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Reference documentation for older polymake versions: release 3.4, release 3.3, release 3.2
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:
Scalar
: An ordered group in which the valuation lives,Rational
by default.- derived from:
Properties
Combinatorics
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 byVALUATION_ON_BASES
(or minusVALUATION_ON_BASES
in the case of max).- Type:
Valuation
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>