/usr/share/gap/lib/upolyirr.gi is in gap-libs 4r8p8-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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##
#W upolyirr.gi GAP Library Frank Lübeck
##
##
#Y Copyright (C) 1997, Lehrstuhl D für Mathematik, RWTH Aachen, Germany
#Y (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland
#Y Copyright (C) 2002 The GAP Group
##
## This file contains methods to compute irreducible univariate polynomials
##
#############################################################################
##
#F AllMonicPolynomialCoeffsOfDegree( <n>, <q> ) . . . . . all coefficient
#F lists of monic polynomials over GF(<q>) of degree <n>
##
AllMonicPolynomialCoeffsOfDegree := function(n, q)
local fq, one, res, a;
fq := AsSortedList(GF(q));
one := One(GF(q));
res := Tuples(fq, n);
for a in res do
Add(a, one);
od;
return res;
end;
#############################################################################
##
#F AllIrreducibleMonicPolynomialCoeffsOfDegree( <n>, <q> ) . all coefficient
#F lists of irreducible monic polynomials over GF(<q>) of degree <n>
##
#V IRR_POLS_OVER_GF_CACHE: a cache for the following function
##
IRR_POLS_OVER_GF_CACHE := [];
## RedCoeffDirectFun := ApplicableMethod(ReduceCoeffs,[[Z(3)],1,[Z(3)],1]);
AllIrreducibleMonicPolynomialCoeffsOfDegree := function(n, q)
local l, zero, i, r, p, new, neverdiv;
if not IsBound(IRR_POLS_OVER_GF_CACHE[q]) then
IRR_POLS_OVER_GF_CACHE[q] := [];
fi;
if IsBound(IRR_POLS_OVER_GF_CACHE[q][n]) then
return IRR_POLS_OVER_GF_CACHE[q][n];
fi;
# this is for going around converting coefficients to polynomials
# and using the \mod operator for divisibility tests
# (I found a speedup factor of about 6 in the example n=9, q=3)
neverdiv := function(r, p)
local lr, lp, rr, pp;
lr := Length(r[1]);
lp := Length(p);
for rr in r do
pp := ShallowCopy(p);
# here we go around method selection which gives a 10% speedup
ReduceCoeffs(pp, lp, rr, lr);
## RedCoeffDirectFun(pp, lp, rr, lr);
ShrinkRowVector(pp);
if Length(pp)=0 then
return false;
fi;
od;
return true;
end;
l := AllMonicPolynomialCoeffsOfDegree(n, q);
zero := 0*Indeterminate(GF(q));
for i in [1..Int(n/2)] do
r := AllIrreducibleMonicPolynomialCoeffsOfDegree(i, q);
new:= [];
for p in l do
if neverdiv(r, p) then
Add(new, p);
fi;
od;
l := new;
od;
IRR_POLS_OVER_GF_CACHE[q][n] := Immutable(l);
return IRR_POLS_OVER_GF_CACHE[q][n];
end;
#############################################################################
##
#F CompanionMat( <poly>
##
InstallGlobalFunction( CompanionMat, function ( arg )
local c, l, res, i, F, c1;
# for the moment allow coefficients as well
if not IsList( arg[1] ) then
c := CoefficientsOfLaurentPolynomial( arg[1] );
if c[2] < 0 then
Error( "This polynomial does not have a companion matrix" );
fi;
F:= DefaultField( c[1] );
c1:= ListWithIdenticalEntries( c[2], Zero(F) );
Append( c1, c[1] );
c:= c1;
else
c := arg[1];
F:= DefaultField( c );
fi;
l := Length( c ) - 1;
if l = 0 then
Error( "This polynomial does not have a companion matrix" );
fi;
res := NullMat( l, l, F );
res[1][l] := -c[1];
for i in [2..l] do
res[i][i-1] := One( F );
res[i][l] := -c[i];
od;
return res;
end );
#############################################################################
##
#F AllIrreducibleMonicPolynomials( <degree>, <field> )
##
InstallGlobalFunction( AllIrreducibleMonicPolynomials,
function( degree, field )
local q, coeffs, fam, nr;
if not IsFinite( field ) then
Error("field must be finite");
fi;
q := Size(field);
nr := IndeterminateNumberOfLaurentPolynomial(
Indeterminate(field,"x"));
coeffs := AllIrreducibleMonicPolynomialCoeffsOfDegree(degree,q);
fam := FamilyObj( Zero(field) );
return List( coeffs,
x -> LaurentPolynomialByCoefficients( fam, x, 0, nr ) );
end );
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