BigObject ValuatedMatroid<Addition, Scalar>

from application matroid

A valuated matroid. It is given by a matroid and some form of valuation, either on bases or circuits. It has two template parameters:

Type Parameters:

Addition: Either Min or Max, has no default on purpose.

Scalar: An ordered group in which the valuation lives, Rational by default.

derived from:

Matroid

These properties capture combinatorial information of the object. Combinatorial properties only depend on combinatorial data of the object like, e.g., the face lattice.

SUBDIVISION

This is the matroid subdivision of POLYTOPE according to the lifting defined by VALUATION_ON_BASES (or minus VALUATION_ON_BASES in the case of max).

Type:

Array<Set<Int>>

properties related to the valuation of the matroid.

VALUATION_ON_BASES

Defines a valuation on each basis. Entry number i is a valuation on the i-th element of BASES. Must fulfill the tropical Plücker relations.

Type:

Vector<TropicalNumber<Addition,Scalar>>

VALUATION_ON_CIRCUITS

Defines a valuation on each circuit. Row i is a representative of the i-th element of CIRCUITS. Must fulfill the tropical circuit valuation axioms. The representative is normalized such that the first non-tropical-zero entry is 0.

Type:

Matrix<TropicalNumber<Addition,Scalar>,NonSymmetric>