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Merged
fingolfin merged 1 commit into from
Apr 10, 2025
Merged

Use field instead of field size in Forms_SQRT2 #76

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43 changes: 23 additions & 20 deletions lib/forms.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -1639,12 +1639,17 @@
end );

InstallGlobalFunction(Forms_SQRT2,
function(a, q)
function(a, gf)
local z, q;
if IsZero( a ) then
return a;
else
return Z(q)^((q*LogFFE(a,Z(q)))/2);
fi;
q:=Size(gf);
if q mod 2 = 0 then
return a^(q/2);
fi;
z:=PrimitiveRoot(gf);
return z^(LogFFE(a,z)/2);

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end );

InstallGlobalFunction(Forms_PERM_VAR,
Expand Down Expand Up @@ -2003,10 +2008,9 @@
InstallMethod(BaseChangeOrthogonalQuadratic, [ IsMatrix and IsFFECollColl, IsField and IsFinite ],
function(mat, gf)
local A,r,w,row,dummy,i,j,h,D,P,t,a,b,c,d,e,s,
zeros,posr,posk,n,q,zero,one;
zeros,posr,posk,n,zero,one;
n := NrRows(mat);
r := n;
q := Size(gf);
row := 1;
zero := Zero(gf);
one := One(gf);
Expand Down Expand Up @@ -2056,10 +2060,10 @@

# If all is zero, STOP
if dummy then
t := Forms_SQRT2(A[row,row],q);
t := Forms_SQRT2(A[row,row],gf);
Forms_MultRow(D,row,1/t);
for i in [row + 1..r] do
Forms_AddRows(D,i,row,Forms_SQRT2(A[i,i],q));
Forms_AddRows(D,i,row,Forms_SQRT2(A[i,i],gf));
od;
# Permutation of the variables, it is a parabolic
r := row;
Expand Down Expand Up @@ -2119,7 +2123,7 @@

# A has now that special form a_11*X_1^2+X_1*X_2 + G(X_0,X_2,...,X_n);
b := A[row,row];
t := Forms_SQRT2(b/A[row+1,row+1],q);
t := Forms_SQRT2(b/A[row+1,row+1],gf);
Forms_AddCols(A,row,row+1,t);
Forms_AddRows(A,row,row+1,t);
Forms_AddRows(D,row,row+1,t);
Expand Down Expand Up @@ -2189,7 +2193,7 @@
r := r - 1;
w := 2;
else
t := Forms_SQRT2(A[r,r],q);
t := Forms_SQRT2(A[r,r],gf);
Forms_MultRow(D,r,1/t);
Forms_PERM_VAR(D,r);
w := 1;
Expand All @@ -2205,7 +2209,7 @@
r := r - 2;
w := 2;
else
Forms_MultRow(D,r,1/Forms_SQRT2(c,q));
Forms_MultRow(D,r,1/Forms_SQRT2(c,gf));

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Forms_PERM_VAR(D,r);
r := r - 1;
w := 1;
Expand All @@ -2222,12 +2226,12 @@
else #a <> t
if b = t then
if c = t then
Forms_MultRow(D,r-1,1/Forms_SQRT2(a,q));
Forms_MultRow(D,r-1,1/Forms_SQRT2(a,gf));
Forms_PERM_VAR(D,r-1);
r := r - 1;
else
Forms_MultRow(D,r-1,1/Forms_SQRT2(a,q));
Forms_AddRows(D,r,r-1,Forms_SQRT2(c,q));
Forms_MultRow(D,r-1,1/Forms_SQRT2(a,gf));
Forms_AddRows(D,r,r-1,Forms_SQRT2(c,gf));
Forms_PERM_VAR(D,r-1);
r := r - 1;
fi;
Expand All @@ -2240,12 +2244,12 @@
else
d := (a*c)/(b^2);
if Trace(gf,d) = t then
e := Forms_SQRT2(a,q);
e := Forms_SQRT2(a,gf);
s := Forms_QUAD_EQ(d,gf,h);
Forms_TRANSFORM_2_BY_2(D, r-1, r, (s+one)/e, e/b, s/e, e/b);
w := 2;
else
c := Forms_SQRT2(c,q);
c := Forms_SQRT2(c,gf);
Forms_MultRow(D,r-1,c/b);
Forms_MultRow(D,r,1/c);
if r > 2 then
Expand Down Expand Up @@ -2278,11 +2282,10 @@
##
InstallMethod(BaseChangeHermitian, [ IsMatrix and IsFFECollColl, IsField and IsFinite ],
function(mat,gf)
local row,i,j,k,A,a,b,P,D,t,r,n,q,one,A2,D2;
local row,i,j,k,A,a,b,P,D,t,r,n,one,A2,D2;
n := NrRows(mat);
q := Size(gf);
one := One(gf);
t := Sqrt(q);
t := Sqrt(Size(gf));

A := MutableCopyMat(mat);
ConvertToMatrixRep(A, gf);
Expand Down Expand Up @@ -2344,7 +2347,7 @@
Forms_SwapRows(A, row + 1, k);
Forms_SwapRows(D, row + 1, k);

b := Z(q)/A[row+1,row];
b := PrimitiveRoot(gf)/A[row+1,row];
Forms_AddCols(A, row, row+1, b^t);
Forms_AddRows(A, row, row+1, b);
Forms_AddRows(D, row, row+1, b);
Expand Down Expand Up @@ -2376,7 +2379,7 @@
for i in [1..r] do
a := A[i,i];
if not IsOne(a) then
# find an b element with norm b*b^t = b^(t+1) equal to a
# find an element b with norm b*b^t = b^(t+1) equal to a
b := RootFFE(gf, a, t+1);
Forms_MultRow(D,i,1/b);
fi;
Expand Down