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ImmutableMatrix creates MatrixObj for Z/nZ #4797

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merged 4 commits into from
Apr 22, 2022
Merged

ImmutableMatrix creates MatrixObj for Z/nZ #4797

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3e2c076
ENHANCE: ImmutableVector/Matrix use matobjs.
hulpke Feb 23, 2022
ce52f02
Improved interaction with zmodnz vectors/mats
hulpke Mar 2, 2022
5f73dc4
Methods for row spaces by vector objects
hulpke Apr 19, 2022
759c4d5
Added/Changed tests for changes
hulpke Feb 25, 2022
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21 changes: 14 additions & 7 deletions lib/dicthf.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -110,14 +110,21 @@ local f,n,bytelen,data,qq,i;
return function(v)
local x,sy,p;
sy := 0;
for x in v do
p := Position(f, x);
if IsZmodnZVectorRep(v) then
for x in v![ELSPOS] do
sy := n*sy + (x-1);
od;
else
for x in v do
p := Position(f, x);
# want to be quick: Assume no failures
# if p = fail then
# Error("NumberFFVector: Vector not over specified field");
# fi;
sy := n*sy + (p-1);
od;
# if p = fail then
# Error("NumberFFVector: Vector not over specified field");
# fi;
sy := n*sy + (p-1);
od;
fi;

return sy;
end;
fi;
Expand Down
19 changes: 16 additions & 3 deletions lib/grpffmat.gi
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Expand Up @@ -39,8 +39,14 @@ end );
InstallMethod(FieldOfMatrixList,"finite field matrices",true,
[IsListOrCollection and IsFFECollCollColl],0,
function(l)
local deg, i, j, char;
local deg, i, j, char,B;
if Length(l)=0 then Error("list must be nonempty");fi;
if ForAll( l, HasBaseDomain ) then
B:= BaseDomain( l[1] );
if ForAll( l, x -> B = BaseDomain( x ) ) then
return B;
fi;
fi;
deg := 1;
for i in l do
for j in i do
Expand All @@ -58,8 +64,15 @@ end);
InstallMethod(DefaultScalarDomainOfMatrixList,"finite field matrices",true,
[IsListOrCollection and IsFFECollCollColl],0,
function(l)
local deg, i, j, char,m;
if Length(l)=0 then Error("list must be nonempty");fi;
local deg, i, j, char,m,B;
if Length(l)=0 then Error("list must be nonempty");fi;
if ForAll( l, HasBaseDomain ) then
B:= BaseDomain( l[1] );
if ForAll( l, x -> B = BaseDomain( x ) ) then
return B;
fi;
fi;

deg := 1;
for i in l do
# treat compact matrices quickly
Expand Down
83 changes: 83 additions & 0 deletions lib/grpmat.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -240,6 +240,7 @@ local field, dict, acts, start, j, zerov, zero, dim, base, partbas, heads,
else
Error("illegal action");
fi;
start:=List(start,x->ImmutableVector(field,x));

zerov:=Zero(start[1]);
zero:=zerov[1];
Expand Down Expand Up @@ -355,7 +356,14 @@ local field, dict, acts, start, j, zerov, zero, dim, base, partbas, heads,
if v<>zerov then
Add(base,orb[i]);
Add(partbas,ShallowCopy(orb[i]));
# filter for vector objects, not compressed FF vectors
if ForAny(partbas,x->IsVectorObj(x) and not IsDataObjectRep(x)) then
partbas:=Matrix(BaseDomain(partbas[1]),partbas);
fi;
TriangulizeMat(partbas);
if IsMatrixObj(partbas) then
partbas:=ShallowCopy(RowsOfMatrix(partbas));
fi;
heads:=List(partbas,PositionNonZero);
if Length(partbas)>=dim then
# full dimension reached
Expand Down Expand Up @@ -972,6 +980,81 @@ local G,fam,typ,f;
return G;
end );

# ditto for nonprime ZmodnZ
InstallMethod( GroupWithGenerators, "list of zmodnz matrices",
[ IsZmodnZObjNonprimeCollCollColl ],
#T ???
function( gens )
local G,typ,f;

if not IsFinite(gens) then TryNextMethod(); fi;
typ:=MakeGroupyType(FamilyObj(gens),
IsGroup and IsAttributeStoringRep
and HasGeneratorsOfMagmaWithInverses
and IsFinitelyGeneratedGroup and HasIsEmpty and IsFinite,
gens,false,true);

f:=DefaultScalarDomainOfMatrixList(gens);
gens:=List(Immutable(gens),i->ImmutableMatrix(f,i));

G:=rec();
ObjectifyWithAttributes(G,typ,GeneratorsOfMagmaWithInverses,AsList(gens));

if IsField(f) then SetDefaultFieldOfMatrixGroup(G,f);fi;

return G;
end );

InstallMethod( GroupWithGenerators,
"list of zmodnz matrices with identity", IsCollsElms,
[ IsZmodnZObjNonprimeCollCollColl,IsMultiplicativeElementWithInverse and
IsZmodnZObjNonprimeCollColl],
function( gens, id )
local G,typ,f;

if not IsFinite(gens) then TryNextMethod(); fi;
typ:=MakeGroupyType(FamilyObj(gens), IsGroup and IsAttributeStoringRep
and HasGeneratorsOfMagmaWithInverses and IsFinitelyGeneratedGroup
and HasIsEmpty and IsFinite and HasOne,
gens,id,true);

f:=DefaultScalarDomainOfMatrixList(gens);
gens:=List(Immutable(gens),i->ImmutableMatrix(f,i));
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Why do we make an immutable copy of gens before applying List to it? OK, you just copied the code (and that's fine), but I am wondering anyway, and asking in case you have an idea why this is done (if not, please simply ignore this question :-) ).

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I suspect this is the result of a global insertion of ImmutableMatrix in many places without considering in each place whether the local code could be improved subsequently.

id:=ImmutableMatrix(f,id);

G:=rec();
ObjectifyWithAttributes(G,typ,GeneratorsOfMagmaWithInverses,AsList(gens),
One,id);

if IsField(f) then SetDefaultFieldOfMatrixGroup(G,f);fi;

return G;
end );

InstallMethod( GroupWithGenerators,
"empty list of zmodnz matrices with identity", true,
[ IsList and IsEmpty,
IsMultiplicativeElementWithInverse and IsZmodnZObjNonprimeCollColl],
function( gens, id )
local G,fam,typ,f;

if not IsFinite(gens) then TryNextMethod(); fi;
typ:=MakeGroupyType(FamilyObj([id]), IsGroup and IsAttributeStoringRep
and HasGeneratorsOfMagmaWithInverses and HasOne and IsTrivial,
gens,id,true);

f:=DefaultScalarDomainOfMatrixList([id]);
id:=ImmutableMatrix(f,id);

G:=rec();
ObjectifyWithAttributes(G,typ,GeneratorsOfMagmaWithInverses,AsList(gens),
One,id);

if IsField(f) then SetDefaultFieldOfMatrixGroup(G,f);fi;

return G;
end );


#############################################################################
##
Expand Down
114 changes: 103 additions & 11 deletions lib/matobjnz.gi
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Expand Up @@ -69,13 +69,20 @@ InstallMethod( NewZeroVector, "for IsZmodnZVectorRep, a ring, and an int",
end );

InstallMethod( ViewObj, "for a zmodnz vector", [ IsZmodnZVectorRep ],
function( v )
function( v )
local l;
if not IsMutable(v) then
Print("<immutable ");
else
Print("<");
fi;
Print("zmodnz vector over ",v![BDPOS]," of length ",Length(v![ELSPOS]),">");
Print("vector mod ",Size(v![BDPOS]));
l:=Length(v![ELSPOS]);
if 0<l and l<=8 then
Print(": ",v![ELSPOS],">");
else
Print(" of length ",Length(v![ELSPOS]),">");
fi;
end );

InstallMethod( PrintObj, "for a zmodnz vector", [ IsZmodnZVectorRep ],
Expand Down Expand Up @@ -395,6 +402,25 @@ local i,m;
fi;
end );

InstallOtherMethod( AddRowVector, "for plist, zmodnz vector, and a scalar",
[ IsPlistRep and IsMutable, IsZmodnZVectorRep, IsObject ],
function( a, b, s )
local i,m;
if not ForAll(a,IsModulusRep) then TryNextMethod();fi;
for i in [1..Length(a)] do
a[i]:=a[i]+b[i]*s;
od;
end);

InstallOtherMethod( AddRowVector, "for plist, plist vector, and a scalar",
[ IsPlistRep and IsMutable, IsPlistVectorRep, IsObject ],
function( a, b, s )
local i,m;
for i in [1..Length(a)] do
a[i]:=a[i]+b[i]*s;
od;
end);

InstallMethod( AddRowVector,
"for two zmodnz vectors, a scalar, and two positions",
[ IsZmodnZVectorRep and IsMutable, IsZmodnZVectorRep,
Expand Down Expand Up @@ -731,9 +757,16 @@ InstallMethod( Matrix, "for a list and a zmodnz matrix",

InstallMethod( ViewObj, "for a zmodnz matrix", [ IsZmodnZMatrixRep ],
function( m )
local l;
Print("<");
if not IsMutable(m) then Print("immutable "); fi;
Print(Length(m![ROWSPOS]),"x",m![RLPOS],"-matrix over ",m![BDPOS],">");
l:=[Length(m![ROWSPOS]),m![RLPOS]];
if Product(l)<=9 and Product(l)<>0 then
Print("matrix mod ",Size(m![BDPOS]),": ",
List(m![ROWSPOS],x->x![ELSPOS]),">");
else
Print(l[1],"x",l[2],"-matrix mod ",Size(m![BDPOS]),">");
fi;
end );

InstallMethod( PrintObj, "for a zmodnz matrix", [ IsZmodnZMatrixRep ],
Expand Down Expand Up @@ -1046,12 +1079,32 @@ InstallMethod( \*, "for two zmodnz matrices",IsIdenticalObj,
return Objectify( ty, [a![BDPOS],a![EMPOS],b![RLPOS],l] );
end );

InstallMethod(\*,"for zmodnz matrix and ordinary matrix",IsIdenticalObj,
[IsZmodnZMatrixRep,IsMatrix],
function(a,b)
return Matrix(BaseDomain(a),List(RowsOfMatrix(a),x->x*b));
end);


InstallMethod( \=, "for two zmodnz matrices",IsIdenticalObj,
[ IsZmodnZMatrixRep, IsZmodnZMatrixRep ],
function( a, b )
return EQ_LIST_LIST_DEFAULT(a![ROWSPOS],b![ROWSPOS]);
end );

InstallMethod( \=, "for zmodnz matrix and matrix",IsIdenticalObj,
[ IsZmodnZMatrixRep, IsMatrix ],
function( a, b )
return Unpack(a)=b;
end );

InstallMethod( \=, "for matrix and zmodnz matrix",IsIdenticalObj,
[ IsMatrix, IsZmodnZMatrixRep ],
function( a, b )
return a=Unpack(b);
end );


InstallMethod( \<, "for two zmodnz matrices",IsIdenticalObj,
[ IsZmodnZMatrixRep, IsZmodnZMatrixRep ],
function( a, b )
Expand Down Expand Up @@ -1302,9 +1355,7 @@ InstallMethod( TransposedMatImmutable, "for a zmodnz matrix",
return n;
end );

InstallMethod( \*, "for a zmodnz vector and a zmodnz matrix",
IsElmsColls, [ IsZmodnZVectorRep, IsZmodnZMatrixRep ],
function( v, m )
ZMZVECMAT:=function( v, m )
local i,res,s,r;
r:=BaseDomain(v);
# do arithmetic over Z first so that we reduce only once
Expand All @@ -1325,11 +1376,17 @@ InstallMethod( \*, "for a zmodnz vector and a zmodnz matrix",
MakeImmutable(res);
fi;
return res;
end );
end;

InstallOtherMethod( \*, "for a plist vector and a zmodnz matrix",
IsElmsColls, [ IsList, IsZmodnZMatrixRep ],
function( v, m )
InstallMethod( \*, "for a zmodnz vector and a zmodnz matrix",
IsElmsColls, [ IsZmodnZVectorRep, IsZmodnZMatrixRep ],
ZMZVECMAT);

InstallOtherMethod( \^, "for a zmodnz vector and a zmodnz matrix",
IsElmsColls, [ IsZmodnZVectorRep, IsZmodnZMatrixRep ],
ZMZVECMAT);

PLISTVECZMZMAT:=function( v, m )
local i,res,s,r;
r:=BaseDomain(m);
# do arithmetic over Z first so that we reduce only once
Expand All @@ -1350,7 +1407,42 @@ InstallOtherMethod( \*, "for a plist vector and a zmodnz matrix",
MakeImmutable(res);
fi;
return res;
end );
end;

InstallOtherMethod( \*, "for a plist vector and a zmodnz matrix",
IsElmsColls, [ IsList, IsZmodnZMatrixRep ],
PLISTVECZMZMAT);

InstallOtherMethod( \^, "for a plist vector and a zmodnz matrix",
IsElmsColls, [ IsList, IsZmodnZMatrixRep ],
PLISTVECZMZMAT);

ZMZVECTIMESPLISTMAT:=function( v, m )
local i,res,s,r;
r:=BaseDomain(v);
# do arithmetic over Z first so that we reduce only once
res:=ListWithIdenticalEntries(Length(m[1]),Zero(r));
for i in [1..Length(v)] do
s := v[i];
if not IsZero(s) then
AddRowVector(res,m[i],s);
fi;
od;
res:=Vector(r,res);

if not IsMutable(v) and not IsMutable(m) then
MakeImmutable(res);
fi;
return res;
end;

InstallOtherMethod( \*, "for a zmodnz vector and plist matrix",
IsElmsColls, [ IsZmodnZVectorRep, IsMatrix ],
ZMZVECTIMESPLISTMAT);

InstallOtherMethod( \^, "for a zmodnz vector and plist matrix",
IsElmsColls, [ IsZmodnZVectorRep, IsMatrix ],
ZMZVECTIMESPLISTMAT);

InstallMethod( CompatibleVector, "for a zmodnz matrix",
[ IsZmodnZMatrixRep ],
Expand Down
4 changes: 2 additions & 2 deletions lib/matrix.gd
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Expand Up @@ -625,7 +625,7 @@ DeclareOperation( "TriangulizedNullspaceMatDestructive", [ IsMatrix and IsMutabl
## </ManSection>
## <#/GAPDoc>
##
DeclareOperation( "GeneralisedEigenvalues", [ IsRing, IsMatrix ] );
DeclareOperation( "GeneralisedEigenvalues", [ IsRing, IsMatrixOrMatrixObj ] );
DeclareSynonym( "GeneralizedEigenvalues", GeneralisedEigenvalues );

#############################################################################
Expand All @@ -644,7 +644,7 @@ DeclareSynonym( "GeneralizedEigenvalues", GeneralisedEigenvalues );
## </ManSection>
## <#/GAPDoc>
##
DeclareOperation( "GeneralisedEigenspaces", [ IsRing, IsMatrix ] );
DeclareOperation( "GeneralisedEigenspaces", [ IsRing, IsMatrixOrMatrixObj ] );
DeclareSynonym( "GeneralizedEigenspaces", GeneralisedEigenspaces );


Expand Down
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