Quelle  acting.gd   Sprache: Shell

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##
##  greens/acting.gd
##  Copyright (C) 2013-2022                              James D. Mitchell
##
##  Licensing information can be found in the README file of this package.
##
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# Green's relations, classes, etc for acting semigroups.

# The category IsInverseActingRepGreensClass should not be a property.  The
# reason is that if a Green's D-class is not created as an InverseOpClass, then
# its rep is rectified wrt Lambda and Rho, but if it is subsequently considered
# as an InverseOpClass, then the Rho value of the rep will be wrong (i.e. not
# nec. in the first position of the scc of the LambdaOrb containing its
# Rho-value, but in the first position of the scc of the RhoOrb containing it).
# Lots of methods in this file use the fact that the rep of an inverse-op
# D-class has the representative with Lambda and Rho values in the first
# position of the scc of the *LambdaOrb* containing them.  The same comments
# apply to inverse-op L-classes, their reps must have their Rho value in the
# first pos of the scc of the *LambdaOrb* containing the Rho value. So, an
# L-class created as a non-inverse-op class, which later becomes an inverse-op
# class will have the wrong representative. Therefore we don't allow classes to
# change from non-inverse-op to inverse-op.

DeclareCategory("IsActingSemigroupGreensClass",
                IsGreensClassOfSemigroupThatCanUseFroidurePinRep);

DeclareCategory("IsRegularActingRepGreensClass", IsActingSemigroupGreensClass);
DeclareCategory("IsInverseActingRepGreensClass", IsRegularActingRepGreensClass);

InstallTrueMethod(IsRegularGreensClass,
                  IsRegularActingRepGreensClass and IsGreensDClass);
InstallTrueMethod(IsRegularGreensClass,
                  IsRegularActingRepGreensClass and IsGreensRClass);
InstallTrueMethod(IsRegularGreensClass,
                  IsRegularActingRepGreensClass and IsGreensLClass);

DeclareAttribute("LambdaOrb", IsActingSemigroupGreensClass, "mutable");
DeclareAttribute("RhoOrb", IsActingSemigroupGreensClass, "mutable");

DeclareAttribute("LambdaOrbSCC", IsActingSemigroupGreensClass);
DeclareAttribute("LambdaOrbSCCIndex", IsActingSemigroupGreensClass);

DeclareAttribute("RhoOrbSCC", IsActingSemigroupGreensClass);
DeclareAttribute("RhoOrbSCCIndex", IsActingSemigroupGreensClass);

DeclareAttribute("LambdaCosets", IsActingSemigroupGreensClass);
DeclareAttribute("RhoCosets", IsActingSemigroupGreensClass);
DeclareAttribute("RhoOrbStabChain", IsActingSemigroupGreensClass);

DeclareAttribute("SemigroupDataIndex", IsActingSemigroupGreensClass);

DeclareOperation("GreensDClassOfElementNC",
                 [IsActingSemigroup, IsMultiplicativeElement, IsBool]);
DeclareOperation("GreensLClassOfElementNC",
                 [IsActingSemigroup, IsMultiplicativeElement, IsBool]);
DeclareOperation("GreensRClassOfElementNC",
                 [IsActingSemigroup, IsMultiplicativeElement, IsBool]);
DeclareOperation("GreensHClassOfElementNC",
                 [IsActingSemigroup, IsMultiplicativeElement, IsBool]);

DeclareOperation("GreensDClassOfElementNC",
                 [IsGreensClass, IsMultiplicativeElement, IsBool]);
DeclareOperation("GreensLClassOfElementNC",
                 [IsGreensClass, IsMultiplicativeElement, IsBool]);
DeclareOperation("GreensRClassOfElementNC",
                 [IsGreensClass, IsMultiplicativeElement, IsBool]);
DeclareOperation("GreensHClassOfElementNC",
                 [IsGreensClass, IsMultiplicativeElement, IsBool]);

DeclareOperation("IteratorOfDClasses", [IsSemigroup]);
DeclareOperation("IteratorOfRClasses", [IsSemigroup]);

DeclareOperation("IteratorOfDClassReps", [IsSemigroup]);
DeclareOperation("IteratorOfRClassReps", [IsSemigroup]);

DeclareOperation("RelativeDClassReps", [IsActingSemigroup, IsActingSemigroup]);
DeclareOperation("RelativeLClassReps", [IsActingSemigroup, IsActingSemigroup]);
DeclareOperation("RelativeRClassReps", [IsActingSemigroup, IsActingSemigroup]);