Metadata-Version: 2.1
Name: veering
Version: 0.2
Summary: Taut and veering triangulations
Home-page: https://github.com/henryseg/Veering
Author: Anna Parlak, Henry Segerman, Saul Schleimer
Author-email: segerman@math.okstate.edu
License: UNKNOWN
Description: # Veering
        
        Python code for working with transverse taut and veering ideal triangulations; 
        implemented by Anna Parlak, Saul Schleimer, and Henry Segerman. The taut and 
        veering polynomials are defined by Michael Landry, Yair Minsky and Sam Taylor. 
        We thank Nathan Dunfield for many helpful comments (and for some code).
        
        ### Installation
        
        
        To install Veering inside Sage via the command line type:
        
            sage -pip install git+https://github.com/henryseg/Veering
        
        If you wish to install in Python, replace `sage -pip` by `pip`
        in the above command.
        
        Essentially all of the veering code relies on regina; some of it
        relies on snappy and some on SageMath. Other parts rely on the 
        Python vector graphics package pyx. Installation instructions for 
        SageMath, snappy, and regina can be found at the following webpages:
        
        https://doc.sagemath.org/html/en/installation/ \
        https://snappy.math.uic.edu/installing.html \
        https://github.com/3-manifolds/regina_wheels
        
        ### Testing
        
        For a sanity check do, run in a sage console:
        
            sage: from veering.test_suite import run_tests
            sage: run_tests()
        
        ### Usage
        
        As an example, start a sage sessiond and type:
        
            sage: from veering.file_io import parse_data_file
            sage: veering_isosigs = parse_data_file('veering_census.txt')
        
        The list `veering_isosigs` now contains all taut isomorphism signatures
        for the veering triangulations with at most 16 tetrahedra. These are
        ordered lexicographically.
        
            sage: sig = veering_isosigs[1]; sig
            'cPcbbbiht_12'
        
        This is the taut isomorphism signature for the only known veering
        structure on the figure eight knot complement. The string before the
        underscore is the isomorphism signature for the triangulation; the
        string after the underscore records the positions of the edges with
        dihedral angle pi in each tetrahedron.
        
            sage: from veering import taut_polytope
            sage: taut_polytope.is_layered(sig)
            True
        
        This taut structure is layered; we deduce that the figure eight knot
        is a fibered knot.
        
            sage: from veering import taut_polynomial
            sage: taut_polynomial.taut_polynomial_via_tree(sig)
            a^2 - 3*a + 1
            sage: taut_polynomial.taut_polynomial_via_tree(sig, mode = 'alexander')
            a^2 - 3*a + 1
            sage: from veering import veering_polynomial
            sage: veering_polynomial.veering_polynomial(sig)
            a^3 - 4*a^2 + 4*a - 1
            
        Note that the taut polynomial divides the veering polynomial; this is 
        true in general. The taut polynomial of this veering triangulation is
        equal to the Alexander polynomial of the underlying manifold; this is
        not true in general.
        
            sage: sig = veering_isosigs[257]
            sage: from veering import taut_polytope
            sage: taut_polytope.cone_in_homology(sig)
            [N(1, -1), N(1, 1)]
            
        The cone of homology classes carried by the veering triangulation 
        `veering_isosigs[257]` is spanned by the rays passing through (1,-1) and
        (1,1). Landry, Minsky and Taylor proved that, if nonempty, this cone is
        equal to a cone on a (not necessarily top-dimensional) face of the Thurston 
        norm ball. The chosen basis on H^1 is dual to the basis of H_1 used to 
        compute the taut and veering polynomials.
        
        ### Webpage
        
        For references, for information about the census, and for many diagrams, 
        please see:
        
        https://math.okstate.edu/people/segerman/veering.html
        
        ### Citation
        
        When citing the codebase, please use the following (updating the year). 
        
        ```
        @Misc{Veering,
            author = {Anna Parlak and Saul Schleimer and Henry Segerman},
            title = {Veering, code for studying taut and veering ideal triangulations},
            howpublished = {\url{https://github.com/henryseg/Veering}},
            year = {20xx},
        }
        ```
        
        ### Contact
        
        Please do contact us with any and all suggestions, questions, and/or corrections.
        
        ### Licence
        
        This work is in the public domain. See the LICENCE for details.
        
Keywords: surfaces,manifolds,geometry,taut triangulation,veering triangulation
Platform: UNKNOWN
Description-Content-Type: text/markdown
