basis(List,VectorSpace) -- compute a basis

Synopsis

• Function: basis

• Usage:

  b=basis(s,V)

• Inputs:
  • s, a list, the weight
  • V, an instance of the type VectorSpace, an instance of type VectorSpace
• Optional inputs:
  • Degree => ..., default value null,
  • Limit => ..., default value infinity,
  • SourceRing => ..., default value null,
  • Strategy => ..., default value null,
  • Truncate => ..., default value false,
  • Variables => ..., default value null,
• Outputs:
  • b, a list, a basis for the part of $V$ of multi-degree $s$.

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 : basis({5,3},H)

o6 = {(b c)}

o6 : List

i7 : Z=cycles Q

o7 = Z

o7 : LieSubAlgebra

i8 : basis({5,3},Z)

o8 = {(b c)}

o8 : List

See also

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