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BindGlobal( "EvalPoly", function( C, elm, pol )
local d, e, i, c, w;
c := CoefficientsOfUnivariatePolynomial(pol);
d := Length(c)-1;
e := [elm]; for i in [2..d] do e[i] := MultByTable(C, elm, e[i-1]); od;
w := 0*elm; for i in [2..d] do w := w + c[i+1]*e[i]; od;
return w;
end );
BindGlobal( "SubspaceByPILaw", function(C, M, f)
local U, w, u;
# init with radical
U := M.ag;
Print(" subspace has dim ",Length(U),"\n");
if Length(U) = C.mul then return U; fi;
# spinn up power
w := List([1..C.dim], x -> Zero(C.fld)); w[1] := One(C.fld);
u := EvalPoly(C, w, f){[C.dim-C.mul+1..C.dim]};
U := CloseSubspace(M.gl, U, [u]);
Print(" subspace has dim ",Length(U),"\n");
return U;
end );
BindGlobal( "PIAlgebra", function( arg )
local d, f, F, T, C, M, U, com;
# get args
d := arg[1];
f := arg[2];
F := arg[3];
if Length(arg) = 4 then com := arg[4]; else com := false; fi;
# the init step
T := TrivialTable(d,F);
# the next steps are more interesting
while true do
Print("next step with dim ",T.dim,"\n");
T.com := com;
C := CoveringTable(T);
Print(" got cover of dim ",C.dim,"\n");
M := AutoActionOnMult(C, T);
Print(" induced autos \n");
U := SubspaceByPILaw( C, M, f );
Print(" found subspace of dim ",Length(U)," in ",C.mul,"\n");
if Length(U) = C.mul then return T; fi;
T := QuotientTableAllowableSpace(C,U);
od;
end );
[ Dauer der Verarbeitung: 0.30 Sekunden
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