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.

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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>>

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properties related to the valuation of the matroid.

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POSITIVE_VALUATION

Whether the valuated matroid is transversal

Type:

Bool

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TRANSVERSAL_VALUATED_MATROID

Whether the valuated matroid is transversal

Type:

Bool

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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>>

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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>

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