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# VectorSpace -- the class of all vector spaces

## Description

This type represents e.g., homology of Lie algebras, and it has the subtypes LieSubSpace, LieSubAlgebra, LieIdeal, FGLieIdeal, FGLieSubAlgebra.

    i1 : L = lieAlgebra{a,b}

    o1 = L

    o1 : LieAlgebra

    i2 : I=lieIdeal{a}

    o2 = I

    o2 : FGLieIdeal

    i3 : showStructure class I

    o3 = Thing : HashTable : VectorSpace : LieSubSpace : LieSubAlgebra : LieIdeal : FGLieIdeal

    o3 : Descent

    i4 : H=lieHomology L

    o4 = H

    o4 : VectorSpace

## See also

- LieSubAlgebra -- the class of all Lie subalgebras
- lieSubAlgebra -- make a Lie subalgebra
- lieIdeal -- make a Lie ideal
- lieHomology -- make the homology as a vector space

## Types of VectorSpace:

- LieSubSpace -- the class of all Lie subspaces

## Methods that use an object of class VectorSpace:

- basis(List,VectorSpace) -- compute a basis
- basis(ZZ,VectorSpace) -- compute a basis
- basis(ZZ,ZZ,VectorSpace) -- compute a basis
- `describe(VectorSpace)` -- see describe(LieAlgebra) -- real description
- dim(List,VectorSpace) -- compute the dimension
- dim(ZZ,VectorSpace) -- compute the dimension
- dim(ZZ,ZZ,VectorSpace) -- compute the dimension
- `dims(ZZ,VectorSpace)` -- see dims -- compute the dimensions of a Lie algebra, Ext-algebra or vector space
- `dims(ZZ,ZZ,VectorSpace)` -- see dims -- compute the dimensions of a Lie algebra, Ext-algebra or vector space

## For the programmer

The object VectorSpace is a type, with ancestor classes HashTable < Thing.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/GradedLieAlgebras/doc.m2:322:0.