Subsections

• Accessing Vector Space Invariants
• Membership and Equality
• Operations on Subspaces

Given an vector space V and a positive integer i, return the i-th generating element of V.

BaseField(V) : ModTupFld -> Fld

Given a K-vector space V, return the field K.

Given a K-vector space V which is a subspace of K^((n)), return n.

Degree(u) : ModTupFldElt -> RngIntElt

Given an vector u belonging to a subspace of the vector space K^((n)), return n.

The dimension of the vector space V.

The generators for the vector space V, returned as a set.

Ngens(M) : ModTupFld -> RngIntElt

The number of generators for the vector space V.

Given a K-vector space V which is a subspace of K^((n)), return n.

OverDimension(u) : ModTupFldElt -> RngIntElt

Given an vector u belonging to a subspace of the vector space K^((n)), return n.

The generic vector space containing V, i.e. the full vector space in which V is naturally embedded.

The power structure for the vector space V (the set consisting of all finite dimensional vector spaces).

True if the element v lies in the vector space V, where v and V belong to a common space.

True if the element v does not lie in the vector space V, where v and V belong to a common space.

True if the K-vector space U is contained in the K-vector space V, where U and V are subspaces of some common vector space.

True if the K-vector space U is not contained in the K-vector space V, where U and V are subspaces of some common vector space.

True if the subspaces U and V are equal, where U and V belong to a common vector space.

True if the subspaces U and V are not equal, where U and V belong to a common vector space.

Sum of the subspaces U and V, where U and V must be subspaces of a common vector space.

Intersection of the subspaces U and V, where U and V must be subspaces of a common vector space.

Replace U with the intersection of the subspaces U and V, where U and V must be subspaces of a common vector space.

Intersection of the subspaces of the set or sequence S, which must be subspaces of a common vector space.

The tensor (Kronecker) product of the vector spaces U and V, generated by all the tensor products of elements of U by elements of V. The resulting vector space has degree equal to the product of the degrees of U and V.

Given a subspace U of the vector space V, construct a complement for U in V (a subspace of V).

Given a subspace U of the vector space V over a finite field, return a transversal for U in V as a set of vectors.