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Quelle fampred.g
Sprache: unbekannt
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Spracherkennung für: .g vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]
#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Etaoin Shrdlu.
##
## 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 defines all family predicates
##
BIND_GLOBAL( "IsFamFamX", function( F1, F2, F3 )
return IsIdenticalObj( F1, F2 );
end );
BIND_GLOBAL( "IsFamXFam", function( F1, F2, F3 )
return IsIdenticalObj( F1, F3 );
end );
BIND_GLOBAL( "IsFamFamXY", function( F1, F2, F3, F4 )
return IsIdenticalObj( F1, F2 );
end );
BIND_GLOBAL( "IsFamXYFamZ", function( F1, F2, F3, F4, F5 )
return IsIdenticalObj( F1, F4 );
end );
BIND_GLOBAL( "IsFamXFamY", function( F1, F2, F3, F4 )
return IsIdenticalObj( F1, F3 );
end );
BIND_GLOBAL( "IsFamFamFam", function( F1, F2, F3 )
return IsIdenticalObj( F1, F2 )
and IsIdenticalObj( F2, F3 );
end );
BIND_GLOBAL( "IsFamFamFamX", function( F1, F2, F3, F4 )
return IsIdenticalObj( F1, F2 )
and IsIdenticalObj( F1, F3 );
end );
#############################################################################
##
#O IsElmsColls(<F1>,<F2>) test if a family is the elements family of another
##
BIND_GLOBAL( "IsElmsColls", function ( F1, F2 )
return HasElementsFamily( F2 )
and IsIdenticalObj( F1, ElementsFamily(F2) );
end );
BIND_GLOBAL( "IsNotElmsColls", function ( F1, F2 )
return not HasElementsFamily( F2 )
or IsNotIdenticalObj( F1, ElementsFamily(F2) );
end );
BIND_GLOBAL( "IsElmsCollColls", function ( F1, F2 )
return HasElementsFamily( F2 )
and HasElementsFamily( ElementsFamily( F2 ) )
and IsIdenticalObj( F1, ElementsFamily( ElementsFamily( F2 ) ) );
end );
BIND_GLOBAL( "IsElmsCollsX", function( F1, F2, F3 )
return HasElementsFamily( F2 )
and IsIdenticalObj( F1, ElementsFamily( F2 ) );
end );
BIND_GLOBAL( "IsElmsCollCollsX", function ( F1, F2, F3 )
return HasElementsFamily( F2 )
and HasElementsFamily( ElementsFamily( F2 ) )
and IsIdenticalObj( F1, ElementsFamily( ElementsFamily( F2 ) ) );
end );
#############################################################################
##
#O IsCollsElms(<F1>,<F2>) test if a family is the elements family of another
##
BIND_GLOBAL( "IsCollsElms", function ( F1, F2 )
return HasElementsFamily( F1 )
and IsIdenticalObj( ElementsFamily(F1), F2 );
end );
BIND_GLOBAL( "IsCollCollsElms", function ( F1, F2 )
return HasElementsFamily( F1 )
and HasElementsFamily( ElementsFamily( F1 ) )
and IsIdenticalObj( ElementsFamily( ElementsFamily( F1 ) ), F2 );
end );
BIND_GLOBAL( "IsCollCollsElmsElmsX", function ( F1, F2, F3, F4 )
return HasElementsFamily( F1 )
and HasElementsFamily( ElementsFamily( F1 ) )
and IsIdenticalObj( ElementsFamily( ElementsFamily( F1 ) ), F2 )
and IsIdenticalObj( F2, F3 );
end );
#############################################################################
##
#O IsCollsElmsElms( <F1>, <F2>, <F3> )
##
BIND_GLOBAL( "IsCollsElmsX", function( F1, F2, F3 )
return HasElementsFamily(F1)
and IsIdenticalObj( ElementsFamily(F1), F2 );
end );
BIND_GLOBAL( "IsCollsElmsElms", function( F1, F2, F3 )
return HasElementsFamily(F1)
and IsIdenticalObj( ElementsFamily(F1), F2 )
and IsIdenticalObj( F2, F3 );
end );
BIND_GLOBAL( "IsCollsElmsElmsElms", function( F1, F2, F3, F4 )
return HasElementsFamily(F1)
and IsIdenticalObj( ElementsFamily(F1), F2 )
and IsIdenticalObj( F2, F3 )
and IsIdenticalObj( F2, F4 );
end );
BIND_GLOBAL( "IsCollsElmsElmsX", function( F1, F2, F3, F4 )
return HasElementsFamily(F1)
and IsIdenticalObj( ElementsFamily(F1), F2 )
and IsIdenticalObj( F2, F3 );
end );
BIND_GLOBAL( "IsCollsElmsXElms", function( F1, F2, F3, F4 )
return HasElementsFamily(F1)
and IsIdenticalObj( ElementsFamily(F1), F2 )
and IsIdenticalObj( F2, F4 );
end );
BIND_GLOBAL( "IsCollCollsElmsElms", function( F1, F2, F3 )
return HasElementsFamily(F1)
and HasElementsFamily( ElementsFamily(F1) )
and IsIdenticalObj( ElementsFamily( ElementsFamily(F1) ), F2 )
and IsIdenticalObj( F2, F3 );
end );
BIND_GLOBAL( "IsCollsCollsElms", function( F1, F2, F3 )
return HasElementsFamily( F1 )
and IsIdenticalObj( F1, F2 )
and IsIdenticalObj( ElementsFamily( F1 ), F3 );
end );
BIND_GLOBAL( "IsCollsCollsElmsX", function( F1, F2, F3, F4 )
return HasElementsFamily( F1 )
and IsIdenticalObj( F1, F2 )
and IsIdenticalObj( ElementsFamily( F1 ), F3 );
end );
BIND_GLOBAL( "IsCollsCollsElmsXX", function( F1, F2, F3, F4, F5 )
return HasElementsFamily( F1 )
and IsIdenticalObj( F1, F2 )
and IsIdenticalObj( ElementsFamily( F1 ), F3 );
end );
BIND_GLOBAL( "IsCollsElmsColls", function( F1, F2, F3 )
return IsIdenticalObj(F1, F3)
and HasElementsFamily(F1)
and IsIdenticalObj(F2, ElementsFamily(F1));
end );
BIND_GLOBAL( "IsCollsXElms", function( F1, F2, F3 )
return HasElementsFamily( F1 )
and IsIdenticalObj( F3, ElementsFamily( F1 ) );
end );
BIND_GLOBAL( "IsCollsXElmsX", function( F1, F2, F3, F4 )
return HasElementsFamily( F1 )
and IsIdenticalObj( F3, ElementsFamily( F1 ) );
end );
BIND_GLOBAL( "IsElmsCollsXX", function( F1, F2, F3, F4)
return HasElementsFamily( F2 ) and
IsIdenticalObj(F1, ElementsFamily(F2));
end );
BIND_GLOBAL( "IsCollsElmsXX", function( F1, F2, F3, F4)
return HasElementsFamily( F1 ) and
IsIdenticalObj(F2, ElementsFamily(F1));
end );
#############################################################################
##
#F IsLieFamFam( <LieFam>, <Fam> ) . . . . . . . . . . . . family predicate
#F IsFamLieFam( <Fam>, <LieFam> ) . . . . . . . . . . . . family predicate
#F IsElmsLieColls( <Fam1>, <Fam2> ) . . . . . . . . . . . family predicate
#F IsElmsCollLieColls( <Fam1>, <Fam2> ) . . . . . . . . . family predicate
##
BIND_GLOBAL( "IsLieFamFam", function( LieFam, Fam )
return HasLieFamily( Fam ) and IsIdenticalObj( LieFamily( Fam ), LieFam );
end );
BIND_GLOBAL( "IsFamLieFam", function( Fam, LieFam )
return HasLieFamily( Fam ) and IsIdenticalObj( LieFamily( Fam ), LieFam );
end );
BIND_GLOBAL( "IsElmsLieColls", function( Fam1, Fam2 )
return HasCollectionsFamily( Fam1 )
and HasLieFamily( CollectionsFamily( Fam1 ) )
and IsIdenticalObj( LieFamily( CollectionsFamily( Fam1 ) ), Fam2 );
end );
BIND_GLOBAL( "IsElmsCollLieColls", function( Fam1, Fam2 )
return HasCollectionsFamily( Fam1 )
and HasLieFamily( CollectionsFamily( Fam1 ) )
and HasCollectionsFamily( LieFamily( CollectionsFamily( Fam1 ) ) )
and IsIdenticalObj( CollectionsFamily( LieFamily(
CollectionsFamily( Fam1 ) ) ), Fam2 );
end );
BIND_GLOBAL( "IsCollLieCollsElms", function( Fam1, Fam2 )
return HasCollectionsFamily( Fam2 )
and HasLieFamily( CollectionsFamily( Fam2 ) )
and HasCollectionsFamily( LieFamily( CollectionsFamily( Fam2 ) ) )
and IsIdenticalObj( CollectionsFamily( LieFamily(
CollectionsFamily( Fam2 ) ) ), Fam1 );
end );
#############################################################################
##
#F IsCoeffsElms( <coeff>, <elm> )
##
BIND_GLOBAL( "IsCoeffsElms", function( F1, F2 )
return HasCoefficientsFamily(F2)
and IsIdenticalObj( F1, CoefficientsFamily(F2) );
end );
#############################################################################
##
#F IsElmsCoeffs( <elm>, <coeff> )
##
BIND_GLOBAL( "IsElmsCoeffs", function( F1, F2 )
return HasCoefficientsFamily(F1)
and IsIdenticalObj( CoefficientsFamily(F1), F2 );
end );
#############################################################################
##
## some usual family predicates for mapping methods
##
#############################################################################
##
#F FamRangeEqFamElm( <FamMap>, <FamElm> )
##
BIND_GLOBAL( "FamRangeEqFamElm", function( FamMap, FamElm )
return HasFamilyRange( FamMap )
and IsIdenticalObj( FamElm, FamilyRange( FamMap ) );
end );
#############################################################################
##
#F FamSourceEqFamElm( <FamMap>, <FamElm> )
##
BIND_GLOBAL( "FamSourceEqFamElm", function( FamMap, FamElm )
return HasFamilySource( FamMap )
and IsIdenticalObj( FamElm, FamilySource( FamMap ) );
end );
#############################################################################
##
#F CollFamRangeEqFamElms( <FamMap>, <FamElms> )
##
BIND_GLOBAL( "CollFamRangeEqFamElms", function( FamMap, FamElms )
return HasFamilyRange( FamMap )
and HasElementsFamily( FamElms )
and IsIdenticalObj( ElementsFamily( FamElms ),
FamilyRange( FamMap ) );
end );
#############################################################################
##
#F CollFamSourceEqFamElms( <FamMap>, <FamElms> )
##
BIND_GLOBAL( "CollFamSourceEqFamElms", function( FamMap, FamElms )
return HasFamilySource( FamMap )
and HasElementsFamily( FamElms )
and IsIdenticalObj( ElementsFamily( FamElms ),
FamilySource( FamMap ) );
end );
#############################################################################
##
#F FamElmEqFamRange( <FamElm>, <FamMap> )
##
BIND_GLOBAL( "FamElmEqFamRange", function( FamElm, FamMap )
return HasFamilyRange( FamMap )
and IsIdenticalObj( FamElm, FamilyRange( FamMap ) );
end );
#############################################################################
##
#F FamElmEqFamSource( <FamElm>, <FamMap> )
##
BIND_GLOBAL( "FamElmEqFamSource", function( FamElm, FamMap )
return HasFamilySource( FamMap )
and IsIdenticalObj( FamElm, FamilySource( FamMap ) );
end );
#############################################################################
##
#F FamSource2EqFamRange1( <Fam1>, <Fam2> )
##
BIND_GLOBAL( "FamSource2EqFamRange1", function( Fam1, Fam2 )
return HasFamilySource( Fam2 )
and HasFamilyRange( Fam1 )
and IsIdenticalObj( FamilyRange( Fam1 ), FamilySource( Fam2 ) );
end );
#############################################################################
##
#F FamSource1EqFamRange2( <Fam1>, <Fam2> )
##
BIND_GLOBAL( "FamSource1EqFamRange2", function( Fam1, Fam2 )
return HasFamilySource( Fam1 )
and HasFamilyRange( Fam2 )
and IsIdenticalObj( FamilyRange( Fam2 ), FamilySource( Fam1 ) );
end );
#############################################################################
##
#F FamRange1EqFamRange2( <Fam1>, <Fam2> )
##
BIND_GLOBAL( "FamRange1EqFamRange2", function( Fam1, Fam2 )
return HasFamilyRange( Fam1 )
and HasFamilyRange( Fam2 )
and IsIdenticalObj( FamilyRange( Fam1 ), FamilyRange( Fam2 ) );
end );
#############################################################################
##
#F FamSource1EqFamSource2( <Fam1>, <Fam2> )
##
BIND_GLOBAL( "FamSource1EqFamSource2", function( Fam1, Fam2 )
return HasFamilySource( Fam1 )
and HasFamilySource( Fam2 )
and IsIdenticalObj( FamilySource( Fam1 ), FamilySource( Fam2 ) );
end );
#############################################################################
##
#F FamMapFamSourceFamRange( <FamMap>, <FamElm1>, <FamElm2> )
##
BIND_GLOBAL( "FamMapFamSourceFamRange", function( FamMap, FamElm1, FamElm2 )
return HasFamilySource( FamMap )
and HasFamilyRange( FamMap )
and IsIdenticalObj( FamilySource( FamMap ), FamElm1 )
and IsIdenticalObj( FamilyRange( FamMap ), FamElm2 );
end );
#############################################################################
##
#F FamSourceRgtEqFamsLft( <FamLft>, <FamRgt> )
##
BIND_GLOBAL( "FamSourceRgtEqFamsLft", function( FamLft, FamRgt )
return HasFamilySource( FamLft )
and HasFamilyRange( FamLft )
and IsIdenticalObj( FamilySource( FamLft ), FamilyRange( FamLft ) )
and HasFamilySource( FamRgt )
and IsIdenticalObj( FamilySource( FamRgt ), FamilyRange( FamLft ) );
end );
#############################################################################
##
#F FamSourceNotEqFamElm( <FamMap>, <FamElm> )
##
BIND_GLOBAL( "FamSourceNotEqFamElm", function( FamMap, FamElm )
return not FamSourceEqFamElm( FamMap, FamElm );
end );
#############################################################################
##
#F FamRangeNotEqFamElm( <FamMap>, <FamElm> )
##
BIND_GLOBAL( "FamRangeNotEqFamElm", function( FamMap, FamElm )
return not FamRangeEqFamElm( FamMap, FamElm );
end );
#############################################################################
##
#F IsMagmaRingsRings( <FamRMelm>, <FamRelm> ) . . . . . . family predicate
#F IsMagmaRingsMagmas( <FamRMelm>, <FamMelm> ) . . . . . . family predicate
#F IsRingsMagmaRings( <FamRelm>, <FamRMelm> ) . . . . . . family predicate
#F IsMagmasMagmaRings( <FamMelm>, <FamRMelm> ) . . . . . . family predicate
##
BIND_GLOBAL( "IsMagmaRingsRings", function( FamRM, FamR )
return IsBound( FamRM!.familyRing )
and IsIdenticalObj( ElementsFamily( FamRM!.familyRing ), FamR );
end );
BIND_GLOBAL( "IsMagmaRingsMagmas", function( FamRM, FamM )
return IsBound( FamRM!.familyMagma )
and IsIdenticalObj( ElementsFamily( FamRM!.familyMagma ), FamM );
end );
BIND_GLOBAL( "IsRingsMagmaRings", function( FamR, FamRM )
return IsBound( FamRM!.familyRing )
and IsIdenticalObj( ElementsFamily( FamRM!.familyRing ), FamR );
end );
BIND_GLOBAL( "IsMagmasMagmaRings", function( FamM, FamRM )
return IsBound( FamRM!.familyMagma )
and IsIdenticalObj( ElementsFamily( FamRM!.familyMagma ), FamM );
end );
BIND_GLOBAL( "IsMagmaCollsMagmaRingColls", function( FamM, FamRM )
return HasElementsFamily( FamM )
and HasElementsFamily( FamRM )
and IsBound( ElementsFamily( FamRM )!.familyMagma )
and IsIdenticalObj( ElementsFamily( FamRM )!.familyMagma, FamM );
end );
BIND_GLOBAL( "IsRingCollsMagmaRingColls", function( FamR, FamRM )
return HasElementsFamily( FamR )
and HasElementsFamily( FamRM )
and IsBound( ElementsFamily( FamRM )!.familyRing )
and IsIdenticalObj( ElementsFamily( FamRM )!.familyRing, FamR );
end );
[ Dauer der Verarbeitung: 0.83 Sekunden
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2026-03-28
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