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BindGlobal( "MySolutionMat", function( mat, vec )
local s;
if vec=0*vec then
return List(mat, x -> 0);
elif mat=[] then
return fail;
fi;
s := SolutionMat(mat, vec);
if IsBool(s) then return s; else return IntVecFFE(s); fi;
end );
BindGlobal( "MyEcheloniseMat", function ( mat )
local ech, tmp, i;
if Length( mat ) = 0 then return mat; fi;
ech := SemiEchelonMat( mat );
tmp := [ ];
for i in [ 1 .. Length( ech.heads ) ] do
if ech.heads[i] <> 0 then
Add( tmp, ech.vectors[ech.heads[i]] );
fi;
od;
return tmp;
end );
BindGlobal( "CoeffsMinimalElement", function( vec, base )
local mat, cof, d;
if Length(base)=0 then return []; fi;
cof := List(base, x -> 0*vec[1]);
mat := SemiEchelonMatTransformation( base );
for d in [1..Length(vec)] do
if mat.heads[d] <> 0 and vec[d] <> 0 * vec[d] then
cof[mat.heads[d]] := cof[mat.heads[d]] - vec[d];
vec := vec - vec[d]*mat.vectors[mat.heads[d]];
fi;
od;
return IntVecFFE(cof * mat.coeffs);
end );
# The following function behaves like `TriangulizedMat`, the only
# difference is that any zero rows are dropped, i.e., as base of
# the row-space is returned (like `BaseMat` does, but there it
# is not necessarily triangular)
BindGlobal( "MyTriangulizedBaseMat", function(mat)
local new, j;
if Length(mat) = 0 then return mat; fi;
new := TriangulizedMat(mat);
j := Position(new, 0*new[1]);
if IsBool(j) then return new; fi;
return new{[1..j-1]};
end );
BindGlobal( "IsInvariantAssert", function( base, mats )
local mat, b;
for mat in mats do
for b in base do
if IsBool(SolutionMat(base, b*mat)) then return false; fi;
od;
od;
return true;
end );
#LastNonZero := function( list, F )
# local i;
# for i in Reversed( [1..Length(list)] ) do
# if list[i] <> Zero(F) then return i; fi;
# od;
# return false;
#end;
BindGlobal( "IndVector", function( g, d, base )
if IsBool(base) then return g; fi;
return SolutionMat(base, g){[1..d]};
end );
BindGlobal( "IndMatrix", function( hom, mat )
local ind, baseI, baseS, b, e, f, g;
ind := [];
baseI := Basis( ImagesSource( hom ) );
baseS := Basis( Source( hom ) );
for b in baseI do
e := PreImagesRepresentative( hom, b );
f := e * mat;
g := ImagesRepresentative( hom, f );
Add( ind, Coefficients( baseI, g ) );
od;
ind := Immutable(ind);
ConvertToMatrixRep( ind );
return ind;
end );
BindGlobal( "BasisSocleSeries", function( G )
local d, F, s, m, M, L, N, W, U, b, i, c, w;
# set up
d := Length(G.one[2]);
F := G.field;
s := [[]];
# construct module
m := Union(List(G.glAutos, x->x[2]),List(G.agAutos,x->x[2]));
M := GModuleByMats( m, d, F );
# construct series stepwise
U := [];
while Length(U) < d do
L := SMTX.InducedActionFactorModuleWithBasis( M, U );
N := GModuleByMats( Set(L[1].generators), F );
W := SMTX.BasisSocle( N );
U := MyEcheloniseMat(Concatenation(W * L[2], U));
Add( s, U );
od;
s := Reversed(s);
# get basis and weights
b := [];
w := [];
for i in [1..Length(s)-1] do
c := BaseSteinitzVectors(s[i],s[i+1]).factorspace;
Append(b, c);
Append(w, List(c, x -> i));
od;
# return basis
return rec( basis := b, weights := w );
end );
BindGlobal( "SeriesByWeights", function( w, F )
local d, s, I;
d := Length(w);
I := IdentityMat( d, F );
s := List( Set(w), x -> I{[Position(w,x)..d]} ); Add(s, []);
return s;
end );
[ Dauer der Verarbeitung: 0.26 Sekunden
(vorverarbeitet)
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