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BindGlobal( "TableByWeightedBasisOfRad", function(A)
local n, F, q, N, C, m, e, b, c, T, W, i, j, d, v, w, k, l;
# set up
n := Dimension(A)-1;
F := LeftActingDomain(A);
q := Size(F);
N := NullMat(n+1,n+1,F);
# get coeffs for basis C = {v_c | c coeff, c <> 0} of I
C := WeightedBasisOfRad(A);
m := C.weights[n];
e := Position(C.weights, 2)-1;
# precompute base change
b := List(C.basis, x -> Coefficients(Basis(A),x));
Add(b, IdentityMat(n+1, F)[n+1]);
#ConvertToMatrixRepNC(b, q);
c := b^-1;
# get structure constants and words
T := [];
W := [];
for i in [1..n] do
if Sum(C.exps[i])=1 then
T[i] := [];
for j in [1..n] do
if C.weights[i]+C.weights[j] <= m then
T[i][j] := Coefficients(Basis(A), C.basis[i]*C.basis[j]);
else
T[i][j] := N[j];
fi;
od;
T[i][n+1] := b[i];
#ConvertToMatrixRepNC(T[i], q);
T[i] := T[i]*c;
T[i] := T[i]{[1..n]}{[1..n]};
#ConvertToMatrixRepNC(T[i], q);
else
d := PositionNonZero(C.exps[i]);
v := 0*C.exps[i]; v[d] := 1; l := Position(C.exps, v);
w := C.exps[i]-v; k := Position(C.exps, w);
W[i] := [l,k];
fi;
od;
# return
return rec( tab := T,
wds := W,
fld := F,
dim := n,
wgs := C.weights,
rnk := RankByWeights(C.weights) );
end );
BindGlobal( "NilpotentTableOfRad", function( A )
return TableByWeightedBasisOfRad(A);
end );
[ Dauer der Verarbeitung: 0.22 Sekunden
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