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Fix Coefficients for large finite fields created via a polynomial #4703

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Nov 17, 2021
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Fix Coefficients for large finite fields created via a polynomial #4703

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11 changes: 6 additions & 5 deletions lib/fieldfin.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -475,7 +475,7 @@ InstallMethod( Basis,
InstallMethod( BasisNC,
"for a finite field, and a hom. list",
IsIdenticalObj,
[ IsField and IsFinite, IsHomogeneousList ], 10,
[ IsField and IsFinite, IsFFECollection and IsList ], 10,
function( F, gens )

local B, # the basis, result
Expand Down Expand Up @@ -581,13 +581,14 @@ InstallMethod( LinearCombination,
##
#M CanonicalBasis( <F> )
##
## The canonical basis of the finite field with $p^n$ elements, viewed over
## its subfield with $p^d$ elements, consists of the vectors `<z> ^ <i>',
## $0 \leq i \< n/d$, where <z> is the primitive root of <F>.
## The canonical basis of the finite field <F> with $p^n$ elements,
## viewed over its subfield with $p^d$ elements,
## consists of the vectors $<z>^i$, $0 \leq i \< n/d$,
## where <z> is `RootOfDefiningPolynomial( <F> )'.
##
InstallMethod( CanonicalBasis,
"for a finite field",
[ IsField and IsFinite ],
[ IsField and IsFinite and IsFFECollection ],
function( F )
local z, # primitive root
B; # basis record, result
Expand Down
33 changes: 32 additions & 1 deletion tst/testinstall/ffe.tst
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Original file line number Diff line number Diff line change
@@ -1,5 +1,5 @@
#@local Rochambeau,e,F,f1,f2,f3,p,pol,qs,r,x,bigPrime,z,odds,evens
#@local r1,r2,r3,sf1,sf2,sf3,q,q2
#@local r1,r2,r3,sf1,sf2,sf3,q,q2,Fp,fields,C,coeffs,B
gap> START_TEST("ffe.tst");

#
Expand Down Expand Up @@ -161,6 +161,37 @@ GF(1152921504606847009^2)
gap> Z(bigPrime,2) = PrimitiveElement(F);
true

#
# Check that `Coefficients` returns objects of the right type.
#
gap> p:= NextPrimeInt( 10^6 );;
gap> fields:= [ GF(3), GF(3^2), GF(p), LargeGaloisField( p, 2 ) ];;
gap> Fp:= LargeGaloisField( p );;
gap> pol:= UnivariatePolynomial( Fp, [ 912543, 810, 1 ] * One( Fp ) );;
gap> Add( fields, GF( Fp, pol ) );
gap> List( fields, IsFFECollection );
[ true, true, true, true, false ]
gap> List( fields, F -> IsSubset( F, LeftActingDomain( F ) ) );
[ true, true, true, true, false ]
gap> for F in fields do
> Fp:= LeftActingDomain( F );
> C:= CanonicalBasis( F );
> coeffs:= Coefficients( C, One( F ) );
> if not IsSubset( Fp, coeffs ) then
> Error( F );
> fi;
> B:= Basis( F, BasisVectors( C ) );
> coeffs:= Coefficients( B, One( F ) );
> if not IsSubset( Fp, coeffs ) then
> Error( F );
> fi;
> B:= BasisNC( F, BasisVectors( C ) );
> coeffs:= Coefficients( B, One( F ) );
> if not IsSubset( Fp, coeffs ) then
> Error( F );
> fi;
> od;

#
# comparing FFEs
#
Expand Down