133 lines
3.6 KiB
Plaintext
133 lines
3.6 KiB
Plaintext
## structure.gi RAQ Implementation of definitiions, reps, and elt operations
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## Create structures with generators
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InstallGlobalFunction(CloneOfTypeByGenerators,
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function(cat, fam, gens, genAttrib)
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local M;
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if not(IsEmpty(gens) or IsIdenticalObj(FamilyObj(gens), fam)) then
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Error("<fam> and family of <gens> do not match");
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fi;
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M := Objectify(NewType( fam, cat and IsAttributeStoringRep), rec());
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Setter(genAttrib)(M, AsList(gens));
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return M;
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end);
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## Functions for each of the magma categories here
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InstallGlobalFunction(LeftQuasigroup, function(arg)
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local fam;
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if Length(arg) = 0 then
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Error("usage: LeftQuasigroup([<family>], <gens>)");
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fi;
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# Extract the family
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if IsFamily(arg[1]) then
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fam = arg[1];
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Remove(arg, 1);
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arg = Flat(arg);
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else
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arg = Flat(arg);
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fam = FamilyObj(arg[1]);
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fi;
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return CloneOfTypeByGenerators(IsLeftQuasigroup, fam, arg,
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GeneratorsOfLeftQuasigroup);
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end);
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InstallGlobalFunction(LeftRack, function(arg)
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local fam;
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if Length(arg) = 0 then
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Error("usage: LeftRack([<family>], <gens>)");
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fi;
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# Extract the family
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if IsFamily(arg[1]) then
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fam = arg[1];
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Remove(arg, 1);
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arg = Flat(arg);
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else
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arg = Flat(arg);
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fam = FamilyObj(arg[1]);
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fi;
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return CloneOfTypeByGenerators(IsLeftRack, fam, arg,
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GeneratorsOfLeftQuasigroup);
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end);
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InstallGlobalFunction(RightQuasigroup, function(arg)
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local fam;
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if Length(arg) = 0 then
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Error("usage: RightQuasigroup([<family>], <gens>)");
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fi;
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# Extract the family
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if IsFamily(arg[1]) then
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fam = arg[1];
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Remove(arg, 1);
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arg = Flat(arg);
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else
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arg = Flat(arg);
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fam = FamilyObj(arg[1]);
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fi;
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return CloneOfTypeByGenerators(IsRightQuasigroup, fam, arg,
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GeneratorsOfRightQuasigroup);
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end);
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InstallGlobalFunction(RightRack, function(arg)
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local fam;
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if Length(arg) = 0 then
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Error("usage: RightRack([<family>], <gens>)");
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fi;
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# Extract the family
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if IsFamily(arg[1]) then
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fam = arg[1];
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Remove(arg, 1);
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arg = Flat(arg);
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else
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arg = Flat(arg);
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fam = FamilyObj(arg[1]);
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fi;
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return CloneOfTypeByGenerators(IsRightRack, fam, arg,
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GeneratorsOfRightQuasigroup);
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end);
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## And now create them from multiplication tables
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InstallGlobalFunction(LeftQuasigroupByMultiplicationTable,
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function(T)
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if not IsLeftQuasigroupTable(T) then
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Error("Multiplication table <T> must have each row a permutation of ",
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"the same entries.");
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fi;
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return MagmaByMultiplicationTableCreatorNC(
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CanonicalCayleyTableOfLeftQuasigroupTable(T),
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LeftQuasigroup,
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IsLeftQuotientElement and IsMagmaByMultiplicationTableObj
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);
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end);
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## And define the operation
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InstallOtherMethod(LeftQuotient,
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"for two elts in magma by mult table, when left has left quotients",
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IsIdenticalObj,
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[IsLeftQuotientElement, IsMagmaByMultiplicationTableObj],
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function (l,r)
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return DivisionTable(FamilyObj(l))[l![1],r![1]];
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end);
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## Create division tables as needed
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InstallMethod(LeftDivisionTable,
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"for a family with a multiplication table",
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[IsFamily and HasMultiplicationTable],
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function(fam)
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local LS, n;
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LS := LeftSectionList(fam);
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n := Size(T);
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return List(T, x->ListPerm(Inverse(x), n));
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end);
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## Create section lists as needed
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InstallMethod(LeftSectionList,
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"for a family with a multiplication table",
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[IsFamily and HasMultiplicationTable],
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function(fam)
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return List(MultiplicationTable(fam), x->PermList(x));
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end);
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