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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);

Quelle rws.gi Sprache: unbekannt

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