|
#############################################################################
##
#W bisets.gi Laurent Bartholdi
##
#Y Copyright (C) 2012-2013, Laurent Bartholdi
##
#############################################################################
##
## This file implements general bisets.
##
#############################################################################
################################################################
# create new bisets
################################################################
InstallMethod(BisetByFRMachine, [IsFRMachine],
function(M)
local b, g;
if IsMealyMachine(M) then
if IsInvertible(M) then
M := AsGroupFRMachine(M);
else
M := AsMonoidFRMachine(M);
fi;
fi;
b := Objectify(NewType(FRBISET_FAMILY,IsFRBiset and IsFRBisetByFRMachineRep),
rec(machine := M));
g := StateSet(M);
SetIsLeftFree(b,true);
SetLeftActingDomain(b,g);
SetRightActingDomain(b,g);
return b;
end);
InstallMethod(BisetByFRSemigroup, [IsFRGroup],
function(G)
local b;
b := Objectify(NewType(FRBISET_FAMILY,IsFRBiset and IsFRBisetByFRSemigroupRep),
rec(semigroup := G));
SetIsLeftFree(b,true);
SetLeftActingDomain(b,G);
SetRightActingDomain(b,G);
return b;
end);
InstallMethod(DualBiset, "(FR) for a biset",
[IsFRBiset],
function(b)
Error("not yet done");
end);
InstallMethod(TensorProductOp, "(FR) for a sequence of bisets and a biset",
[IsList,IsFRBiset],
function(b,b0)
Error("not yet done");
end);
InstallMethod(ViewString, "(FR) for a biset",
[IsFRBiset],
function(b)
local s, v;
s := "<";
for v in [[IsLeftFree,"left-free"],
[IsRightFree,"right-free"],
[IsLeftTransitive,"left-transitive"],
[IsRightTransitive,"right-transitive"]] do
if Tester(v[1])(b) then
if not v[1](b) then Append(s,"non-"); fi;
Append(s,v[2]);
fi;
od;
if not s[Length(s)] in " <" then Append(s," "); fi;
if HasName(LeftActingDomain(b)) and HasName(RightActingDomain(b)) then
APPEND@(s,Name(LeftActingDomain(b)),"-",Name(RightActingDomain(b)),"-");
fi;
Append(s,"biset>");
return s;
end);
InstallMethod(DisplayString, "(FR) for a biset",
[IsFRBiset and IsFRBisetByFRMachineRep],
function(b)
return Concatenation("Biset:\n",DisplayString(b!.machine));
end);
INSTALLPRINTERS@(IsFRBiset);
################################################################
# biset elements
################################################################
InstallMethod(BisetElement, "(FR) for a machine biset",
[IsFRBiset,IsMultiplicativeElement,IsObject],
function(biset,g,x)
local type, elt;
type := NewType(FRBISET_FAMILY,IsBisetElement and IsBisetElementByPair);
elt := rec(biset := biset, element := g, letter := x);
return Objectify(type,elt);
end);
InstallMethod(BisetElement, "(FR) for a homomorphism biset",
[IsFRBisetByHomomorphismRep,IsMultiplicativeElement],
function(biset,g)
local type, elt;
type := NewType(FRBISET_FAMILY,IsBisetElement and IsBisetElementByElement);
elt := rec(biset := biset, element := g);
return Objectify(type,elt);
end);
InstallMethod(\=, "(FR) for two biset elements",
[IsBisetElementByPair,IsBisetElementByPair],
function(e,f)
return e!.biset=f!.biset and e!.element=f!.element and e!.letter=f!.letter;
end);
InstallMethod(\<, "(FR) for two biset elements",
[IsBisetElementByPair,IsBisetElementByPair],
function(e,f)
return e!.biset<f!.biset or (e!.biset=f!.biset and (e!.letter<f!.letter or (e!.letter=f!.letter and e!.element<f!.element)));
end);
InstallMethod(\=, "(FR) for two biset elements",
[IsBisetElementByElement,IsBisetElementByElement],
function(e,f)
return e!.biset=f!.biset and e!.element=f!.element;
end);
InstallMethod(\<, "(FR) for two biset elements",
[IsBisetElementByElement,IsBisetElementByElement],
function(e,f)
return e!.biset<f!.biset or (e!.biset=f!.biset and e!.element<f!.element);
end);
InstallOtherMethod(\*, "(FR) for a biset element and a semigroup element",
[IsBisetElementByPair,IsMultiplicativeElement],
function(b,g)
local biset, newelement;
biset := b!.biset;
if not g in LeftActingDomain(biset) then TryNextMethod(); fi;
if IsFRBisetByFRMachineRep(biset) then
return BisetElement(biset,b!.element*Transition(biset!.machine,g,b!.letter),Output(biset!.machine,g,b!.letter));
elif IsFRElement(g) then
return BisetElement(b!.biset,b!.element*State(g,b!.letter),b!.letter^g);
else
TryNextMethod();
fi;
end);
InstallOtherMethod(\*, "(FR) for a semigroup element and a biset element",
[IsMultiplicativeElement,IsBisetElementByPair],
function(g,b)
if not g in RightActingDomain(b!.biset) then TryNextMethod(); fi;
return BisetElement(b!.biset,g*b!.element,b!.letter);
end);
InstallMethod(ViewString, "(FR) for a biset element by pair",
[IsBisetElement and IsBisetElementByPair],
function(e)
return CONCAT@("(",e!.element,"*",e!.letter,")");
end);
InstallMethod(PrintString, "(FR) for a biset element by pair",
[IsBisetElement and IsBisetElementByPair],
function(e)
return CONCAT@("BisetElement(",e!.biset,",",e!.element,",",e!.letter,")");
end);
INSTALLPRINTERS@(IsBisetElement);
################################################################
# bases
################################################################
InstallMethod(Basis, "(FR) for a machine biset",
[IsFRBiset],
LeftBasis);
InstallMethod(LeftBasis, "(FR) for a machine biset",
[IsFRBiset and IsLeftFree],
CanonicalBasis);
BindGlobal("CANONICALBASIS@", function(b,alphabet)
return Objectify(NewType(FRBISET_FAMILY,IsLeftBisetBasis and IsCanonicalBasis),
List(alphabet,i->BisetElement(b,One(LeftActingDomain(b)),i)));
end);
InstallMethod(CanonicalBasis, "(FR) for a machine biset",
[IsFRBisetByFRMachineRep],
b->CANONICALBASIS@(b,AlphabetOfFRObject(b!.machine)));
InstallMethod(CanonicalBasis, "(FR) for a machine biset",
[IsFRBisetByFRSemigroupRep],
b->CANONICALBASIS@(b,AlphabetOfFRSemigroup(b!.semigroup)));
InstallMethod(ELM_LIST, "(FR) for a biset basis",
[IsBisetBasis,IsPosInt],
function(basis,i)
return basis![i];
end);
InstallMethod(BasisVectors, "(FR) for a biset basis",
[IsBisetBasis],
function(basis)
local v, i;
v := [];
i := 1;
while IsBound(basis![i]) do
Add(v,basis![i]);
i := i+1;
od;
return v;
end);
InstallMethod(WreathRecursion, "(FR) for a biset",
[IsFRBiset and IsFRBisetByFRMachineRep],
b->WreathRecursion(b!.machine));
InstallMethod(WreathRecursion, "(FR) for a biset",
[IsFRBiset],
b->WreathRecursion(b,Basis(b)));
InstallMethod(WreathRecursion, "(FR) for a biset with basis",
[IsFRBiset,IsLeftBisetBasis],
function(biset,basis)
Error("not yet done");
end);
InstallMethod(FRMachineOfBiset, "(FR) for a machine biset",
[IsFRBiset and IsFRBisetByFRMachineRep],
b->b!.machine);
InstallMethod(FRMachineOfBiset, "(FR) for a biset",
[IsFRBiset],
b->FRMachine(b,Basis(b)));
InstallMethod(FRMachine, "(FR) for a biset",
[IsFRBiset],
FRMachineOfBiset);
InstallMethod(FRMachine, "(FR) for a biset with basis",
[IsFRBiset,IsLeftBisetBasis],
function(biset,basis)
Error("not yet done");
end);
InstallMethod(ViewString, "(FR) for a biset basis",
[IsLeftBisetBasis],
function(basis)
return "LeftBasis(...)";
end);
InstallMethod(ViewString, "(FR) for a biset basis",
[IsRightBisetBasis],
function(basis)
return "RightBasis(...)";
end);
INSTALLPRINTERS@(IsBisetBasis);
[ Verzeichnis aufwärts0.43unsichere Verbindung
Übersetzung europäischer Sprachen durch Browser
]
|
