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27 lines
1.0 KiB
27 lines
1.0 KiB
# 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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IsLSelfDistElement and IsIdempotent); |
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DeclareCategoryCollections("IsConjugatorObject"); |
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DeclareAttribute("ConjugatorFamily", IsFamily); |
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DeclareAttribute("ConjugatorType", IsFamily); |
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DeclareSynonym("IsDefaultConjugatorObject", |
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IsConjugatorObject and IsPositionalObjectOneSlotRep); |
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# As far as I can tell, we are not losing any generality here; |
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# to define the conjugator, we need the quotient on one side, to define |
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# left quotients of conjugators we need the quotient on the other side, and |
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# to prove it works we need associativity, which makes the underlying elements |
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# of conjugator objects automatically group elements. |
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DeclareAttribute("ConjugatorObj", IsMultiplicativeElementWithInverse); |
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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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