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sagemathgh-39155: Salvage work on gammoids Add matroid classes `Gammoid` and `TransversalMatroid`. Transversal matroids are also gammoids. From the archived [sagetrac- mirror](https://github.com/sagemath/sagetrac-mirror) repository (branches [public/matroids/transversal_matroids- 23536](https://github.com/sagemath/sagetrac- mirror/tree/public/matroids/transversal_matroids-23536) and [u/zgershkoff/gammoids](https://github.com/sagemath/sagetrac- mirror/tree/u/zgershkoff/gammoids)). Resolves sagemath#23536, resolves sagemath#23601, resolves sagemath#23628. URL: sagemath#39155 Reported by: gmou3 Reviewer(s): Kwankyu Lee
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‎src/doc/en/reference/matroids/index.rst

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:maxdepth: 1
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sage/matroids/basis_matroid
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sage/matroids/circuits_matroid
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sage/matroids/circuit_closures_matroid
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sage/matroids/circuits_matroid
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sage/matroids/flats_matroid
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sage/matroids/gammoid
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sage/matroids/graphic_matroid
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sage/matroids/linear_matroid
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sage/matroids/rank_matroid
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sage/matroids/graphic_matroid
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sage/matroids/transversal_matroid
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Chow rings of matroids
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----------------------
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.. toctree::
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:maxdepth: 1
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sage/matroids/basis_exchange_matroid
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sage/matroids/dual_matroid
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sage/matroids/minor_matroid
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sage/matroids/basis_exchange_matroid
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Advanced functionality
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----------------------
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:maxdepth: 1
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sage/matroids/advanced
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sage/matroids/utilities
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sage/matroids/extension
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sage/matroids/utilities
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Internals
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---------

‎src/doc/en/reference/references/index.rst

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.. [BrHu2019] Petter Brändén, June Huh. *Lorentzian polynomials*.
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Ann. Math. (2) 192, No. 3, 821-891 (2020).
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:arxiv:`1902.03719`, :doi:`10.4007/annals.2020.192.3.4`.
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.. [Bru2014] Erwan Brugalle and Kristin Shaw. *A bit of tropical geometry*.
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Amer. Math. Monthly, 121(7):563-589, 2014.
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.. [Bo2009] Bosch, S., Algebra, Springer 2009
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.. [Bon2017] Joseph E. Bonin, *Lattices Related to Extensions of
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Presentations of Transversal Matroids*.
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Electronic Journal of Combinatorics (2017), #P1.49.
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.. [Bor1993] Lev A. Borisov,
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"Towards the mirror symmetry for Calabi-Yau complete
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intersections in Gorenstein Fano toric varieties", 1993.
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.. [NT2007] Serguei Norine and Robin Thomas. *Minimally Non-Pfaffian Graphs*.
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Combinatorica, vol. 27, no. 5, pages: 587 -- 600, Springer. 2007.
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:doi:`10.1016/j.jctb.2007.12.005`.
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.. [Nur2004] K. Nurmela. *Upper bounds for covering arrays by tabu search*.
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Discrete Applied Math., 138 (2004), 143-152.
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of the chromatic polynomial of a graph*, Adv. Math., ***111***
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no.1 (1995), 166-194. :doi:`10.1006/aima.1995.1020`.
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.. [Sta1998] \R. P. Stanley, *Graph colorings and related symmetric functions:
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.. [Sta1998] \R. P. Stanley, *Graph colorings and related symmetric functions:
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ideas and applications A description of results, interesting applications,
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& notable open problems*, Discrete Mathematics, 193, no.1-3, (1998),
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267-286. :doi:`10.1016/S0012-365X(98)00146-0`.

‎src/sage/matroids/basis_matroid.pyx

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"""
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def __init__(self, M=None, groundset=None, bases=None, nonbases=None, rank=None):
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"""
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See class definition for full documentation.
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See the class definition for full documentation.
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EXAMPLES::
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.. WARNING::
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This method is linked to __richcmp__ (in Cython) and __cmp__ or
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__eq__/__ne__ (in Python). If you override one, you should (and in
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Cython: MUST) override the other!
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This method is linked to ``__richcmp__`` (in Cython) and ``__cmp__``
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or ``__eq__``/``__ne__`` (in Python). If you override one, you
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should (and, in Cython, \emph{must}) override the other!
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EXAMPLES::
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‎src/sage/matroids/circuit_closures_matroid.pyx

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def __init__(self, M=None, groundset=None, circuit_closures=None):
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"""
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Initialization of the matroid. See class docstring for full
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Initialization of the matroid. See the class docstring for full
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documentation.
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EXAMPLES::
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.. WARNING::
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This method is linked to __richcmp__ (in Cython) and __cmp__ or
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__eq__/__ne__ (in Python). If you override one, you should
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(and in Cython: MUST) override the other!
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This method is linked to ``__richcmp__`` (in Cython) and ``__cmp__``
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or ``__eq__``/``__ne__`` (in Python). If you override one, you
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should (and, in Cython, \emph{must}) override the other!
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EXAMPLES::
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‎src/sage/matroids/circuits_matroid.pyx

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def __init__(self, M=None, groundset=None, circuits=None, nsc_defined=False):
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"""
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Initialization of the matroid. See class docstring for full
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Initialization of the matroid. See the class docstring for full
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documentation.
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TESTS::
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.. WARNING::
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This method is linked to __richcmp__ (in Cython) and __cmp__ or
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__eq__/__ne__ (in Python). If you override one, you should
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(and in Cython: MUST) override the other!
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This method is linked to ``__richcmp__`` (in Cython) and ``__cmp__``
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or ``__eq__``/``__ne__`` (in Python). If you override one, you
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should (and, in Cython, \emph{must}) override the other!
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EXAMPLES::
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‎src/sage/matroids/dual_matroid.py

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def __init__(self, matroid):
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See the class definition for documentation.
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EXAMPLES::
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.. WARNING::
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This method is linked to __richcmp__ (in Cython) and __cmp__ or
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__eq__/__ne__ (in Python). If you override one, you should (and in
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Cython: MUST) override the other!
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This method is linked to ``__richcmp__`` (in Cython) and ``__cmp__``
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or ``__eq__``/``__ne__`` (in Python). If you override one, you
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should (and, in Cython, \emph{must}) override the other!
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EXAMPLES::
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‎src/sage/matroids/extension.pyx

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"""
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def __init__(self, M, line_length=None, subsets=None, splice=None):
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"""
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See the class docstring for full documentation.
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EXAMPLES::
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"""
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def __init__(self, M, e, line_length=None, subsets=None, splice=None, orderly=False):
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"""
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See the class docstring for full documentation.
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EXAMPLES::
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‎src/sage/matroids/flats_matroid.pyx

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def __init__(self, M=None, groundset=None, flats=None):
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"""
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Initialization of the matroid. See class docstring for full
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Initialization of the matroid. See the class docstring for full
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documentation.
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.. WARNING::
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This method is linked to __richcmp__ (in Cython) and __cmp__ or
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__eq__/__ne__ (in Python). If you override one, you should
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(and in Cython: MUST) override the other!
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This method is linked to ``__richcmp__`` (in Cython) and ``__cmp__``
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or ``__eq__``/``__ne__`` (in Python). If you override one, you
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should (and, in Cython, \emph{must}) override the other!
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EXAMPLES::
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