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Use DegreeOverPrimeField to simplify some code #37

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Jul 27, 2023
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Use DegreeOverPrimeField to simplify some code #37

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23 changes: 7 additions & 16 deletions lib/forms.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -1185,29 +1185,25 @@
InstallOtherMethod( \^, "for a pair of FFE vectors and an hermitian form",
[ IsVectorList and IsFFECollColl, IsHermitianForm ],
function( pair, f )
local frob,hh,bf,p;
local frob,hh,bf;
if Size(pair) <> 2 then
Error("The first argument must be a pair of vectors");
fi;
bf := f!.basefield;
p := Characteristic(bf);
hh := LogInt(Size(bf),p)/2;
#frob := FrobeniusAutomorphism(f!.basefield); #here was a mistake!
hh := DegreeOverPrimeField(bf) / 2;
frob := FrobeniusAutomorphism(bf)^hh;
return pair[1] * f!.matrix * (pair[2]^frob);
end );

InstallOtherMethod( \^, "for a pair of FFE matrices and an hermitian form",
[ IsFFECollCollColl, IsHermitianForm ],
function( pair, f )
local frob,hh,bf,p;
local frob,hh,bf;
if Size(pair) <> 2 then
Error("The first argument must be a pair of vectors");
fi;
bf := f!.basefield;
p := Characteristic(bf);
hh := LogInt(Size(bf),p)/2;
#frob := FrobeniusAutomorphism(f!.basefield); #here was a mistake, noticed by using fining.
hh := DegreeOverPrimeField(bf) / 2;

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frob := FrobeniusAutomorphism(bf)^hh;
return pair[1] * f!.matrix * (TransposedMat(pair[2])^frob);
end );
Expand Down Expand Up @@ -2944,18 +2940,13 @@
return v*f!.matrix*TransposedMat(w);
end );

# jdb 20/01/2016: here was a bug, there is no method for w^t, w a GF(q) vector
# t just a natural number! Bugfix: look at the method for \^
InstallMethod( EvaluateForm, "for an hermitian form and a pair of vectors",
[IsHermitianForm and IsFormRep,
IsVector and IsFFECollection, IsVector and IsFFECollection],
function(f,v,w)
local gf,t,p,hh,frob;
#t := Sqrt(Size(gf));
#return v*f!.matrix*(w^t); # here was the mistake.
local gf,t,hh,frob;
gf := f!.basefield;
p := Characteristic(gf);
hh := LogInt(Size(gf),p)/2;
hh := DegreeOverPrimeField(gf) / 2;
frob := FrobeniusAutomorphism(gf)^hh;
return v*f!.matrix*(w^frob);
end );
Expand All @@ -2967,7 +2958,7 @@
gf := f!.basefield;
t := Sqrt(Size(gf));
wCONJ := MutableTransposedMat(w);
m := Size(wCONJ); n := Size(wCONJ[1]);
m := NrRows(wCONJ); n := NrCols(wCONJ);
for i in [1..m] do
for j in [1..n] do
wCONJ[i,j] := wCONJ[i,j]^t;
Expand Down
6 changes: 3 additions & 3 deletions lib/recognition.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -32,7 +32,7 @@ InstallGlobalFunction( ClassicalForms_ScalarMultipleFrobenius,

I := Filtered( [0 .. d], x -> not IsZero(c[x+1]) );
q := Size(F);
qq := Characteristic(F)^(LogInt(q,Characteristic(F))/2);
qq := Characteristic(F)^(DegreeOverPrimeField(F)/2);

Minv := M^-1;
tM := Trace(M); tMi := Trace(Minv)^qq; # Frobenius of trace
Expand Down Expand Up @@ -530,7 +530,7 @@ local F, k, dim, mats, dmats, qq, i, j, l;
return GModuleByMats([],module.dimension,SMTX.Field(module));
else
F := MTX.Field(module);
k := LogInt( Size(F), Characteristic(F) );
k := DegreeOverPrimeField(F);
if k mod 2 = 1 then
Error( "field <F> is not a square" );
fi;
Expand Down Expand Up @@ -570,7 +570,7 @@ ClassicalForms_InvariantFormFrobenius := function( module, fmodule )
field := MTX.Field(module);
form := hom[1];
q := Size(field);
qq := Characteristic(field)^(LogInt(q,Characteristic(field))/2);
qq := Characteristic(field)^(DegreeOverPrimeField(field)/2);
k := PositionNonZero(form[1]);
a := form[1,k] / form[k,1]^qq;
a := NthRoot(field,a,(1-qq) mod (q-1));
Expand Down