Decode the bases of a given matroid from a string containing all possible binom(n,r) tuples of indices in revlex order. If the current tuple is a basis, a '*' is recorded, else a '0'.

Encode the bases of a given matroid as a string. All possible binom(n,r) tuples of indices are traversed in revlex order. If the current tuple is a basis, a '*' is recorded, else a '0'.

Check if a given list of sets satisfies the axioms to be the bases of a matroid.

Check if a given list of sets satisfies the axioms to be the flats of a matroid.

Check if a given list of sets satisfies the axioms to be the hyperplanes of a matroid.

calculate the internal activity of a base with respect to a given ordering of all bases. Let the given base B = B_j be the j-th one in the given ordering B_1, B_2, ... The internal activity of B_j is the number of "necessary" elements in B_j, i.e., the number of elements i in B_j such that B_j - {i} is not a subset of any B_k, k<j.

Check if a subset of the lattice of flats of a matroid is a modular cut

Creates the characteristic- and the rank-plueckervector of a matroid.

Calculates a minimal weight basis.

The matroid obtained from a matroid m by contraction of element .

The matroid obtained from a matroid m by deletion of element .

The direct sum of matroids m1 and m2

Produces the dual of a given matroid m.

Calculate the free extension of a matroid

Calculate the lexicographic extension of a matroid in a modular cut

The parallel extension of matroids m1 and m2 with basepoints e1 and e2

The parallel extension of a matroid m and uniform(2,4) with basepoint e

The series extension of matroids m1 and m2 with basepoints e1 and e2

The series extension of a matroid m and uniform(2,4) with basepoint e

The 2-sum of matroids m1 and m2 with basepoints e1 and e2

Creates the matroid with a given characteristic plueckervector of rank r and a ground set of n elements.

Creates a graphical matroid from a graph g.

Creates a matroid from the corresponding matroid polytope p.

Producing a positroid from a decorated permuatation

Configuration of the 9 points in the affine plane AG(2,3).

Configuration of all points in the affine 3-space AG(3,2) or the binary affine cube.

The unique relaxation of ag32_matroid.

A minimal non-representable matroid. Non-algebraic.

Creates the Fano plane matroid of rank 3 with 7 elements.

An excluded minor for some properties (see [Oxley:matroid theory (2nd ed.) page 650]). Non binary. Algebraic over all fields.

The 4-point planes are the six faces of the cube an the two twisted plannes. Identically self-dual. Representable over all field with more then 4 elements and algebraic over all fields.

An excluded minor for the dyadic matroids (see [Oxley:matroid theory (2nd ed.) page 558]).

An excluded minor for the dyadic matroids (see [Oxley:matroid theory (2nd ed.) page 558]).

The embedding into the reals of the seven points that define the Fano matroid. Representable if and only if the field has not characteristic 2.

Obtained from p8_matroid by relaxing its only pair of disjoint circuit-hyperplanes.

Create the matroid encoding the violation of Pappus' Theorem. Not realizable over any field. An excluded minor for all finite fields with more than four elements. Algebraic over all field that do not have characteristic 0.

A matroid related to the Vamos matroid (see [Oxley:matroid theory (2nd ed.) page 72])

The complement of the rank-3 whirl in PG(2,3). Non binary. Algebraic over all fields.

Produces many oxley matroids: ag23_matroid, ag32_matroid, ag32_prime_matroid, f8_matroid, j_matroid, l8_matroid, n1_matroid, n2_matroid, o7_matroid, p7_matroid, p8_matroid, non_p8_matroid, pappus_matroid, non_pappus_matroid, pg23_matroid, q3_gf3_star_matroid, q8_matroid, r8_matroid, r9a_matroid, r9b_matroid, r10_matroid, t8_matroid, vamos_matroid, non_vamos_matroid, wheel4_matroid

The only other ternary 3-spike apart from the non-Fano matroid. Non binary. Algebraic over all fields.

The repesentation over the reals is obtained from a 3-cube where one face is rotated by 45°. Non-representable if and only if the characeristic of the field is 2. Algebraic over all fields.

Create the matroid corresponding to Pappus' Theorem. Realizable if and only if the size of the field is not 2,3 or 5. An excluded minor for the field with 5 elements.

Configuration of the 13 points in the projective plane PG(2,3).

Creates the projective plane matroid of rank 3 with p**2+p+1 elements, where p is a prime.

The rank-3-ternary Dowling Geometry. Representable if and only if the field has not characteristic 2.

A minimal non-representable matroid. An excluded minor for fields that are not of characteristic 2 or have 3 elements. Non-algebraic.

A regular matroid that's not graphical nor cographical. Algebraic over all fields.

The real affine cube.

Not representable over any field. Taken from http://doc.sagemath.org/html/en/reference/matroids/sage/matroids/catalog.html

Not representable over any field. Taken from http://doc.sagemath.org/html/en/reference/matroids/sage/matroids/catalog.html

Representable if and only if the field has characteristic 3. An excluded minor for fields that are not of characteristic 2 or 3.

Creates the uniform matroid of rank r with n elements.

A minimal non-representable matroid. An excluded minor for all finite fields with more than four elements. Non-algebraic.

The rank-4 wheel.