Collections of matroids#
This module contains functions that access the collections of matroids in the
database. Each of these functions returns an iterator over the nonparametrized
matroids from the corresponding collection. These functions can be viewed by
typing matroids.
+ Tab.
AUTHORS:
Giorgos Mousa (2023-12-08): initial version
- sage.matroids.database_collections.AllMatroids(n, r=None, type='all')[source]#
Return an iterator over all matroids of certain number of elements (and, optionally, of specific rank and type).
INPUT:
n
– integer; the number of elements of the matroidsr
– integer (optional); the rank of the matroids; \(0 \le r \le n\)type
– string (default:'all'
); the type of the matroids; must be one of the following:'all'
– all matroids; available: (n=0-9), (n=0-12, r=0-2), (n=0-11, r=3)'unorientable'
– all unorientable matroids; the rankr
must be specified; available: (n=7-11, r=3), (n=7-9, r=4)any other type for which there exists an
is_type
method; availability same as for'all'
OUTPUT: an iterator over matroids
EXAMPLES:
sage: for M in matroids.AllMatroids(2): # optional - matroid_database ....: M all_n02_r00_#0: Matroid of rank 0 on 2 elements with 1 bases all_n02_r01_#0: Matroid of rank 1 on 2 elements with 2 bases all_n02_r01_#1: Matroid of rank 1 on 2 elements with 1 bases all_n02_r02_#0: Matroid of rank 2 on 2 elements with 1 bases
>>> from sage.all import * >>> for M in matroids.AllMatroids(Integer(2)): # optional - matroid_database ... M all_n02_r00_#0: Matroid of rank 0 on 2 elements with 1 bases all_n02_r01_#0: Matroid of rank 1 on 2 elements with 2 bases all_n02_r01_#1: Matroid of rank 1 on 2 elements with 1 bases all_n02_r02_#0: Matroid of rank 2 on 2 elements with 1 bases
sage: for M in matroids.AllMatroids(5, 3, "simple"): # optional - matroid_database ....: M simple_n05_r03_#0: Matroid of rank 3 on 5 elements with 10 bases simple_n05_r03_#1: Matroid of rank 3 on 5 elements with 9 bases simple_n05_r03_#2: Matroid of rank 3 on 5 elements with 8 bases simple_n05_r03_#3: Matroid of rank 3 on 5 elements with 6 bases
>>> from sage.all import * >>> for M in matroids.AllMatroids(Integer(5), Integer(3), "simple"): # optional - matroid_database ... M simple_n05_r03_#0: Matroid of rank 3 on 5 elements with 10 bases simple_n05_r03_#1: Matroid of rank 3 on 5 elements with 9 bases simple_n05_r03_#2: Matroid of rank 3 on 5 elements with 8 bases simple_n05_r03_#3: Matroid of rank 3 on 5 elements with 6 bases
sage: # optional - matroid_database sage: for M in matroids.AllMatroids(4, type="paving"): ....: M paving_n04_r00_#0: Matroid of rank 0 on 4 elements with 1 bases paving_n04_r01_#0: Matroid of rank 1 on 4 elements with 4 bases paving_n04_r01_#1: Matroid of rank 1 on 4 elements with 3 bases paving_n04_r01_#2: Matroid of rank 1 on 4 elements with 2 bases paving_n04_r01_#3: Matroid of rank 1 on 4 elements with 1 bases paving_n04_r02_#0: Matroid of rank 2 on 4 elements with 6 bases paving_n04_r02_#1: Matroid of rank 2 on 4 elements with 5 bases paving_n04_r02_#2: Matroid of rank 2 on 4 elements with 4 bases paving_n04_r02_#3: Matroid of rank 2 on 4 elements with 3 bases paving_n04_r03_#0: Matroid of rank 3 on 4 elements with 4 bases paving_n04_r03_#1: Matroid of rank 3 on 4 elements with 3 bases paving_n04_r04_#0: Matroid of rank 4 on 4 elements with 1 bases
>>> from sage.all import * >>> # optional - matroid_database >>> for M in matroids.AllMatroids(Integer(4), type="paving"): ... M paving_n04_r00_#0: Matroid of rank 0 on 4 elements with 1 bases paving_n04_r01_#0: Matroid of rank 1 on 4 elements with 4 bases paving_n04_r01_#1: Matroid of rank 1 on 4 elements with 3 bases paving_n04_r01_#2: Matroid of rank 1 on 4 elements with 2 bases paving_n04_r01_#3: Matroid of rank 1 on 4 elements with 1 bases paving_n04_r02_#0: Matroid of rank 2 on 4 elements with 6 bases paving_n04_r02_#1: Matroid of rank 2 on 4 elements with 5 bases paving_n04_r02_#2: Matroid of rank 2 on 4 elements with 4 bases paving_n04_r02_#3: Matroid of rank 2 on 4 elements with 3 bases paving_n04_r03_#0: Matroid of rank 3 on 4 elements with 4 bases paving_n04_r03_#1: Matroid of rank 3 on 4 elements with 3 bases paving_n04_r04_#0: Matroid of rank 4 on 4 elements with 1 bases
sage: # optional - matroid_database sage: for M in matroids.AllMatroids(10, 4): ....: M Traceback (most recent call last): ... ValueError: (n=10, r=4, type="all") is not available in the database sage: for M in matroids.AllMatroids(12, 3, "unorientable"): ....: M Traceback (most recent call last): ... ValueError: (n=12, r=3, type="unorientable") is not available in the database sage: for M in matroids.AllMatroids(8, type="unorientable"): ....: M Traceback (most recent call last): ... ValueError: The rank needs to be specified for type "unorientable" sage: for M in matroids.AllMatroids(6, type="nice"): ....: M Traceback (most recent call last): ... AttributeError: The type "nice" is not available. There needs to be an "is_nice()" attribute for the type to be supported.
>>> from sage.all import * >>> # optional - matroid_database >>> for M in matroids.AllMatroids(Integer(10), Integer(4)): ... M Traceback (most recent call last): ... ValueError: (n=10, r=4, type="all") is not available in the database >>> for M in matroids.AllMatroids(Integer(12), Integer(3), "unorientable"): ... M Traceback (most recent call last): ... ValueError: (n=12, r=3, type="unorientable") is not available in the database >>> for M in matroids.AllMatroids(Integer(8), type="unorientable"): ... M Traceback (most recent call last): ... ValueError: The rank needs to be specified for type "unorientable" >>> for M in matroids.AllMatroids(Integer(6), type="nice"): ... M Traceback (most recent call last): ... AttributeError: The type "nice" is not available. There needs to be an "is_nice()" attribute for the type to be supported.
REFERENCES:
The underlying database was retrieved from Yoshitake Matsumoto’s Database of Matroids; see [Mat2012].
- sage.matroids.database_collections.BrettellMatroids()[source]#
Return an iterator over Brettell’s matroid collection.
EXAMPLES:
sage: BM = list(matroids.BrettellMatroids()); len(BM) 68 sage: import random sage: M = random.choice(BM) sage: M.is_valid() True
>>> from sage.all import * >>> BM = list(matroids.BrettellMatroids()); len(BM) 68 >>> import random >>> M = random.choice(BM) >>> M.is_valid() True
See also
Matroid catalog
, underBrettell's matroid collection
.
- sage.matroids.database_collections.OxleyMatroids()[source]#
Return an iterator over Oxley’s matroid collection.
EXAMPLES:
sage: OM = list(matroids.OxleyMatroids()); len(OM) 44 sage: import random sage: M = random.choice(OM) sage: M.is_valid() True
>>> from sage.all import * >>> OM = list(matroids.OxleyMatroids()); len(OM) 44 >>> import random >>> M = random.choice(OM) >>> M.is_valid() True
See also
Matroid catalog
, underOxley's matroid collection
.REFERENCES:
These matroids are the nonparametrized matroids that appear in the Appendix
Some Interesting Matroids
in [Oxl2011] (p. 639-64).
- sage.matroids.database_collections.VariousMatroids()[source]#
Return an iterator over various other named matroids.
EXAMPLES:
sage: VM = list(matroids.VariousMatroids()); len(VM) 16 sage: import random sage: M = random.choice(VM) sage: M.is_valid() True
>>> from sage.all import * >>> VM = list(matroids.VariousMatroids()); len(VM) 16 >>> import random >>> M = random.choice(VM) >>> M.is_valid() True
See also
Matroid catalog
, underCollection of various matroids
.