next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
GradedLieAlgebras :: invImageBasisLie

invImageBasisLie -- computes a basis for the inverse image of a map or derivation

Synopsis

Description

The list b should contain LieElement of the same degree. The output bb is a list of LieElement, which is a basis for the inverse image under f of the space generated by b.

i1 : L=lieAlgebra({x,y},genSigns=>1)

o1 = L

o1 : LieAlgebra
i2 : M=lieAlgebra({a,b},genSigns=>1)

o2 = M

o2 : LieAlgebra
i3 : f = mapLie(L,M,{x+y,x-y})

o3 = f

o3 : MapLie
i4 : d = derLie(f,{x x,x y})

o4 = d

o4 : DerLie
i5 : invImageBasisLie(f,{x y x})

o5 = {(1/2)(b a a) + (b b a)}

o5 : List
i6 : invImageBasisLie(d,{x y x})

o6 = {(a a), 2 (b a) + (b b)}

o6 : List

See also

Ways to use invImageBasisLie :