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Remove namespace usage from 'fr' #66

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4 changes: 2 additions & 2 deletions TODO
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Original file line number Diff line number Diff line change
Expand Up @@ -21,7 +21,7 @@ group:
* Exponent, IsSolvable, IsNilpotent, IsSimple
* smarter IsTorsion, IsTorsionFree, HasCongruenceProperty
* SubexponentialGrowth
* SEARCH@.BALL should not compute full balls if #gens is large (>100)
* Fr.SEARCH.BALL should not compute full balls if #gens is large (>100)
* complex of groups covering contracting group

vhgroup:
Expand All @@ -48,7 +48,7 @@ linear, vector:
* Minimize, nice vectors for algebra elements
* extend / restrict scalars
* "in" method

algebra:
* test membership in an algebra
* test nillity of algebra (akin to IsTorsion for groups)
2 changes: 1 addition & 1 deletion doc/fr.xml
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Expand Up @@ -1406,7 +1406,7 @@ gap> Inverse(bacher(3));
<Package>FR</Package>.
</Description>
</ManSection>
<#Include Label="SEARCH@">
<#Include Label="Fr.SEARCH">
</Section>

</Chapter>
Expand Down
82 changes: 41 additions & 41 deletions gap/algebra.gi
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Expand Up @@ -73,26 +73,26 @@ end);
InstallMethod(SCAlgebra, "(FR) for a linear machine",
[IsLinearFRMachine], SCAlgebraNC);

BindGlobal("SCALGEBRAWITHONE@", function(M)
Fr.SCALGEBRAWITHONE := ( function(M)
local a;
a := Objectify(NewType(CollectionsFamily(FREFamily(M)),
IsFRAlgebraWithOne and IsAttributeStoringRep),
rec());
SetLeftActingDomain(a,LeftActingDomain(M));
SetCorrespondence(a,List(GeneratorsOfFRMachine(M),x->FRElement(M,x)));
SetCorrespondence(a,List(GeneratorsOfFRMachine(M),x->FRElement(M,x)));
SetUnderlyingFRMachine(a,M);
if IsVectorFRMachineRep(M) then
SetFilterObj(a,IsVectorFRElementSpace);
fi;
SetFilterObj(a,IsLinearFRElementSpace);
return a;
end);

InstallMethod(SCAlgebraWithOneNC, "(FR) for a linear machine",
[IsLinearFRMachine],
function(M)
local a;
a := SCALGEBRAWITHONE@(M);
a := Fr.SCALGEBRAWITHONE(M);
SetGeneratorsOfLeftOperatorRingWithOne(a,Correspondence(a));
return a;
end);
Expand All @@ -101,7 +101,7 @@ InstallMethod(SCAlgebraWithOne, "(FR) for a linear machine",
[IsLinearFRMachine],
function(M)
local a, g, p;
a := SCALGEBRAWITHONE@(M);
a := Fr.SCALGEBRAWITHONE(M);
g := DuplicateFreeList(Correspondence(a));
if Length(g)>=1 then
p := Position(g,One(g[1]));
Expand All @@ -115,11 +115,11 @@ InstallMethod(SCLieAlgebra, "(FR) for a linear machine",
[IsLinearFRMachine],
function(M)
local a;
a := Objectify(NewType(CollectionsFamily(FRJFAMILY@(M)),
a := Objectify(NewType(CollectionsFamily(Fr.FRJFAMILY(M)),
IsFRAlgebra and IsAttributeStoringRep),
rec());
SetLeftActingDomain(a,LeftActingDomain(M));
SetGeneratorsOfLeftOperatorRing(a,List(GeneratorsOfFRMachine(M),x->FRElement(M,x,IsJacobianElement)));
SetGeneratorsOfLeftOperatorRing(a,List(GeneratorsOfFRMachine(M),x->FRElement(M,x,IsJacobianElement)));
SetUnderlyingFRMachine(a,M);
if IsVectorFRMachineRep(M) then
SetFilterObj(a,IsVectorFRElementSpace);
Expand All @@ -134,7 +134,7 @@ end);
#F FRAlgebra
#F FRAlgebraWithOne
##
BindGlobal("TOTALDEGREE@", function(x)
Fr.TOTALDEGREE := ( function(x)
local d, i;
d := -1;
x := ExtRepOfObj(x)[2];
Expand All @@ -144,7 +144,7 @@ BindGlobal("TOTALDEGREE@", function(x)
return d;
end);

BindGlobal("STRINGSTOLMACHINE@", function(r,args,creator)
Fr.STRINGSTOLMACHINE := ( function(r,args,creator)
local temp, i, j, gens, transitions, output, data;

if not IsRing(r) or not ForAll(args,IsString) then
Expand All @@ -165,11 +165,11 @@ BindGlobal("STRINGSTOLMACHINE@", function(r,args,creator)
for temp in List(temp,x->x[2]) do
temp := SplitString(temp,":");
if Length(temp)=2 then
Add(output,STRING_ATOM2GAP@(temp[2])*One(r));
Add(output,Fr.STRING_ATOM2GAP(temp[2])*One(r));
else
Add(output,One(r));
fi;
temp := STRING_WORD2GAP@(gens,GeneratorsOfAlgebraWithOne(data.holder),temp[1])*One(data.holder);
temp := Fr.STRING_WORD2GAP(gens,GeneratorsOfAlgebraWithOne(data.holder),temp[1])*One(data.holder);
if not IsMatrix(temp) then
Error("<arg> should have the form a=[[...]...]\n");
fi;
Expand All @@ -178,7 +178,7 @@ BindGlobal("STRINGSTOLMACHINE@", function(r,args,creator)

i := AlgebraMachine(r,data.holder,transitions,output);
if ValueOption("IsVectorElement")=true or
(ForAll(Flat(transitions),x->TOTALDEGREE@(x)<=1) and ValueOption("IsAlgebraElement")<>true) then
(ForAll(Flat(transitions),x->Fr.TOTALDEGREE(x)<=1) and ValueOption("IsAlgebraElement")<>true) then
i := AsVectorMachine(i);
i := List(Correspondence(i),x->FRElement(i,x));
for temp in [1..Length(gens)] do
Expand All @@ -194,24 +194,24 @@ end);

InstallGlobalFunction(FRAlgebra,
function(arg)
return STRINGSTOLMACHINE@(arg[1],arg{[2..Length(arg)]},Algebra);
return Fr.STRINGSTOLMACHINE(arg[1],arg{[2..Length(arg)]},Algebra);
end);

InstallGlobalFunction(FRAlgebraWithOne,
function(arg)
return STRINGSTOLMACHINE@(arg[1],arg{[2..Length(arg)]},AlgebraWithOne);
return Fr.STRINGSTOLMACHINE(arg[1],arg{[2..Length(arg)]},AlgebraWithOne);
end);

InstallMethod(AssignGeneratorVariables, "(FR) for an FR algebra",
[IsFRAlgebra],
function(G)
ASSIGNGENERATORVARIABLES@(GeneratorsOfAlgebra(G));
Fr.ASSIGNGENERATORVARIABLES(GeneratorsOfAlgebra(G));
end);

InstallMethod(AssignGeneratorVariables, "(FR) for an FR algebra with one",
[IsFRAlgebraWithOne],
function(G)
ASSIGNGENERATORVARIABLES@(GeneratorsOfAlgebraWithOne(G));
Fr.ASSIGNGENERATORVARIABLES(GeneratorsOfAlgebraWithOne(G));
end);
############################################################################

Expand Down Expand Up @@ -240,7 +240,7 @@ InstallMethod(ThinnedAlgebra, "(FR) for a ring and a FR semigroup",
return a;
end);

BindGlobal("THINNEDALGEBRAWITHONE@",
Fr.THINNEDALGEBRAWITHONE := (
function(r,G,s)
local a, g;
g := List(s,x->AsLinearElement(r,x));
Expand All @@ -259,7 +259,7 @@ end);
InstallMethod(ThinnedAlgebraWithOne, "(FR) for a ring and a FR monoid",
[IsRing, IsFRMonoid],
function(r,G)
return THINNEDALGEBRAWITHONE@(r,G,GeneratorsOfMonoid(G));
return Fr.THINNEDALGEBRAWITHONE(r,G,GeneratorsOfMonoid(G));
end);

InstallMethod(Embedding, "(FR) for a semigroup and a FR algebra",
Expand All @@ -277,7 +277,7 @@ end);
##
#O Nillity
##
BindGlobal("ISNIL_GENERIC@", function(x) # returns false or 2-powers of x till 0
Fr.ISNIL_GENERIC := ( function(x) # returns false or 2-powers of x till 0
local powx, rank, oldrank, ring;

powx := [x];
Expand Down Expand Up @@ -309,7 +309,7 @@ BindGlobal("ISNIL_GENERIC@", function(x) # returns false or 2-powers of x till 0
return powx;
end);

BindGlobal("ISNIL_FR@", function(x)
Fr.ISNIL_FR := ( function(x)
# return either a list of non-trivial 2-powers of x, or false
local powx, deg, testing, found, recur;

Expand All @@ -319,7 +319,7 @@ BindGlobal("ISNIL_FR@", function(x)
found := NewDictionary(x,true); # elements for which we found the nillity
AddDictionary(testing,Zero(x),infinity);
AddDictionary(found,Zero(x),1);

recur := function(x,mult,level,depth)
local i, c, d, order;

Expand All @@ -334,13 +334,13 @@ BindGlobal("ISNIL_FR@", function(x)
fi;

AddDictionary(testing,x,mult);

# first see if element is triangular
d := DecompositionOfFRElement(x);

# c are indices of diagonal blocks of size 1
c := List(Filtered(List(EquivalenceClasses(StronglyConnectedComponents(TransitiveClosureBinaryRelation(BinaryRelationOnPoints(List([1..deg],i->Filtered([1..deg],j->not IsZero(d[i][j]))))))),AsList),x->Length(x)=1),c->c[1]);

order := 1;
for i in c do
i := recur(d[i][i],mult,level+1,1);
Expand All @@ -350,7 +350,7 @@ BindGlobal("ISNIL_FR@", function(x)
if IsDiagonalMat(d) then
return order;
fi;

# now see if a projection is non-nil

if IsVectorFRMachineRep(x) then
Expand All @@ -359,11 +359,11 @@ BindGlobal("ISNIL_FR@", function(x)
d := LogInt(Length(Flat(ExtRepOfObj(InitialState(x)))),deg)+2;
fi;
if d > depth then # work at new depth
if ISNIL_GENERIC@(Activity(x,depth))=false then
if Fr.ISNIL_GENERIC(Activity(x,depth))=false then
return infinity;
fi;
fi;

i := recur(x*x,mult+1,level,d);
AddDictionary(found,x,i);
return i;
Expand All @@ -375,14 +375,14 @@ BindGlobal("ISNIL_FR@", function(x)
return powx;
end);

BindGlobal("NILLITY@", function(x,isnil)
Fr.NILLITY := ( function(x,isnil)
local powx, pown, n, y;

powx := isnil(x);

if powx=false then return infinity; fi;

Append(powx,ISNIL_GENERIC@(Remove(powx))); # get all 2-powers of x
Append(powx,Fr.ISNIL_GENERIC(Remove(powx))); # get all 2-powers of x
Remove(powx);
pown := List([0..Length(powx)-1],i->2^i);

Expand All @@ -405,36 +405,36 @@ end);
InstallOtherMethod(Nillity, "(FR) for an associative element",
# [IsAssociativeElement and IsMultiplicativeElementWithZero],
[IsAssociativeElement and IsMultiplicativeElement],
x->NILLITY@(x,ISNIL_GENERIC@));
x->Fr.NILLITY(x,Fr.ISNIL_GENERIC));

InstallMethod(Nillity, "(FR) for an FR element",
[IsLinearFRElement],
x->NILLITY@(x,ISNIL_FR@));
x->Fr.NILLITY(x,Fr.ISNIL_FR));

InstallOtherMethod(IsNilElement, "(FR) for an associative element",
# [IsAssociativeElement and IsMultiplicativeElementWithZero], ## removed "WithZero" filter, because GAP doesn't set it for linear elements
[IsAssociativeElement and IsMultiplicativeElement],
x->ISNIL_GENERIC@(x)<>false);
x->Fr.ISNIL_GENERIC(x)<>false);

InstallMethod(IsNilElement, "(FR) for an FR element",
[IsLinearFRElement],
x->ISNIL_FR@(x)<>false);
x->Fr.ISNIL(x)<>false);

InstallTrueMethod(IsHomogeneousElement,# "(FR) for a vector with degree",
IsLinearFRElement and HasDegreeOfHomogeneousElement);

InstallMethod(NucleusOfFRAlgebra, "(FR) for a ss algebra",
[IsFRAlgebra],
A->LINEARNUCLEUS@(VectorSpace(LeftActingDomain(A),GeneratorsOfAlgebra(A))));
A->Fr.LINEARNUCLEUS(VectorSpace(LeftActingDomain(A),GeneratorsOfAlgebra(A))));

InstallMethod(NucleusOfFRAlgebra, "(FR) for a ss algebra with one",
[IsFRAlgebraWithOne],
A->LINEARNUCLEUS@(VectorSpace(LeftActingDomain(A),GeneratorsOfAlgebraWithOne(A))));
A->Fr.LINEARNUCLEUS(VectorSpace(LeftActingDomain(A),GeneratorsOfAlgebraWithOne(A))));

InstallMethod(NucleusMachine, "(FR) for a ss algebra",
[IsFRAlgebra],
A->AsVectorMachine(NucleusOfFRAlgebra(A)));

InstallMethod(IsContracting, "(FR) for a ss algebra",
[IsFRAlgebra],
function(A)
Expand Down Expand Up @@ -486,7 +486,7 @@ end);
##
#M View
##
BindGlobal("VIEWALGEBRA@", function(A)
Fr.VIEWALGEBRA := ( function(A)
local n, x, y, s;
if HasIsJacobianRing(A) and IsJacobianRing(A) then
x := "Lie ";
Expand All @@ -511,11 +511,11 @@ end);

InstallMethod(ViewString, "(FR) for an FR algebra",
[IsFRAlgebra],
VIEWALGEBRA@);
Fr.VIEWALGEBRA);
InstallMethod(ViewString, "(FR) for an FR algebra-with-one",
[IsFRAlgebraWithOne],
VIEWALGEBRA@);
INSTALLPRINTERS@(IsFRAlgebra);
INSTALLPRINTERS@(IsFRAlgebraWithOne);
Fr.VIEWALGEBRA);
Fr.INSTALLPRINTERS(IsFRAlgebra);
Fr.INSTALLPRINTERS(IsFRAlgebraWithOne);
############################################################################

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