Metadata-Version: 2.1
Name: veering
Version: 0.3
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 (using regina, snappy, and sage) for working with transverse taut
        and veering ideal triangulations -- implemented by Anna Parlak, Saul Schleimer,
        and Henry Segerman.  We thank Nathan Dunfield for many helpful comments (and
        for some code).
        
        ### Installation
        
        To install (or uninstall) veering inside Sage via the command line, using pip, type:
        
            sage -pip install veering
        
        or
        
            sage -pip uninstall veering
        
        For installation into your system's Python, replace `sage -pip` by `pip3`.
        Note that the github repository of veering contains further data and scripts
        which are not installed by pip.
        
        Almost all of the veering code relies on regina; some of it relies on
        snappy and some relies 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
        
        After installation start a sage session and run the following:
        
            sage: import veering
            sage: from veering import test_suite
            sage: test_suite.run_tests()
        
        Each test should take at most a few seconds.
        
        ### Usage
        
        As a simple example:
        
            sage: census = veering.veering_census(); len(census)
            87047
        
        The veering census contains the 87047 taut isomorphism signatures
        of the veering triangulations with at most 16 tetrahedra.  These are
        ordered lexicographically.
        
            sage: sig = census[1]; sig
            'cPcbbbiht_12'
        
        This is the taut isomorphism signature for the only 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, for each tetrahedron, which two
        edges have dihedral angle pi; the other four edges have dihedral angle 
        zero.
        
            sage: from veering import taut_polytope
            sage: taut_polytope.is_layered(sig)
            True
        
        This taut structure is layered; thus the figure-eight knot is fibered.
        
            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
        
        The taut and veering polynomials are defined by Michael Landry, Yair 
        Minsky and Sam Taylor.  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 = census[257]; sig
            'iLLLQPcbeegefhhhhhhahahha_01110221'
            sage: taut_polytope.cone_in_homology(sig)
            [N(1, -1), N(1, 1)]
            
        The cone of homology classes carried by the veering triangulation
        `iLLLQPcbeegefhhhhhhahahha_01110221` 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 
        version number and the year). 
        
        ```
        @Misc{Veering,
            author = {Anna Parlak and Saul Schleimer and Henry Segerman},
            title = {veering x.y, code for studying taut and veering ideal triangulations},
            howpublished = {\url{https://github.com/henryseg/Veering}},
            year = {20zz},
        }
        ```
        
        ### Contact
        
        Please 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
