&self->exc_type, &self->exc_value,
22038  &self->exc_traceback);
22039  } else {
22040  __Pyx_Coroutine_ExceptionClear(self);
22041  }
22042  self->is_running = 1;
22043  retval = self->body((PyObject *) self, value);
22044  self->is_running = 0;
22045  if (retval) {
22046  __Pyx_ExceptionSwap(&self->exc_type, &self->exc_value,
22047  &self->exc_traceback);
22048 #if CYTHON_COMPILING_IN_PYPY
22049 #else
22050  if (self->exc_traceback) {
22051  PyTracebackObject *tb = (PyTracebackObject *) self->exc_traceback;
22052  PyFrameObject *f = tb->tb_frame;
22053  Py_CLEAR(f->f_back);
22054  }
22055 #endif
22056  } else {
22057  __Pyx_Coroutine_ExceptionClear(self);
22058  }
22059  return retval;
22060 }
22061 static CYTHON_INLINE
22062 PyObject *__Pyx_Coroutine_MethodReturn(PyObject *retval) {
22063  if (unlikely(!retval && !PyErr_Occurred())) {
22064  PyErr_SetNone(PyExc_StopIteration);
22065  }
22066  return retval;
22067 }
22068 static CYTHON_INLINE
22069 PyObject *__Pyx_Coroutine_FinishDelegation(__pyx_CoroutineObject *gen) {
22070  PyObject *ret;
22071  PyObject *val = NULL;
22072  __Pyx_Coroutine_Undelegate(gen);
22073  __Pyx_PyGen_FetchStopIterationValue(&val);
22074  ret = __Pyx_Coroutine_SendEx(gen, val);
22075  Py_XDECREF(val);
22076  return ret;
22077 }
22078 static PyObject *__Pyx_Coroutine_Send(PyObject *self, PyObject *value) {
22079  PyObject *retval;
22080  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject*) self;
22081  PyObject *yf = gen->yieldfrom;
22082  if (unlikely(__Pyx_Coroutine_CheckRunning(gen)))
22083  return NULL;
22084  if (yf) {
22085  PyObject *ret;
22086  gen->is_running = 1;
22087  #ifdef __Pyx_Generator_USED
22088  if (__Pyx_Generator_CheckExact(yf)) {
22089  ret = __Pyx_Coroutine_Send(yf, value);
22090  } else
22091  #endif
22092  #ifdef __Pyx_Coroutine_USED
22093  if (__Pyx_Coroutine_CheckExact(yf)) {
22094  ret = __Pyx_Coroutine_Send(yf, value);
22095  } else
22096  #endif
22097  {
22098  if (value == Py_None)
22099  ret = PyIter_Next(yf);
22100  else
22101  ret = __Pyx_PyObject_CallMethod1(yf, __pyx_n_s_send, value);
22102  }
22103  gen->is_running = 0;
22104  if (likely(ret)) {
22105  return ret;
22106  }
22107  retval = __Pyx_Coroutine_FinishDelegation(gen);
22108  } else {
22109  retval = __Pyx_Coroutine_SendEx(gen, value);
22110  }
22111  return __Pyx_Coroutine_MethodReturn(retval);
22112 }
22113 static int __Pyx_Coroutine_CloseIter(__pyx_CoroutineObject *gen, PyObject *yf) {
22114  PyObject *retval = NULL;
22115  int err = 0;
22116  #ifdef __Pyx_Generator_USED
22117  if (__Pyx_Generator_CheckExact(yf)) {
22118  retval = __Pyx_Coroutine_Close(yf);
22119  if (!retval)
22120  return -1;
22121  } else
22122  #endif
22123  #ifdef __Pyx_Coroutine_USED
22124  if (__Pyx_Coroutine_CheckExact(yf)) {
22125  retval = __Pyx_Coroutine_Close(yf);
22126  if (!retval)
22127  return -1;
22128  } else
22129  #endif
22130  {
22131  PyObject *meth;
22132  gen->is_running = 1;
22133  meth = __Pyx_PyObject_GetAttrStr(yf, __pyx_n_s_close);
22134  if (unlikely(!meth)) {
22135  if (!PyErr_ExceptionMatches(PyExc_AttributeError)) {
22136  PyErr_WriteUnraisable(yf);
22137  }
22138  PyErr_Clear();
22139  } else {
22140  retval = PyObject_CallFunction(meth, NULL);
22141  Py_DECREF(meth);
22142  if (!retval)
22143  err = -1;
22144  }
22145  gen->is_running = 0;
22146  }
22147  Py_XDECREF(retval);
22148  return err;
22149 }
22150 static PyObject *__Pyx_Generator_Next(PyObject *self) {
22151  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject*) self;
22152  PyObject *yf = gen->yieldfrom;
22153  if (unlikely(__Pyx_Coroutine_CheckRunning(gen)))
22154  return NULL;
22155  if (yf) {
22156  PyObject *ret;
22157  gen->is_running = 1;
22158  ret = Py_TYPE(yf)->tp_iternext(yf);
22159  gen->is_running = 0;
22160  if (likely(ret)) {
22161  return ret;
22162  }
22163  return __Pyx_Coroutine_FinishDelegation(gen);
22164  }
22165  return __Pyx_Coroutine_SendEx(gen, Py_None);
22166 }
22167 static PyObject *__Pyx_Coroutine_Close(PyObject *self) {
22168  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
22169  PyObject *retval, *raised_exception;
22170  PyObject *yf = gen->yieldfrom;
22171  int err = 0;
22172  if (unlikely(__Pyx_Coroutine_CheckRunning(gen)))
22173  return NULL;
22174  if (yf) {
22175  Py_INCREF(yf);
22176  err = __Pyx_Coroutine_CloseIter(gen, yf);
22177  __Pyx_Coroutine_Undelegate(gen);
22178  Py_DECREF(yf);
22179  }
22180  if (err == 0)
22181  PyErr_SetNone(PyExc_GeneratorExit);
22182  retval = __Pyx_Coroutine_SendEx(gen, NULL);
22183  if (retval) {
22184  Py_DECREF(retval);
22185  PyErr_SetString(PyExc_RuntimeError,
22186  "generator ignored GeneratorExit");
22187  return NULL;
22188  }
22189  raised_exception = PyErr_Occurred();
22190  if (!raised_exception
22191  || raised_exception == PyExc_StopIteration
22192  || raised_exception == PyExc_GeneratorExit
22193  || PyErr_GivenExceptionMatches(raised_exception, PyExc_GeneratorExit)
22194  || PyErr_GivenExceptionMatches(raised_exception, PyExc_StopIteration))
22195  {
22196  if (raised_exception) PyErr_Clear();
22197  Py_INCREF(Py_None);
22198  return Py_None;
22199  }
22200  return NULL;
22201 }
22202 static PyObject *__Pyx_Coroutine_Throw(PyObject *self, PyObject *args) {
22203  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
22204  PyObject *typ;
22205  PyObject *tb = NULL;
22206  PyObject *val = NULL;
22207  PyObject *yf = gen->yieldfrom;
22208  if (!PyArg_UnpackTuple(args, (char *)"throw", 1, 3, &typ, &val, &tb))
22209  return NULL;
22210  if (unlikely(__Pyx_Coroutine_CheckRunning(gen)))
22211  return NULL;
22212  if (yf) {
22213  PyObject *ret;
22214  Py_INCREF(yf);
22215  if (PyErr_GivenExceptionMatches(typ, PyExc_GeneratorExit)) {
22216  int err = __Pyx_Coroutine_CloseIter(gen, yf);
22217  Py_DECREF(yf);
22218  __Pyx_Coroutine_Undelegate(gen);
22219  if (err < 0)
22220  return __Pyx_Coroutine_MethodReturn(__Pyx_Coroutine_SendEx(gen, NULL));
22221  goto throw_here;
22222  }
22223  gen->is_running = 1;
22224  #ifdef __Pyx_Generator_USED
22225  if (__Pyx_Generator_CheckExact(yf)) {
22226  ret = __Pyx_Coroutine_Throw(yf, args);
22227  } else
22228  #endif
22229  #ifdef __Pyx_Coroutine_USED
22230  if (__Pyx_Coroutine_CheckExact(yf)) {
22231  ret = __Pyx_Coroutine_Throw(yf, args);
22232  } else
22233  #endif
22234  {
22235  PyObject *meth = __Pyx_PyObject_GetAttrStr(yf, __pyx_n_s_throw);
22236  if (unlikely(!meth)) {
22237  Py_DECREF(yf);
22238  if (!PyErr_ExceptionMatches(PyExc_AttributeError)) {
22239  gen->is_running = 0;
22240  return NULL;
22241  }
22242  PyErr_Clear();
22243  __Pyx_Coroutine_Undelegate(gen);
22244  gen->is_running = 0;
22245  goto throw_here;
22246  }
22247  ret = PyObject_CallObject(meth, args);
22248  Py_DECREF(meth);
22249  }
22250  gen->is_running = 0;
22251  Py_DECREF(yf);
22252  if (!ret) {
22253  ret = __Pyx_Coroutine_FinishDelegation(gen);
22254  }
22255  return __Pyx_Coroutine_MethodReturn(ret);
22256  }
22257 throw_here:
22258  __Pyx_Raise(typ, val, tb, NULL);
22259  return __Pyx_Coroutine_MethodReturn(__Pyx_Coroutine_SendEx(gen, NULL));
22260 }
22261 static int __Pyx_Coroutine_traverse(PyObject *self, visitproc visit, void *arg) {
22262  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
22263  Py_VISIT(gen->closure);
22264  Py_VISIT(gen->classobj);
22265  Py_VISIT(gen->yieldfrom);
22266  Py_VISIT(gen->exc_type);
22267  Py_VISIT(gen->exc_value);
22268  Py_VISIT(gen->exc_traceback);
22269  return 0;
22270 }
22271 static int __Pyx_Coroutine_clear(PyObject *self) {
22272  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
22273  Py_CLEAR(gen->closure);
22274  Py_CLEAR(gen->classobj);
22275  Py_CLEAR(gen->yieldfrom);
22276  Py_CLEAR(gen->exc_type);
22277  Py_CLEAR(gen->exc_value);
22278  Py_CLEAR(gen->exc_traceback);
22279  Py_CLEAR(gen->gi_name);
22280  Py_CLEAR(gen->gi_qualname);
22281  return 0;
22282 }
22283 static void __Pyx_Coroutine_dealloc(PyObject *self) {
22284  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
22285  PyObject_GC_UnTrack(gen);
22286  if (gen->gi_weakreflist != NULL)
22287  PyObject_ClearWeakRefs(self);
22288  if (gen->resume_label > 0) {
22289  PyObject_GC_Track(self);
22290 #if PY_VERSION_HEX >= 0x030400a1
22291  if (PyObject_CallFinalizerFromDealloc(self))
22292 #else
22293  Py_TYPE(gen)->tp_del(self);
22294  if (self->ob_refcnt > 0)
22295 #endif
22296  {
22297  return;
22298  }
22299  PyObject_GC_UnTrack(self);
22300  }
22301  __Pyx_Coroutine_clear(self);
22302  PyObject_GC_Del(gen);
22303 }
22304 static void __Pyx_Coroutine_del(PyObject *self) {
22305  PyObject *res;
22306  PyObject *error_type, *error_value, *error_traceback;
22307  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
22308  if (gen->resume_label <= 0)
22309  return ;
22310 #if PY_VERSION_HEX < 0x030400a1
22311  assert(self->ob_refcnt == 0);
22312  self->ob_refcnt = 1;
22313 #endif
22314  __Pyx_ErrFetch(&error_type, &error_value, &error_traceback);
22315  res = __Pyx_Coroutine_Close(self);
22316  if (res == NULL)
22317  PyErr_WriteUnraisable(self);
22318  else
22319  Py_DECREF(res);
22320  __Pyx_ErrRestore(error_type, error_value, error_traceback);
22321 #if PY_VERSION_HEX < 0x030400a1
22322  assert(self->ob_refcnt > 0);
22323  if (--self->ob_refcnt == 0) {
22324  return;
22325  }
22326  {
22327  Py_ssize_t refcnt = self->ob_refcnt;
22328  _Py_NewReference(self);
22329  self->ob_refcnt = refcnt;
22330  }
22331 #if CYTHON_COMPILING_IN_CPYTHON
22332  assert(PyType_IS_GC(self->ob_type) &&
22333  _Py_AS_GC(self)->gc.gc_refs != _PyGC_REFS_UNTRACKED);
22334  _Py_DEC_REFTOTAL;
22335 #endif
22336 #ifdef COUNT_ALLOCS
22337  --Py_TYPE(self)->tp_frees;
22338  --Py_TYPE(self)->tp_allocs;
22339 #endif
22340 #endif
22341 }
22342 static PyObject *
22343 __Pyx_Coroutine_get_name(__pyx_CoroutineObject *self)
22344 {
22345  Py_INCREF(self->gi_name);
22346  return self->gi_name;
22347 }
22348 static int
22349 __Pyx_Coroutine_set_name(__pyx_CoroutineObject *self, PyObject *value)
22350 {
22351  PyObject *tmp;
22352 #if PY_MAJOR_VERSION >= 3
22353  if (unlikely(value == NULL || !PyUnicode_Check(value))) {
22354 #else
22355  if (unlikely(value == NULL || !PyString_Check(value))) {
22356 #endif
22357  PyErr_SetString(PyExc_TypeError,
22358  "__name__ must be set to a string object");
22359  return -1;
22360  }
22361  tmp = self->gi_name;
22362  Py_INCREF(value);
22363  self->gi_name = value;
22364  Py_XDECREF(tmp);
22365  return 0;
22366 }
22367 static PyObject *
22368 __Pyx_Coroutine_get_qualname(__pyx_CoroutineObject *self)
22369 {
22370  Py_INCREF(self->gi_qualname);
22371  return self->gi_qualname;
22372 }
22373 static int
22374 __Pyx_Coroutine_set_qualname(__pyx_CoroutineObject *self, PyObject *value)
22375 {
22376  PyObject *tmp;
22377 #if PY_MAJOR_VERSION >= 3
22378  if (unlikely(value == NULL || !PyUnicode_Check(value))) {
22379 #else
22380  if (unlikely(value == NULL || !PyString_Check(value))) {
22381 #endif
22382  PyErr_SetString(PyExc_TypeError,
22383  "__qualname__ must be set to a string object");
22384  return -1;
22385  }
22386  tmp = self->gi_qualname;
22387  Py_INCREF(value);
22388  self->gi_qualname = value;
22389  Py_XDECREF(tmp);
22390  return 0;
22391 }
22392 static __pyx_CoroutineObject *__Pyx__Coroutine_New(PyTypeObject* type, __pyx_coroutine_body_t body,
22393  PyObject *closure, PyObject *name, PyObject *qualname) {
22394  __pyx_CoroutineObject *gen = PyObject_GC_New(__pyx_CoroutineObject, type);
22395  if (gen == NULL)
22396  return NULL;
22397  gen->body = body;
22398  gen->closure = closure;
22399  Py_XINCREF(closure);
22400  gen->is_running = 0;
22401  gen->resume_label = 0;
22402  gen->classobj = NULL;
22403  gen->yieldfrom = NULL;
22404  gen->exc_type = NULL;
22405  gen->exc_value = NULL;
22406  gen->exc_traceback = NULL;
22407  gen->gi_weakreflist = NULL;
22408  Py_XINCREF(qualname);
22409  gen->gi_qualname = qualname;
22410  Py_XINCREF(name);
22411  gen->gi_name = name;
22412  PyObject_GC_Track(gen);
22413  return gen;
22414 }
22415 
22416 static PyObject* __Pyx_Coroutine_patch_module(PyObject* module, const char* py_code) {
22417 #if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
22418  int result;
22419  PyObject *globals, *result_obj;
22420  globals = PyDict_New(); if (unlikely(!globals)) goto ignore;
22421  result = PyDict_SetItemString(globals, "_cython_coroutine_type",
22422  #ifdef __Pyx_Coroutine_USED
22423  (PyObject*)__pyx_CoroutineType);
22424  #else
22425  Py_None);
22426  #endif
22427  if (unlikely(result < 0)) goto ignore;
22428  result = PyDict_SetItemString(globals, "_cython_generator_type",
22429  #ifdef __Pyx_Generator_USED
22430  (PyObject*)__pyx_GeneratorType);
22431  #else
22432  Py_None);
22433  #endif
22434  if (unlikely(result < 0)) goto ignore;
22435  if (unlikely(PyDict_SetItemString(globals, "_module", module) < 0)) goto ignore;
22436  if (unlikely(PyDict_SetItemString(globals, "__builtins__", __pyx_b) < 0)) goto ignore;
22437  result_obj = PyRun_String(py_code, Py_file_input, globals, globals);
22438  if (unlikely(!result_obj)) goto ignore;
22439  Py_DECREF(result_obj);
22440  Py_DECREF(globals);
22441  return module;
22442 ignore:
22443  Py_XDECREF(globals);
22444  PyErr_WriteUnraisable(module);
22445  if (unlikely(PyErr_WarnEx(PyExc_RuntimeWarning, "Cython module failed to patch module with custom type", 1) < 0)) {
22446  Py_DECREF(module);
22447  module = NULL;
22448  }
22449 #else
22450  py_code++;
22451 #endif
22452  return module;
22453 }
22454 
22455 #if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
22456 static PyObject* __Pyx_patch_abc_module(PyObject *module);
22457 static PyObject* __Pyx_patch_abc_module(PyObject *module) {
22458  module = __Pyx_Coroutine_patch_module(
22459  module, ""
22460 "if _cython_generator_type is not None:\n"
22461 " try: Generator = _module.Generator\n"
22462 " except AttributeError: pass\n"
22463 " else: Generator.register(_cython_generator_type)\n"
22464 "if _cython_coroutine_type is not None:\n"
22465 " try: Coroutine = _module.Coroutine\n"
22466 " except AttributeError: pass\n"
22467 " else: Coroutine.register(_cython_coroutine_type)\n"
22468  );
22469  return module;
22470 }
22471 #endif
22472 static int __Pyx_patch_abc(void) {
22473 #if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
22474  static int abc_patched = 0;
22475  if (!abc_patched) {
22476  PyObject *module;
22477  module = PyImport_ImportModule((PY_VERSION_HEX >= 0x03030000) ? "collections.abc" : "collections");
22478  if (!module) {
22479  PyErr_WriteUnraisable(NULL);
22480  if (unlikely(PyErr_WarnEx(PyExc_RuntimeWarning,
22481  ((PY_VERSION_HEX >= 0x03030000) ?
22482  "Cython module failed to register with collections.abc module" :
22483  "Cython module failed to register with collections module"), 1) < 0)) {
22484  return -1;
22485  }
22486  } else {
22487  module = __Pyx_patch_abc_module(module);
22488  abc_patched = 1;
22489  if (unlikely(!module))
22490  return -1;
22491  Py_DECREF(module);
22492  }
22493  module = PyImport_ImportModule("backports_abc");
22494  if (module) {
22495  module = __Pyx_patch_abc_module(module);
22496  Py_XDECREF(module);
22497  }
22498  if (!module) {
22499  PyErr_Clear();
22500  }
22501  }
22502 #else
22503  if (0) __Pyx_Coroutine_patch_module(NULL, NULL);
22504 #endif
22505  return 0;
22506 }
22507 
22508 static PyMethodDef __pyx_Generator_methods[] = {
22509  {"send", (PyCFunction) __Pyx_Coroutine_Send, METH_O,
22510  (char*) PyDoc_STR("send(arg) -> send 'arg' into generator,\nreturn next yielded value or raise StopIteration.")},
22511  {"throw", (PyCFunction) __Pyx_Coroutine_Throw, METH_VARARGS,
22512  (char*) PyDoc_STR("throw(typ[,val[,tb]]) -> raise exception in generator,\nreturn next yielded value or raise StopIteration.")},
22513  {"close", (PyCFunction) __Pyx_Coroutine_Close, METH_NOARGS,
22514  (char*) PyDoc_STR("close() -> raise GeneratorExit inside generator.")},
22515  {0, 0, 0, 0}
22516 };
22517 static PyMemberDef __pyx_Generator_memberlist[] = {
22518  {(char *) "gi_running", T_BOOL, offsetof(__pyx_CoroutineObject, is_running), READONLY, NULL},
22519  {(char*) "gi_yieldfrom", T_OBJECT, offsetof(__pyx_CoroutineObject, yieldfrom), READONLY,
22520  (char*) PyDoc_STR("object being iterated by 'yield from', or None")},
22521  {0, 0, 0, 0, 0}
22522 };
22523 static PyGetSetDef __pyx_Generator_getsets[] = {
22524  {(char *) "__name__", (getter)__Pyx_Coroutine_get_name, (setter)__Pyx_Coroutine_set_name,
22525  (char*) PyDoc_STR("name of the generator"), 0},
22526  {(char *) "__qualname__", (getter)__Pyx_Coroutine_get_qualname, (setter)__Pyx_Coroutine_set_qualname,
22527  (char*) PyDoc_STR("qualified name of the generator"), 0},
22528  {0, 0, 0, 0, 0}
22529 };
22530 static PyTypeObject __pyx_GeneratorType_type = {
22531  PyVarObject_HEAD_INIT(0, 0)
22532  "generator",
22533  sizeof(__pyx_CoroutineObject),
22534  0,
22535  (destructor) __Pyx_Coroutine_dealloc,
22536  0,
22537  0,
22538  0,
22539  0,
22540  0,
22541  0,
22542  0,
22543  0,
22544  0,
22545  0,
22546  0,
22547  0,
22548  0,
22549  0,
22550  Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC | Py_TPFLAGS_HAVE_FINALIZE,
22551  0,
22552  (traverseproc) __Pyx_Coroutine_traverse,
22553  0,
22554  0,
22555  offsetof(__pyx_CoroutineObject, gi_weakreflist),
22556  0,
22557  (iternextfunc) __Pyx_Generator_Next,
22558  __pyx_Generator_methods,
22559  __pyx_Generator_memberlist,
22560  __pyx_Generator_getsets,
22561  0,
22562  0,
22563  0,
22564  0,
22565  0,
22566  0,
22567  0,
22568  0,
22569  0,
22570  0,
22571  0,
22572  0,
22573  0,
22574  0,
22575  0,
22576 #if PY_VERSION_HEX >= 0x030400a1
22577  0,
22578 #else
22579  __Pyx_Coroutine_del,
22580 #endif
22581  0,
22582 #if PY_VERSION_HEX >= 0x030400a1
22583  __Pyx_Coroutine_del,
22584 #endif
22585 };
22586 static int __pyx_Generator_init(void) {
22587  __pyx_GeneratorType_type.tp_getattro = PyObject_GenericGetAttr;
22588  __pyx_GeneratorType_type.tp_iter = PyObject_SelfIter;
22589  __pyx_GeneratorType = __Pyx_FetchCommonType(&__pyx_GeneratorType_type);
22590  if (unlikely(!__pyx_GeneratorType)) {
22591  return -1;
22592  }
22593  return 0;
22594 }
22595 
22596 static int __Pyx_check_binary_version(void) {
22597  char ctversion[4], rtversion[4];
22598  PyOS_snprintf(ctversion, 4, "%d.%d", PY_MAJOR_VERSION, PY_MINOR_VERSION);
22599  PyOS_snprintf(rtversion, 4, "%s", Py_GetVersion());
22600  if (ctversion[0] != rtversion[0] || ctversion[2] != rtversion[2]) {
22601  char message[200];
22602  PyOS_snprintf(message, sizeof(message),
22603  "compiletime version %s of module '%.100s' "
22604  "does not match runtime version %s",
22605  ctversion, __Pyx_MODULE_NAME, rtversion);
22606  return PyErr_WarnEx(NULL, message, 1);
22607  }
22608  return 0;
22609 }
22610 
22611 static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {
22612  while (t->p) {
22613  #if PY_MAJOR_VERSION < 3
22614  if (t->is_unicode) {
22615  *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);
22616  } else if (t->intern) {
22617  *t->p = PyString_InternFromString(t->s);
22618  } else {
22619  *t->p = PyString_FromStringAndSize(t->s, t->n - 1);
22620  }
22621  #else
22622  if (t->is_unicode | t->is_str) {
22623  if (t->intern) {
22624  *t->p = PyUnicode_InternFromString(t->s);
22625  } else if (t->encoding) {
22626  *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);
22627  } else {
22628  *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);
22629  }
22630  } else {
22631  *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);
22632  }
22633  #endif
22634  if (!*t->p)
22635  return -1;
22636  ++t;
22637  }
22638  return 0;
22639 }
22640 
22641 static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {
22642  return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str));
22643 }
22644 static CYTHON_INLINE char* __Pyx_PyObject_AsString(PyObject* o) {
22645  Py_ssize_t ignore;
22646  return __Pyx_PyObject_AsStringAndSize(o, &ignore);
22647 }
22648 static CYTHON_INLINE char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
22649 #if CYTHON_COMPILING_IN_CPYTHON && (__PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT)
22650  if (
22651 #if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
22652  __Pyx_sys_getdefaultencoding_not_ascii &&
22653 #endif
22654  PyUnicode_Check(o)) {
22655 #if PY_VERSION_HEX < 0x03030000
22656  char* defenc_c;
22657  PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL);
22658  if (!defenc) return NULL;
22659  defenc_c = PyBytes_AS_STRING(defenc);
22660 #if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
22661  {
22662  char* end = defenc_c + PyBytes_GET_SIZE(defenc);
22663  char* c;
22664  for (c = defenc_c; c < end; c++) {
22665  if ((unsigned char) (*c) >= 128) {
22666  PyUnicode_AsASCIIString(o);
22667  return NULL;
22668  }
22669  }
22670  }
22671 #endif
22672  *length = PyBytes_GET_SIZE(defenc);
22673  return defenc_c;
22674 #else
22675  if (__Pyx_PyUnicode_READY(o) == -1) return NULL;
22676 #if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
22677  if (PyUnicode_IS_ASCII(o)) {
22678  *length = PyUnicode_GET_LENGTH(o);
22679  return PyUnicode_AsUTF8(o);
22680  } else {
22681  PyUnicode_AsASCIIString(o);
22682  return NULL;
22683  }
22684 #else
22685  return PyUnicode_AsUTF8AndSize(o, length);
22686 #endif
22687 #endif
22688  } else
22689 #endif
22690 #if (!CYTHON_COMPILING_IN_PYPY) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE))
22691  if (PyByteArray_Check(o)) {
22692  *length = PyByteArray_GET_SIZE(o);
22693  return PyByteArray_AS_STRING(o);
22694  } else
22695 #endif
22696  {
22697  char* result;
22698  int r = PyBytes_AsStringAndSize(o, &result, length);
22699  if (unlikely(r < 0)) {
22700  return NULL;
22701  } else {
22702  return result;
22703  }
22704  }
22705 }
22706 static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
22707  int is_true = x == Py_True;
22708  if (is_true | (x == Py_False) | (x == Py_None)) return is_true;
22709  else return PyObject_IsTrue(x);
22710 }
22711 static CYTHON_INLINE PyObject* __Pyx_PyNumber_Int(PyObject* x) {
22712  PyNumberMethods *m;
22713  const char *name = NULL;
22714  PyObject *res = NULL;
22715 #if PY_MAJOR_VERSION < 3
22716  if (PyInt_Check(x) || PyLong_Check(x))
22717 #else
22718  if (PyLong_Check(x))
22719 #endif
22720  return __Pyx_NewRef(x);
22721  m = Py_TYPE(x)->tp_as_number;
22722 #if PY_MAJOR_VERSION < 3
22723  if (m && m->nb_int) {
22724  name = "int";
22725  res = PyNumber_Int(x);
22726  }
22727  else if (m && m->nb_long) {
22728  name = "long";
22729  res = PyNumber_Long(x);
22730  }
22731 #else
22732  if (m && m->nb_int) {
22733  name = "int";
22734  res = PyNumber_Long(x);
22735  }
22736 #endif
22737  if (res) {
22738 #if PY_MAJOR_VERSION < 3
22739  if (!PyInt_Check(res) && !PyLong_Check(res)) {
22740 #else
22741  if (!PyLong_Check(res)) {
22742 #endif
22743  PyErr_Format(PyExc_TypeError,
22744  "__%.4s__ returned non-%.4s (type %.200s)",
22745  name, name, Py_TYPE(res)->tp_name);
22746  Py_DECREF(res);
22747  return NULL;
22748  }
22749  }
22750  else if (!PyErr_Occurred()) {
22751  PyErr_SetString(PyExc_TypeError,
22752  "an integer is required");
22753  }
22754  return res;
22755 }
22756 static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {
22757  Py_ssize_t ival;
22758  PyObject *x;
22759 #if PY_MAJOR_VERSION < 3
22760  if (likely(PyInt_CheckExact(b))) {
22761  if (sizeof(Py_ssize_t) >= sizeof(long))
22762  return PyInt_AS_LONG(b);
22763  else
22764  return PyInt_AsSsize_t(x);
22765  }
22766 #endif
22767  if (likely(PyLong_CheckExact(b))) {
22768  #if CYTHON_USE_PYLONG_INTERNALS
22769  const digit* digits = ((PyLongObject*)b)->ob_digit;
22770  const Py_ssize_t size = Py_SIZE(b);
22771  if (likely(__Pyx_sst_abs(size) <= 1)) {
22772  ival = likely(size) ? digits[0] : 0;
22773  if (size == -1) ival = -ival;
22774  return ival;
22775  } else {
22776  switch (size) {
22777  case 2:
22778  if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
22779  return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
22780  }
22781  break;
22782  case -2:
22783  if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
22784  return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
22785  }
22786  break;
22787  case 3:
22788  if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
22789  return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
22790  }
22791  break;
22792  case -3:
22793  if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
22794  return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
22795  }
22796  break;
22797  case 4:
22798  if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
22799  return (Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
22800  }
22801  break;
22802  case -4:
22803  if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
22804  return -(Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
22805  }
22806  break;
22807  }
22808  }
22809  #endif
22810  return PyLong_AsSsize_t(b);
22811  }
22812  x = PyNumber_Index(b);
22813  if (!x) return -1;
22814  ival = PyInt_AsSsize_t(x);
22815  Py_DECREF(x);
22816  return ival;
22817 }
22818 static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
22819  return PyInt_FromSize_t(ival);
22820 }
22821 
22822 
22823 #endif /* Py_PYTHON_H */
glucat::compare
int compare(const index_set< LO, HI > &a, const index_set< LO, HI > &b)
"lexicographic compare" eg. {3,4,5} is less than {3,7,8}
Definition: index_set_imp.h:573
glucat::sqrt
const Multivector< Scalar_T, LO, HI > sqrt(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Square root of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:589
clifford_to_str
String clifford_to_str(const Multivector_T &mv)
The "informal" string representation of Multivector_T mv.
Definition: PyClical.h:98
glucat::acosh
const Multivector< Scalar_T, LO, HI > acosh(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Inverse hyperbolic cosine of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:738
index_set_to_repr
String index_set_to_repr(const Index_Set_T &ist)
The “official” string representation of Index_Set_T ist.
Definition: PyClical.h:69
glucat::sinh
const Multivector< Scalar_T, LO, HI > sinh(const Multivector< Scalar_T, LO, HI > &val)
Hyperbolic sine of multivector.
Definition: clifford_algebra_imp.h:826
IndexSet
index_set< lo_ndx, hi_ndx > IndexSet
Definition: PyClical.h:157
glucat::abs
Scalar_T abs(const Multivector< Scalar_T, LO, HI > &val)
Absolute value == sqrt(norm)
Definition: clifford_algebra_imp.h:491
glucat::log
const Multivector< Scalar_T, LO, HI > log(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Natural logarithm of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:704
clifford_to_repr
String clifford_to_repr(const Multivector_T &mv)
The “official” string representation of Multivector_T mv.
Definition: PyClical.h:87
cga3::cga3
Multivector_T cga3(const Multivector_T &x)
Convert Euclidean 3D vector to Conformal Geometric Algebra null vector [DL (10.50)].
Definition: PyClical.h:115
glucat::sin
const Multivector< Scalar_T, LO, HI > sin(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Sine of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:872
glucat::atanh
const Multivector< Scalar_T, LO, HI > atanh(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Inverse hyperbolic tangent of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:952
glucat::exp
const framed_multi< Scalar_T, LO, HI > exp(const framed_multi< Scalar_T, LO, HI > &val)
Exponential of multivector.
Definition: framed_multi_imp.h:1947
glucat::cos
const Multivector< Scalar_T, LO, HI > cos(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Cosine of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:765
glucat::tanh
const Multivector< Scalar_T, LO, HI > tanh(const Multivector< Scalar_T, LO, HI > &val)
Hyperbolic tangent of multivector.
Definition: clifford_algebra_imp.h:933
glucat::min_neg
index_t min_neg(const index_set< LO, HI > &ist)
Minimum negative index, or 0 if none.
Definition: index_set_imp.h:967
glucat::asin
const Multivector< Scalar_T, LO, HI > asin(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Inverse sine of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:905
Clifford
matrix_multi< scalar_t > Clifford
Definition: PyClical.h:160
glucat::complexifier
const Multivector< Scalar_T, LO, HI > complexifier(const Multivector< Scalar_T, LO, HI > &val)
Square root of -1 which commutes with all members of the frame of the given multivector.
Definition: clifford_algebra_imp.h:506
PyFloat_FromDouble
PyObject * PyFloat_FromDouble(Scalar_T v)
Definition: PyClical.h:59
glucat::atan
const Multivector< Scalar_T, LO, HI > atan(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Inverse tangent of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:1005
scalar_t
double scalar_t
Definition: PyClical.h:159
glucat::tan
const Multivector< Scalar_T, LO, HI > tan(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Tangent of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:977
glucat::acos
const Multivector< Scalar_T, LO, HI > acos(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Inverse cosine of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:798
index_set_to_str
String index_set_to_str(const Index_Set_T &ist)
The "informal" string representation of Index_Set_T ist.
Definition: PyClical.h:78
glucat::max_pos
index_t max_pos(const index_set< LO, HI > &ist)
Maximum positive index, or 0 if none.
Definition: index_set_imp.h:974
glucat::asinh
const Multivector< Scalar_T, LO, HI > asinh(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Inverse hyperbolic sine of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:845
glucat::max_abs
Scalar_T max_abs(const Multivector< Scalar_T, LO, HI > &val)
Maximum of absolute values of components of multivector: multivector infinity norm.
Definition: clifford_algebra_imp.h:499
PyClical.e
def e(obj)
Definition: PyClical.pyx:1887
glucat::cosh
const Multivector< Scalar_T, LO, HI > cosh(const Multivector< Scalar_T, LO, HI > &val)
Hyperbolic cosine of multivector.
Definition: clifford_algebra_imp.h:720
cga3::cga3std
Multivector_T cga3std(const Multivector_T &X)
Convert CGA3 null vector to standard Conformal Geometric Algebra null vector [DL (10.52)].
Definition: PyClical.h:126
cga3::agc3
Multivector_T agc3(const Multivector_T &X)
Convert CGA3 null vector to Euclidean 3D vector [DL (10.50)].
Definition: PyClical.h:138
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