add conjugation quandles!
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# byconj.gd RAQ Quandles by conjugation
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# The following outline of defining c
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DeclareCategory( "IsConjugatorObject",
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IsMultiplicativeElement and IsLeftQuotientElement and
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IsLDistributiveElement and IsIdempotent);
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DeclareCategoryCollections("IsConjugatorObject");
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DeclareAttribute("ConjugatorFamily", IsFamily);
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DeclareSynonym("IsDefaultConjugatorObject",
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IsConjugatorObject and IsPositionalObjectOneSlotRep);
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DeclareAttribute("ConjugatorObj",
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IsMultiplicativeElement and IsLeftQuotientElement and
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IsRightQuotientElement
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);
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DeclareAttribute("UnderlyingMultiplicativeElement", IsConjugatorObject);
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# The meat of the matter:
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DeclareAttribute("ConjugationQuandle", IsGroup);
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# byconj.gi RAQ Implementation of quandles by conjugation
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InstallMethod(ConjugatorFamily, "for a family",
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[IsFamily],
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function(fam)
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local F;
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# Does GAP provide any way to get at the name of a family other than
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# fam!.NAME ?
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F := NewFamily(Concatenation("ConjugatorFamily(", fam!.NAME, ")"),
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IsConjugatorObject);
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F!.ConjType := NewType(F, IsDefaultConjugatorObject);
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return F;
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end);
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ConjugatorType@ := obj -> ConjugatorFamily(FamilyObj(obj))!.ConjType;
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InstallMethod(ConjugatorObj,
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"for a mult element that allows left quotients (and should be assoc)",
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[IsMultiplicativeElement and IsLeftQuotientElement],
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obj -> Objectify(ConjugatorType(Obj), Immutable(obj))
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);
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## Printing and viewing
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InstallMethod(String, "for conjugator objects",
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[IsDefaultConjugatorObject],
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obj -> Concatenation("ConjugatorObj( ", String(obj![1]), " )")
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);
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InstallMethod(ViewString, "for conjugator objects",
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[IsDefaultConjugatorObject],
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obj -> Concatenation("^", ViewString(obj![1]), ":")
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);
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InstallMethod(UnderlyingMultiplicativeElement, "for a conjugator object",
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[IsDefaultConjugatorObject],
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obj -> obj![1]
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);
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InstallMethod( \=, "for two conjugator objects",
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IsIdenticalObj,
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[IsDefaultConjugatorObject, IsDefaultConjugatorObject],
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function(l,r) return l![1] = r![1]; end
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);
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InstallMethod( \<, "for two conjugator objects",
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IsIdenticalObj,
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[IsDefaultConjugatorObject, IsDefaultConjugatorObject],
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function(l,r) return l![1] < r![1]; end
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);
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InstallMethod( \*, "for two conjugator objects",
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IsIdenticalObj,
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[IsDefaultConjugatorObject, IsDefaultConjugatorObject],
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function(l,r) return LeftQuotient(l![1],r![1])*l![1]; end
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);
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InstallMethod(LeftQuotient, "for two conjugator objects",
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IsIdenticalObj,
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[IsDefaultConjugatorObject,IsDefaultConjugatorObject],
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function(l,r) return (l*r)/l; end
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);
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InstallMethod("ConjugationQuandle", "for a group",
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[IsGroup and IsFinite],
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function(G)
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local fam, elts;
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fam := CollectionFamily(ConjugatorFamily(ElementsFamily(FamilyObj(G))));
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# Question: how do we easily/quickly determine a set of generators of
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# Conj(G) from a set of generators of G, so that we can handle infinite
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# conj-quandles here?
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elts := List(Elements(G), g -> ConjugatorObj(g));
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# What we would like to do is
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# return AsLeftQuandle[NC?](elts);
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# but that's NIY.
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return LeftQuandleNC(fam, elts);
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end);
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2
init.g
2
init.g
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@ -7,5 +7,5 @@ ReadPackage("raq", "gap/structure.gd");
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ReadPackage("raq", "gap/bytable.gd");
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ReadPackage("raq", "gap/bytable.gd");
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# Quandles by conjugation
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# Quandles by conjugation
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#Readpackage("raq", "gap/byconj.gd");
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Readpackage("raq", "gap/byconj.gd");
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3
read.g
3
read.g
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@ -5,3 +5,6 @@ ReadPackage("raq", "gap/structure.gi");
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# Quasigroups, racks, and quandles by multiplication tables
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# Quasigroups, racks, and quandles by multiplication tables
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ReadPackage("raq", "gap/bytable.gi");
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ReadPackage("raq", "gap/bytable.gi");
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# Quandles by conjugation
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Readpackage("raq", "gap/byconj.gi");
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