2017-10-20 09:08:09 +00:00
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## bytable.gd RAQ Quasigroups, racks, and quandles by multiplication tables.
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## Self-distributivity
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# Predicates on tables:
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DeclareProperty( "IsLeftSelfDistributiveTable", IsMatrix );
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DeclareProperty( "IsRightSelfDistributiveTable", IsMatrix );
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DeclareProperty( "IsElementwiseIdempotentTable", IsMatrix );
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## Attributes (typically used on the families of elements created from a
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## multiplication table) to store sections and division tables
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DeclareAttribute("LeftPerms", HasMultiplicationTable);
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DeclareAttribute("RightPerms", HasMultiplicationTable);
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DeclareAttribute("LeftDivisionTable", HasMultiplicationTable);
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DeclareAttribute("RightDivisionTable", HasMultiplicationTable);
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## Create Quasigroups and racks from multiplication tables
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DeclareGlobalFunction("LeftQuasigroupByMultiplicationTable");
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DeclareGlobalFunction("LeftQuasigroupByMultiplicationTableNC");
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DeclareGlobalFunction("LeftRackByMultiplicationTable");
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DeclareGlobalFunction("LeftRackByMultiplicationTableNC");
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DeclareGlobalFunction("LeftQuandleByMultiplicationTable");
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DeclareGlobalFunction("LeftQuandleByMultiplicationTableNC");
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DeclareGlobalFunction("RightQuasigroupByMultiplicationTable");
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DeclareGlobalFunction("RightQuasigroupByMultiplicationTableNC");
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DeclareGlobalFunction("RightRackByMultiplicationTable");
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DeclareGlobalFunction("RightRackByMultiplicationTableNC");
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DeclareGlobalFunction("RightQuandleByMultiplicationTable");
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DeclareGlobalFunction("RightQuandleByMultiplicationTableNC");
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## Property of a collection that its elements know their multiplication table
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DeclareProperty("IsBuiltFromMultiplicationTable", IsCollection);
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2017-10-24 20:57:19 +00:00
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## Create quasigroups etc by permutations
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DeclareGlobalFunction("LeftQuasigroupByPerms");
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DeclareGlobalFunction("LeftRackByPerms");
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DeclareGlobalFunction("LeftRackByPermsNC");
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DeclareGlobalFunction("LeftQuandleByPerms");
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DeclareGlobalFunction("LeftQuandleByPermsNC");
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DeclareGlobalFunction("RightQuasigroupByPerms");
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DeclareGlobalFunction("RightRackByPerms");
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DeclareGlobalFunction("RightRackByPermsNC");
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DeclareGlobalFunction("RightQuandleByPerms");
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DeclareGlobalFunction("RightQuandleByPermsNC");
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