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GradedLieAlgebras :: invImageLie

invImageLie -- computes the dimension for the inverse image of a map or derivation

Synopsis

Description

The list b should contain generalExpressionLie of the same degree n (and also homological degree d in the second case). The output is the dimension for the inverse image under f of the space generated by b. This dimension for a MapLie f may also be computed as the dimension of the intersection of image(f) and b plus the dimension of kernel(f) in degree n.

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],[]})

o3 = f

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

o4 = d

o4 : DerLie
i5 : invImageLie(3,f,{[x,y,x]})

o5 = 2
i6 : invImageLie(3,d,{[x,y,x]})

o6 = 3
i7 : length intersectionLie(3,{imageBasisLie(3,f),{[x,y,x]}})+length kernelBasisLie(3,f)

o7 = 2

See also

Ways to use invImageLie :