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#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Frank Celler.
##
## Copyright of GAP belongs to its developers, whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
## This file contains generic methods for rewriting systems.
##
#############################################################################
##
#M AddGenerators( <rws>, <gens> )
##
InstallMethod( AddGenerators,
true,
[ IsRewritingSystem and IsMutable,
IsHomogeneousList ],
0,
function( rws, gens )
local lst;
lst := GeneratorsOfRws(rws);
if not IsEmpty( Intersection( lst, gens ) ) then
Error( "new generators contain old ones" );
fi;
lst := Concatenation( lst, gens );
SetGeneratorsOfRws( rws, lst );
SetNumberGeneratorsOfRws( rws, Length(lst) );
end );
#############################################################################
##
#M NumberGeneratorsOfRws( <rws> )
##
InstallMethod( NumberGeneratorsOfRws,
true,
[ IsRewritingSystem ],
0,
function( rws )
return Length( GeneratorsOfRws(rws) );
end );
#############################################################################
##
#M UnderlyingFamily( <rws> )
##
InstallMethod( UnderlyingFamily,
true,
[ IsRewritingSystem ],
0,
function( rws )
return FamilyObj(rws)!.underlyingFamily;
end );
#############################################################################
##
#M ViewObj( <rws> )
##
#############################################################################
InstallMethod( ViewObj,
true,
[ IsRewritingSystem ],
0,
function( rws )
Print( "<<rewriting system>>" );
end );
#############################################################################
InstallMethod( ViewObj, true,
[ IsRewritingSystem and IsBuiltFromGroup ],
0,
function( rws )
Print( "<<group rewriting system>>" );
end );
#############################################################################
##
#M PrintObj( <rws> )
##
#############################################################################
InstallMethod( PrintObj,
true,
[ IsRewritingSystem ],
0,
function( rws )
Print( "<<rewriting system>>" );
end );
#T install a better `PrintObj' method!
#############################################################################
InstallMethod( PrintObj, true,
[ IsRewritingSystem and IsBuiltFromGroup ],
0,
function( rws )
Print( "<<group rewriting system>>" );
end );
#T install a better `PrintObj' method!
#############################################################################
##
#M ReduceRules( <rws> )
##
InstallMethod( ReduceRules,
true,
[ IsRewritingSystem and IsMutable ],
0,
function( rws ) return; end );
#############################################################################
##
#F IsIdenticalObjFamiliesRwsObj( <rws>, <obj> )
##
BindGlobal( "IsIdenticalObjFamiliesRwsObj", function( a, b )
return IsIdenticalObj( a!.underlyingFamily, b );
end );
#############################################################################
##
#F IsIdenticalObjFamiliesRwsObjObj( <rws>, <obj>, <obj> )
##
BindGlobal( "IsIdenticalObjFamiliesRwsObjObj", function( a, b, c )
return IsIdenticalObj( a!.underlyingFamily, b )
and IsIdenticalObj( b, c );
end );
#############################################################################
##
#F IsIdenticalObjFamiliesRwsObjXXX( <rws>, <obj>, <obj> )
##
BindGlobal( "IsIdenticalObjFamiliesRwsObjXXX", function( a, b, c )
return IsIdenticalObj( a!.underlyingFamily, b );
end );
#############################################################################
##
#M ReducedAdditiveInverse( <rws>, <obj> )
##
InstallMethod( ReducedAdditiveInverse,
"ReducedForm",
IsIdenticalObjFamiliesRwsObj,
[ IsRewritingSystem and IsBuiltFromAdditiveMagmaWithInverses,
IsAdditiveElementWithInverse ],
0,
function( rws, obj )
return ReducedForm( rws, -obj );
end );
#############################################################################
##
#M ReducedComm( <rws>, <left>, <right> )
##
InstallMethod( ReducedComm,
"ReducedLeftQuotient/ReducedProduct",
IsIdenticalObjFamiliesRwsObjObj,
[ IsRewritingSystem and IsBuiltFromGroup,
IsMultiplicativeElementWithInverse,
IsMultiplicativeElementWithInverse ],
0,
function( rws, left, right )
return ReducedLeftQuotient( rws,
ReducedProduct( rws, right, left ),
ReducedProduct( rws, left, right ) );
end );
#############################################################################
##
#M ReducedConjugate( <rws>, <left>, <right> )
##
InstallMethod( ReducedConjugate,
"ReducedLeftQuotient/ReducedProduct",
IsIdenticalObjFamiliesRwsObjObj,
[ IsRewritingSystem and IsBuiltFromGroup,
IsMultiplicativeElementWithInverse,
IsMultiplicativeElementWithInverse ], 0,
function( rws, left, right )
return ReducedLeftQuotient( rws, right,
ReducedProduct( rws, left, right ) );
end );
#############################################################################
##
#M ReducedDifference( <rws>, <left>, <right> )
##
InstallMethod( ReducedDifference,
"ReducedSum/ReducedAdditiveInverse",
IsIdenticalObjFamiliesRwsObjObj,
[ IsRewritingSystem and IsBuiltFromAdditiveMagmaWithInverses,
IsAdditiveElementWithInverse,
IsAdditiveElementWithInverse ],
0,
function( rws, left, right )
return ReducedSum( rws, left, ReducedAdditiveInverse( rws, right ) );
end );
#############################################################################
##
#M ReducedInverse( <rws>, <obj> )
##
InstallMethod( ReducedInverse,
"ReducedForm",
IsIdenticalObjFamiliesRwsObj,
[ IsRewritingSystem and IsBuiltFromMagmaWithInverses,
IsMultiplicativeElementWithInverse ],
0,
function( rws, obj )
return ReducedForm( rws, obj^-1 );
end );
#############################################################################
##
#M ReducedLeftQuotient( <rws>, <left>, <right> )
##
InstallMethod( ReducedLeftQuotient,
"ReducedProduct/ReducedInverse",
IsIdenticalObjFamiliesRwsObjObj,
[ IsRewritingSystem and IsBuiltFromMagmaWithInverses,
IsMultiplicativeElementWithInverse,
IsMultiplicativeElementWithInverse ],
0,
function( rws, left, right )
return ReducedProduct( rws, ReducedInverse( rws, left ), right );
end );
#############################################################################
##
#M ReducedOne( <rws> )
##
InstallMethod( ReducedOne,
"ReducedForm",
true,
[ IsRewritingSystem and IsBuiltFromMagmaWithOne ],
0,
function( rws )
return ReducedForm( rws, One(UnderlyingFamily(rws)) );
end );
#############################################################################
##
#M ReducedPower( <rws>, <obj>, <pow> )
##
InstallMethod( ReducedPower,
"ReducedProduct/ReducedInverse",
IsIdenticalObjFamiliesRwsObjXXX,
[ IsRewritingSystem and IsBuiltFromGroup,
IsMultiplicativeElement,
IsInt ],
0,
function( rws, obj, pow )
local res, i;
# if <pow> is negative invert <obj> first
if pow < 0 then
obj := ReducedInverse( rws, obj );
pow := -pow;
fi;
# if <pow> is zero, reduce the identity
if pow = 0 then
return ReducedOne(rws);
# catch some trivial cases
elif pow <= 5 then
if pow = 1 then
return obj;
elif pow = 2 then
return ReducedProduct( rws, obj, obj );
elif pow = 3 then
res := ReducedProduct( rws, obj, obj );
return ReducedProduct( rws, res, obj );
elif pow = 4 then
res := ReducedProduct( rws, obj, obj );
return ReducedProduct( rws, res, res );
elif pow = 5 then
res := ReducedProduct( rws, obj, obj );
res := ReducedProduct( rws, res, res );
return ReducedProduct( rws, res, obj );
fi;
fi;
# use repeated squaring (right to left)
res := ReducedOne(rws);
i := 1;
while i <= pow do i := i * 2; od;
while 1 < i do
res := ReducedProduct( rws, res, res );
i := QuoInt( i, 2 );
if i <= pow then
res := ReducedProduct( rws, res, obj );
pow := pow - i;
fi;
od;
return res;
end );
#############################################################################
##
#M ReducedProduct( <rws>, <left>, <right> )
##
InstallMethod( ReducedProduct,
"ReducedForm",
IsIdenticalObjFamiliesRwsObjObj,
[ IsRewritingSystem and IsBuiltFromMagma,
IsMultiplicativeElement,
IsMultiplicativeElement ],
0,
function( rws, left, right )
return ReducedForm( rws, left * right );
end );
#############################################################################
##
#M ReducedQuotient( <rws>, <left>, <right> )
##
InstallMethod( ReducedQuotient,
"ReducedProduct/ReducedInverse",
IsIdenticalObjFamiliesRwsObjObj,
[ IsRewritingSystem and IsBuiltFromMagmaWithInverses,
IsMultiplicativeElementWithInverse,
IsMultiplicativeElementWithInverse ],
0,
function( rws, left, right )
return ReducedProduct( rws, left, ReducedInverse( rws, right ) );
end );
#############################################################################
##
#M ReducedSum( <rws>, <left>, <right> )
##
InstallMethod( ReducedSum,
"ReducedForm",
IsIdenticalObjFamiliesRwsObjObj,
[ IsRewritingSystem and IsBuiltFromAdditiveMagmaWithInverses,
IsAdditiveElement,
IsAdditiveElement ],
0,
function( rws, left, right )
return ReducedForm( rws, left + right );
end );
#############################################################################
##
#M ReducedZero( <rws> )
##
InstallMethod( ReducedOne,
"ReducedForm",
true,
[ IsRewritingSystem and IsBuiltFromAdditiveMagmaWithInverses ],
0,
function( rws )
return ReducedForm( rws, Zero(UnderlyingFamily(rws)) );
end );
#############################################################################
##
#M IsReducedForm( <rws>,<w> )
##
InstallMethod(IsReducedForm,
"for a rewriting system and an object", true,
[IsRewritingSystem,IsObject],
function(rws,w)
return ReducedForm(rws,w)=w;
end);
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