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#
# walrus: Computational Methods for Finitely Generated Monoids and Groups
#
InstallGlobalFunction(NewPregroupWord,
function(pg, word)
local maxk, rel;
maxk := MaxPowerK(word);
return Objectify(IsPregroupRelatorType,
rec( pregroup := pg
, base := maxk[1]
, exponent := maxk[2]
, baselen := Length(maxk[1]) ) );
end);
InstallGlobalFunction(NewPregroupRelator,
function(pres, word, id)
local maxk, rel;
maxk := MaxPowerK(word);
rel := Objectify(IsPregroupRelatorType,
rec( pres := pres
, base := maxk[1]
, exponent := maxk[2]
, baselen := Length(maxk[1])
, __ID := id)
);
return rel;
end);
InstallMethod(Base, "for a pregroup relator",
[IsPregroupRelator and IsPregroupRelatorRep ],
r -> r!.base);
InstallMethod(Exponent, "for a pregroup relator",
[IsPregroupRelator and IsPregroupRelatorRep ],
r -> r!.exponent);
InstallMethod(Inverse, "for a pregroup relator",
[ IsPregroupRelator and IsPregroupRelatorRep ],
r -> Objectify(IsPregroupRelatorType,
rec( pres := r!.pres
, base := List(Reversed(r!.base), PregroupInverse)
, exponent := r!.exponent
, baselen := r!.baselen
, __ID := -r!.__ID)
));
InstallMethod(PregroupPresentationOf,
"for pregroup relators",
[IsPregroupRelator],
r -> r!.pres);
InstallMethod(Locations, "for a pregroup relator",
[IsPregroupRelator],
function(r)
return List([1..r!.baselen], i -> NewLocation(r, i));
end);
InstallMethod(\[\], "for a pregroup relator",
[IsPregroupRelator and IsPregroupRelatorRep, IsInt],
function(r, p)
local i, l;
i := RemInt(p - 1, r!.baselen);
if i < 0 then
i := i + r!.baselen;
fi;
return r!.base[i + 1];
end);
InstallMethod(Length, "for a pregroup relator",
[ IsPregroupRelator and IsPregroupRelatorRep ],
function(r)
return r!.baselen * r!.exponent;
end);
# we could possibly store this on creation
# But this is run at most once anyway
InstallMethod(Places, "for a pregroup relator",
[ IsPregroupRelator and IsPregroupRelatorRep ],
function(r)
local P, res;
res := [];
for P in Places(PregroupPresentationOf(r)) do
if Relator(P) = r then
Add(res, P);
fi;
od;
return res;
end);
InstallMethod(ViewString, "for a pregroup relator",
[IsPregroupRelator],
function(r)
if Exponent(r) > 1 then
return STRINGIFY("<pregroup relator ("
, List(r!.base, ViewString)
, ")^", r!.exponent, ">");
else
return STRINGIFY("<pregroup relator "
, List(r!.base, ViewString)
, ">");
fi;
end);
InstallMethod(IsBound\[\], "for a pregroup relator, and an position",
[IsPregroupRelator, IsInt], ReturnTrue );
InstallMethod(\=, "for a pregroup relator, and a pregroup relator",
[IsPregroupRelator, IsPregroupRelator],
function(l,r)
# id is uniqe wrt pregroup presentation. We should probably
# make a family of relators for each presentation etc
return l!.__ID = r!.__ID;
return (l!.exponent = r!.exponent)
and (l!.base = r!.base);
end);
InstallMethod(\in, "for a generator and a pregroup relator",
[ IsElementOfPregroup, IsPregroupRelator and IsPregroupRelatorRep],
function(e,r)
return e in r!.base;
end);
#T redo and move to pregroup files
InstallGlobalFunction(ReduceUPregroupWord,
function(word)
local rw, rw2, i, j, one;
if Length(word) = 0 then
return [];
fi;
one := PregroupOf(word[1])[1];
rw := ShallowCopy(word);
for i in [2..Length(rw)] do
if rw[i-1] * rw[i] <> fail then
rw[i] := rw[i-1] * rw[i];
rw[i-1] := one;
fi;
od;
i := 1; j := 1;
rw2 := [];
while i <= Length(rw) do
if rw[i] <> one then
rw2[j] := rw[i];
j := j + 1;
fi;
i := i + 1;
od;
return rw2;
end);
[ Dauer der Verarbeitung: 0.23 Sekunden
(vorverarbeitet)
]
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