dim(ZZ,VectorSpace) -- compute the dimension

Synopsis

• Function: dim

• Usage:

  d=dim(m,V)

• Inputs:
  • m, an integer,
  • V, an instance of the type VectorSpace, an instance of type VectorSpace
• Outputs:
  • d, an integer, the dimension of $V$ in first degree $m$.

Description

i1 : L = lieAlgebra({a,b,c},Weights=>{{1,0},{2,1},{3,2}},
           Signs=>{1,1,1},LastWeightHomological=>true)

o1 = L

o1 : LieAlgebra

i2 : D= differentialLieAlgebra({0_L,a a,a b})

o2 = D

o2 : LieAlgebra

i3 : J=lieIdeal({b b + 4 a c})

o3 = J

o3 : FGLieIdeal

i4 : Q=D/J

o4 = Q

o4 : LieAlgebra

i5 : H=lieHomology Q

o5 = H

o5 : VectorSpace

i6 : dim(5,H)

o6 = 1

i7 : Z=cycles Q

o7 = Z

o7 : LieSubAlgebra

i8 : dim(5,Z)

o8 = 2

See also

• dims -- compute the dimensions of a Lie algebra, Ext-algebra or vector space
• basis(ZZ,VectorSpace) -- compute a basis
• dim(ZZ,LieAlgebra) -- compute the dimension
• dim(ZZ,ZZ,LieAlgebra) -- compute the dimension
• dim(List,LieAlgebra) -- compute the dimension
• dim(ZZ,ExtAlgebra) -- compute the dimension
• dim(ZZ,ZZ,ExtAlgebra) -- compute the dimension
• dim(List,ExtAlgebra) -- compute the dimension
• dim(ZZ,ZZ,VectorSpace) -- compute the dimension
• dim(List,VectorSpace) -- compute the dimension