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#############################################################################
##
## HAPPRIME - singular.gi
## Functions, Operations and Methods to interface with singular
## Paul Smith
##
## Copyright (C) 2008
## Paul Smith
## National University of Ireland Galway
##
## This file is part of HAPprime.
##
## HAPprime is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## HAPprime is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program. If not, see <https://www.gnu.org/licenses/>.
##
##
#############################################################################
#####################################################################
## <#GAPDoc Label="SingularSetNormalFormIdeal_manSingular">
## <ManSection>
## <Oper Name="SingularSetNormalFormIdeal" Arg="I"/>
## <Oper Name="SingularSetNormalFormIdealNC" Arg="I"/>
## <Returns>
## nothing
## </Returns>
## <Description>
## Sets the ideal to be used by singular for any subsequent calls to
## <Ref Func="SingularPolynomialNormalForm"/> to be <A>I</A>. After calling
## this function, the singular base ring and term ordering (see
## <Ref Func="SingularBaseRing" BookName="singular"/> and
## <Ref Func="TermOrdering" BookName="singular"/>) will be set to be that of
## the ring containing <A>I</A>, so an additional call to
## <Ref Func="SingularSetBaseRing" BookName="singular"/> is not necessary.
## <P/>
## The standard form of this function ensures that <A>I</A> is
## a reduced Gröbner basis with respect to the value of
## <Ref Func="TermOrdering" BookName="singular"/> for the ring containing the
## ideal, while the <C>NC</C> assumes that <A>I</A> is already such a Gröbner
## basis.
## </Description>
## </ManSection>
## <#/GAPDoc>
#####################################################################
InstallMethod(SingularSetNormalFormIdeal,
[IsPolynomialRingIdeal],
function(I)
SingularSetNormalFormIdealNC(
Ideal(LeftActingRingOfIdeal(I), SingularReducedGroebnerBasis(I)));
end
);
#####################################################################
InstallMethod(SingularSetNormalFormIdealNC,
[IsPolynomialRingIdeal],
function(I)
local input, out;
# Set the base ring if it is not the same or it doesn't have
# the same indeterminate order
if LeftActingRingOfIdeal(I) <> SingularBaseRing or
IndeterminatesOfPolynomialRing(LeftActingRingOfIdeal(I)) <>
IndeterminatesOfPolynomialRing(SingularBaseRing) then
SingularSetBaseRing(LeftActingRingOfIdeal(I));
fi;
Info( InfoSingular, 2, "setting GAP_ideal ideal..." );
# preparing the input for Singular
input := "";
if not HasGeneratorsOfTwoSidedIdeal(I) then
# An ideal has no generators if the list of relations is empty.
input := "ideal GAP_NFideal = ideal();\n";
else
Append( input, "ideal GAP_NFideal = " );
Append( input, ParseGapIdealToSingIdeal( I ) );
Append( input, ";\n" );
fi;
out := SingularCommand( input, "" );
Info( InfoSingular, 2, "done SingularSetIdeal." );
end
);
#####################################################################
#####################################################################
## <#GAPDoc Label="SingularPolynomialNormalForm_manSingular">
## <ManSection>
## <Oper Name="SingularPolynomialNormalForm" Arg="poly[, I]"/>
## <Returns>
## Polynomial
## </Returns>
## <Description>
## Returns the normal form of the polynomial <A>poly</A> after reduction
## by the ideal <A>I</A>. The ideal can either be passed to this function,
## in which case it is converted to a Gröbner basis (with respect to the
## term ordering of the ideal's ring - see
## <Ref Func="TermOrdering" BookName="singular"/>), or the ideal to use can
## be set first be calling <Ref Func="SingularSetNormalFormIdeal"/>, which
## is more efficient for repeated use of this function (the latter function
## also sets the base ring and term ordering).
## </Description>
## </ManSection>
## <#/GAPDoc>
#####################################################################
InstallMethod(SingularPolynomialNormalForm,
[IsPolynomial, IsPolynomialRingIdeal],
function(poly, I)
SingularSetNormalFormIdeal(I);
return SingularPolynomialNormalForm(poly);
end
);
#####################################################################
InstallOtherMethod(SingularPolynomialNormalForm,
[IsPolynomial],
function(poly)
local input, out;
Info( InfoSingular, 2, "reducing polynomial to normal form..." );
# preparing the input for Singular
input := "";
Append( input, "poly GAP_poly = reduce( " );
Append( input, ParseGapPolyToSingPoly( poly ) );
Append( input, ", GAP_NFideal);\n" );
out := SingularCommand( input, "string (GAP_poly)" );
Info( InfoSingular, 2, "done SingularPolynomialNF." );
# Fix for singular ordering bug
return PolynomialByExtRep(FamilyObj(poly),
ExtRepPolynomialRatFun(ParseSingPolyToGapPoly(out)));
end
);
#####################################################################
#####################################################################
## <#GAPDoc Label="SingularGroebnerBasis_manSingular">
## <ManSection>
## <Attr Name="SingularGroebnerBasis" Arg="I"/>
## <Returns>
## List
## </Returns>
## <Description>
## Returns a list of relations which form a Gröbner basis for the ideal
## <A>I</A> given the <Ref Attr="TermOrdering" BookName="singular"/>
## associated with the ring containing <A>I</A>. This function is the
## same as the <Package>singular</Package> function
## <Ref Meth="GroebnerBasis" BookName="singular"/>, but fixes a bug in
## that package when using unusual term ordering.
## </Description>
## </ManSection>
## <#/GAPDoc>
#####################################################################
InstallMethod(SingularGroebnerBasis,
[IsPolynomialRingIdeal],
function(I)
local rels, fam;
# An ideal has no generators if the list of relations is empty.
# If so, return the empty list (singular doesn't check for this)
if not HasGeneratorsOfTwoSidedIdeal(I) then
return [];
fi;
rels := GroebnerBasis(I);
if IsEmpty(rels) then
return rels;
fi;
fam := FamilyObj(rels[1]);
# Fix for singular ordering bug
return List(rels, i->PolynomialByExtRep(fam, ExtRepPolynomialRatFun(i)));
end
);
#####################################################################
#####################################################################
## <#GAPDoc Label="SingularReducedGroebnerBasis_manSingular">
## <ManSection>
## <Attr Name="SingularReducedGroebnerBasis" Arg="I"/>
## <Returns>
## List
## </Returns>
## <Description>
## Returns a list of relations which form a reduced Gröbner basis for the
## ideal <A>I</A> given the <Ref Attr="TermOrdering" BookName="singular"/>
## associated with the ring containing <A>I</A>. This function is the
## equivalent of the <Package>singular</Package> function
## <Ref Meth="GroebnerBasis" BookName="singular"/> (and uses that function),
## but ensures that a reduced basis is returned.
## </Description>
## </ManSection>
## <#/GAPDoc>
#####################################################################
InstallMethod(SingularReducedGroebnerBasis,
[IsPolynomialRingIdeal],
function(I)
local rels;
# Remember the current singular options
SingularCommand( "", "intvec GAP_optionsstore = option(get);");
# set redSB to ask for reduced a Groebner basis
SingularCommand( "", "option(redSB);");
rels := SingularGroebnerBasis(I);
# Set the options back to where they were
SingularCommand( "", "option(set, GAP_optionsstore);");
return rels;
end
);
#####################################################################
|
