|
#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Frank Celler.
##
## Copyright of GAP belongs to its developers, whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
## This file contains the basic methods for creating and doing arithmetic
## with GF2 vectors and matrices.
##
#############################################################################
##
#F IsLockedRepresentationVector . . filter used by GF2 and GF(q)
## matrix reps to stop their rows
## changing representation
DeclareFilter( "IsLockedRepresentationVector" );
#############################################################################
##
#V TYPE_LIST_GF2VEC . . . . . . . . . . . . . . type of mutable GF2 vectors
##
BindGlobal( "TYPE_LIST_GF2VEC",
NewType( CollectionsFamily( FFEFamily(2) ),
IsHomogeneousList and IsListDefault and IsNoImmediateMethodsObject
and IsMutable and IsCopyable and IsGF2VectorRep )
);
#############################################################################
##
#V TYPE_LIST_GF2VEC_IMM . . . . . . . . . . . type of immutable GF2 vectors
##
BindGlobal( "TYPE_LIST_GF2VEC_IMM",
NewType( CollectionsFamily( FFEFamily(2) ),
IsHomogeneousList and IsListDefault and IsNoImmediateMethodsObject
and IsCopyable and IsGF2VectorRep )
);
#############################################################################
##
#V TYPE_LIST_GF2VEC_IMM_LOCKED . . . . type of immutable locked GF2 vectors
##
BindGlobal( "TYPE_LIST_GF2VEC_IMM_LOCKED",
NewType( CollectionsFamily( FFEFamily(2) ),
IsHomogeneousList and IsListDefault and IsNoImmediateMethodsObject
and IsCopyable and IsGF2VectorRep and IsLockedRepresentationVector)
);
#############################################################################
##
#V TYPE_LIST_GF2VEC_LOCKED . . . . type of mutable locked GF2 vectors
##
BindGlobal( "TYPE_LIST_GF2VEC_LOCKED",
NewType( CollectionsFamily( FFEFamily(2) ),
IsHomogeneousList and IsListDefault and IsNoImmediateMethodsObject
and IsCopyable and IsGF2VectorRep and
IsLockedRepresentationVector and IsMutable)
);
#############################################################################
##
#V TYPE_LIST_GF2MAT . . . . . . . . . . . . . type of mutable GF2 matrices
##
BindGlobal( "TYPE_LIST_GF2MAT",
NewType( CollectionsFamily(CollectionsFamily(FFEFamily(2))),
IsMatrix and IsListDefault and IsSmallList and
IsFFECollColl and IsNoImmediateMethodsObject
and IsMutable and IsCopyable and IsGF2MatrixRep and
HasIsRectangularTable and IsRectangularTable )
);
#############################################################################
##
#V TYPE_LIST_GF2MAT_IMM . . . . . . . . . . type of immutable GF2 matrices
##
BindGlobal( "TYPE_LIST_GF2MAT_IMM",
NewType( CollectionsFamily(CollectionsFamily(FFEFamily(2))),
IsMatrix and IsListDefault and IsCopyable and IsGF2MatrixRep
and IsNoImmediateMethodsObject
and IsSmallList and IsFFECollColl and
HasIsRectangularTable and IsRectangularTable)
);
#############################################################################
##
## HPC-GAP serialization
##
if IsHPCGAP then
InstallTypeSerializationTag(TYPE_LIST_GF2VEC,
SERIALIZATION_BASE_GF2VEC + SERIALIZATION_TAG_BASE * 1);
InstallTypeSerializationTag(TYPE_LIST_GF2VEC_IMM,
SERIALIZATION_BASE_GF2VEC + SERIALIZATION_TAG_BASE * 2);
InstallTypeSerializationTag(TYPE_LIST_GF2VEC_IMM_LOCKED,
SERIALIZATION_BASE_GF2VEC + SERIALIZATION_TAG_BASE * 3);
InstallTypeSerializationTag(TYPE_LIST_GF2VEC_LOCKED,
SERIALIZATION_BASE_GF2VEC + SERIALIZATION_TAG_BASE * 4);
InstallTypeSerializationTag(TYPE_LIST_GF2MAT,
SERIALIZATION_BASE_GF2MAT + SERIALIZATION_TAG_BASE * 1);
InstallTypeSerializationTag(TYPE_LIST_GF2MAT_IMM,
SERIALIZATION_BASE_GF2MAT + SERIALIZATION_TAG_BASE * 2);
fi;
#############################################################################
##
#M Length( <gf2vec> ) . . . . . . . . . . . . . . . length of a GF2 vector
##
InstallOtherMethod( Length,
"for GF2 vector",
true,
[ IsList and IsGF2VectorRep ],
0,
LEN_GF2VEC );
#############################################################################
##
#M ELM_LIST( <gf2vec>, <pos> ) . . . . . select an element from a GF2 vector
##
InstallOtherMethod( ELM_LIST,
"for GF2 vector",
true,
[ IsList and IsGF2VectorRep,
IsPosInt ],
0,
ELM_GF2VEC );
#############################################################################
##
#M ELMS_LIST( <gf2vec>, <poss> ) . . . . . select elements from a GF2 vector
##
InstallOtherMethod( ELMS_LIST,
"for GF2 vector",
true,
[ IsList and IsGF2VectorRep,
IsList and IsDenseList and IsInternalRep ],
0,
ELMS_GF2VEC );
#############################################################################
##
#M ASS_LIST( <gf2vec>, <pos>, <elm> ) . . assign an element to a GF2 vector
##
## We use an OtherMethod and trap assignment to immutable vectors in
## the kernel method.
InstallOtherMethod( ASS_LIST,
"for GF2 vector",
true,
[ IsList and IsGF2VectorRep,
IsPosInt,
IsObject ],
0,
ASS_GF2VEC );
#############################################################################
##
#M ASS_LIST( <empty-list>, <pos>, <ffe> ) . . . . . start a new GF2 vector
##
#InstallMethod( ASS_LIST,
# "for empty plain list and finite field element",
# true,
# [ IsMutable and IsList and IsPlistRep and IsEmpty,
# IsPosInt,
# IsFFE ],
# 0,
#function( list, pos, val )
# if pos = 1 and ( val = GF2Zero or val = GF2One ) then
# CONV_GF2VEC(list);
# ASS_GF2VEC( list, pos, val );
# else
# ASS_PLIST_DEFAULT( list, pos, val );
# # force kernel to notice that this is now a list of FFEs
# ConvertToVectorRep( list );
# fi;
#end );
#############################################################################
##
#M UNB_LIST( <gf2vec>, <pos> ) . . . . . . unbind a position of a GF2 vector
##
## We use an OtherMethod and trap assignment to immutable vectors in
## the kernel method.
InstallOtherMethod( UNB_LIST,
"for GF2 vector",
true,
[ IsList and IsGF2VectorRep,
IsPosInt ],
0,
UNB_GF2VEC );
#############################################################################
##
#M PrintObj( <gf2vec> ) . . . . . . . . . . . . . . . . print a GF2 vector
##
InstallMethod( PrintObj,
"for GF2 vector",
true,
[ IsGF2VectorRep ],
0,
function( vec )
local i;
Print( "[ " );
for i in [ 1 .. Length(vec) ] do
if 1 < i then Print( ", " ); fi;
Print( vec[i] );
od;
Print( " ]" );
end );
#############################################################################
##
#M ViewObj( <gf2vec> ) . . . . . . . . . . . . . . . . . . view a GF2 vector
##
InstallMethod( ViewObj,
"for GF2 vector",
true,
[ IsRowVector and IsFinite and IsGF2VectorRep ],
0,
function( vec )
if IsMutable(vec) then
Print( "<a GF2 vector of length ", Length(vec), ">" );
else
Print( "<an immutable GF2 vector of length ", Length(vec), ">" );
fi;
end );
#############################################################################
##
#M AdditiveInverseOp( <gf2vec> ) . mutable additive inverse of a GF2 vector
##
InstallMethod( AdditiveInverseMutable,
"for GF2 vector",
true,
[ IsRowVector and IsListDefault and IsGF2VectorRep ],
0,
ShallowCopy );
InstallMethod( AdditiveInverseSameMutability,
"for GF2 vector, mutable",
true,
[ IsRowVector and IsListDefault and IsGF2VectorRep and IsMutable],
0,
ShallowCopy );
InstallMethod( AdditiveInverseSameMutability,
"for GF2 vector, immutable",
true,
[ IsRowVector and IsListDefault and IsGF2VectorRep],
0,
function(v)
if IsMutable(v) then
TryNextMethod();
fi;
return v;
end );
#############################################################################
##
#M AdditiveInverse( <gf2vec> ) . . . . . . additive inverse of a GF2 vector
##
InstallMethod( AdditiveInverse,
"for GF2 vector",
true,
[ IsRowVector and IsListDefault and IsGF2VectorRep ],
0,
Immutable );
#############################################################################
##
#M ZeroOp( <gf2vec> ) . . . . . . . . . . . . . . . mutable zero GF2 vector
##
InstallMethod( ZeroOp,
"for GF2 vector",
true,
[ IsRowVector and IsListDefault and IsGF2VectorRep ],
0,
ZERO_GF2VEC );
#############################################################################
##
#M ZeroSameMutability( <gf2vec> ) . . . . . same mutability zero GF2 vector
##
InstallMethod( ZeroSameMutability,
"for GF2 vector, mutable",
true,
[ IsRowVector and IsListDefault and IsGF2VectorRep and IsMutable],
0,
ZERO_GF2VEC );
InstallMethod( ZeroSameMutability,
"for GF2 vector, immutable",
true,
[ IsRowVector and IsListDefault and IsGF2VectorRep],
0,
function(v)
local z;
if IsMutable(v) then
TryNextMethod();
fi;
z := ZERO_GF2VEC(v);
MakeImmutable(z);
return z;
end);
#############################################################################
##
#M \=( <gf2vec>, <gf2vec> ) . . . . . . . . . . . . equality of GF2 vectors
##
InstallMethod( \=,"for GF2 vectors",IsIdenticalObj,
[ IsRowVector and IsGF2VectorRep,
IsRowVector and IsGF2VectorRep ], 0, EQ_GF2VEC_GF2VEC );
#############################################################################
##
#M \<( <gf2vec>, <gf2vec> ) . . . . . . . . . . . . equality of GF2 vectors
##
InstallMethod( \<,"for GF2 vectors",IsIdenticalObj,
[ IsRowVector and IsGF2VectorRep,
IsRowVector and IsGF2VectorRep ], 0, LT_GF2VEC_GF2VEC );
#############################################################################
##
#M \+( <gf2vec>, <gf2vec> ) . . . . . . . . . . . . sum of two GF2 vectors
##
InstallMethod( \+,
"for GF2 vectors",
IsIdenticalObj,
[ IsRowVector and IsListDefault and IsGF2VectorRep,
IsRowVector and IsListDefault and IsGF2VectorRep ],
0,
SUM_GF2VEC_GF2VEC );
#############################################################################
##
#M \-( <gf2vec>, <gf2vec> ) . . . . . . . . . difference of two GF2 vectors
##
InstallMethod( \-,
"for GF2 vectors",
IsIdenticalObj,
[ IsRowVector and IsListDefault and IsGF2VectorRep,
IsRowVector and IsListDefault and IsGF2VectorRep ],
0,
# we are in GF(2)
SUM_GF2VEC_GF2VEC );
#############################################################################
##
#M \*( <gf2vec>, <gf2vec> ) . . . . . . . . . . product of two GF2 vectors
##
InstallMethod( \*,
"for GF2 vectors",
IsIdenticalObj,
[ IsRingElementList and IsListDefault and IsRowVector and IsGF2VectorRep,
IsRingElementList and IsListDefault and IsRowVector and IsGF2VectorRep ],
0,
PROD_GF2VEC_GF2VEC );
#############################################################################
##
#M \*( <ffe>, <gf2vec> ) . . . . . . . . . . . product of FFE and GF2 vector
##
## This method is installed with positive rank because it is the
## specialised method for GF(2) elements and should fall through to
## the general method for GF(2^k).
##
InstallMethod( \*,
"for FFE and GF2 vector",
IsElmsColls,
[ IsFFE,
IsRingElementList and IsRowVector and IsGF2VectorRep ],
10,
function( a, b )
if a = GF2Zero then
return ZeroSameMutability(b);
elif a = GF2One then
if IsMutable(b) then
return ShallowCopy(b);
else
return b;
fi;
else
TryNextMethod();
fi;
end );
#############################################################################
##
#M \*( <gf2vec>, <ffe> ) . . . . . . . . . . . product of GF2 vector and FFE
##
## This method is installed with positive rank because it is the
## specialised method for GF(2) elements and should fall through to
## the general method for GF(2^k).
##
InstallMethod( \*,
"for GF2 vector and FFE",
IsCollsElms,
[ IsRingElementList and IsRowVector and IsGF2VectorRep,
IsFFE ],
10,
function( a, b )
if b = GF2Zero then
return ZeroSameMutability(a);
elif b = GF2One then
if IsMutable(a) then
return ShallowCopy(a);
else
return a;
fi;
else
TryNextMethod();
fi;
end );
#############################################################################
##
#M AddCoeffs( <gf2vec>, <gf2vec>, <mul> ) . . . . . . . . add coefficients
##
InstallOtherMethod( AddCoeffs,
"for GF2 vectors and FFE",
function(a,b,c) return IsIdenticalObj(a,b); end,
[ IsRowVector and IsGF2VectorRep and IsMutable,
IsRowVector and IsGF2VectorRep,
IsFFE ],
0,
ADDCOEFFS_GF2VEC_GF2VEC_MULT );
#############################################################################
##
#M AddCoeffs( <gf2vec>, <gf2vec> ) . . . . . . . . . . . . add coefficients
##
InstallOtherMethod( AddCoeffs,
"for GF2 vectors",
IsIdenticalObj,
[ IsRowVector and IsGF2VectorRep and IsMutable,
IsRowVector and IsGF2VectorRep ],
0,
ADDCOEFFS_GF2VEC_GF2VEC );
#############################################################################
##
#M AddCoeffs( <empty-list>, <gf2vec>, <mul> ) . . . . . . add coefficients
##
InstallOtherMethod( AddCoeffs,
"for empty list, GF2 vector and FFE",
true,
[ IsList and IsEmpty and IsMutable,
IsRowVector and IsGF2VectorRep,
IsFFE ],
0,
function( a, b, c )
a:=COPY_GF2VEC(a);
return ADDCOEFFS_GF2VEC_GF2VEC_MULT( a, b, c );
end );
#############################################################################
##
#M AddCoeffs( <empty-list>, <gf2vec> ) . . . . . . . . . . add coefficients
##
InstallOtherMethod( AddCoeffs,
"for empty list, GF2 vector",
true,
[ IsList and IsEmpty and IsMutable,
IsRowVector and IsGF2VectorRep ],
0,
function( a, b )
a:=COPY_GF2VEC(a);
return ADDCOEFFS_GF2VEC_GF2VEC(a,b);
end );
#############################################################################
##
#M PadCoeffs( <gf2vec>, <len> ) . . . . . . . . . . . expand a GF2 vector
##
InstallMethod( PadCoeffs,
"for GF2 vector",
true,
[ IsMutable and IsRowVector and IsAdditiveElementWithZeroCollection and IsGF2VectorRep,
IsPosInt ],
0,
function(v,len)
if len > LEN_GF2VEC(v) then
RESIZE_GF2VEC(v,len);
fi;
end);
#############################################################################
##
#M QuotRemCoeffs( <gf2vec>, <len>, <gf2vec>, <len> )
##
InstallMethod( QuotRemCoeffs,
"GF2 vectors",
[ IsRowVector and IsGF2VectorRep, IsInt, IsRowVector and IsGF2VectorRep, IsInt],
QUOTREM_COEFFS_GF2VEC);
#############################################################################
##
#M NormedRowVector( <v> )
##
InstallMethod( NormedRowVector, "for GF(2) vector", true,
[ IsRowVector and IsGF2VectorRep and IsScalarCollection ],0,
# Over GF(2) one can norm only to 1
x->x);
#############################################################################
##
#M Length( <list> ) . . . . . . . . . . . . . . . . length of a GF2 matrix
##
InstallOtherMethod( Length,
"for GF2 matrix",
true,
[ IsMatrix and IsGF2MatrixRep ],
0,
function( list )
return list![1];
end );
#############################################################################
##
#M <list> [ <pos> ] . . . . . . . . . . . select an element of a GF2 matrix
##
InstallOtherMethod( \[\], "for GF2 matrix",
[ IsMatrix and IsGF2MatrixRep,
IsPosInt ],
ELM_GF2MAT );
InstallMethod( \[\,\], "for GF2 matrix",
[ IsGF2MatrixRep,
IsPosInt, IsPosInt ],
MAT_ELM_GF2MAT );
#############################################################################
##
#M <gf2mat> [ <pos> ] := <elm> . . . . . . assign an element to a GF2 matrix
##
InstallOtherMethod( \[\]\:\=,
"for GF2 matrix",
[ IsList and IsGF2MatrixRep and IsMutable,
IsPosInt,
IsObject ],
ASS_GF2MAT );
InstallOtherMethod( \[\]\:\=,
"for GF2 matrix",
[ IsList and IsGF2MatrixRep,
IsPosInt,
IsObject ],
ASS_GF2MAT );
InstallMethod( \[\,\]\:\=,
"for GF2 matrix",
[ IsGF2MatrixRep and IsMutable,
IsPosInt, IsPosInt,
IsObject ],
SET_MAT_ELM_GF2MAT );
#############################################################################
##
#M ASS_LIST( <empty-list>, <pos>, <gf2vec> ) . . . . start a new GF2 matrix
##
#InstallMethod( ASS_LIST,
# "for empty plain list and GF2 vector",
# true,
# [ IsMutable and IsList and IsPlistRep and IsEmpty,
# IsPosInt,
# IsGF2VectorRep ],
# 0,
#function( list, pos, val )
# if pos = 1 and not IsMutable(val) then
# list[1] := 1;
# list[2] := val;
# SetFilterObj(val, IsLockedRepresentationVector);
# Objectify( TYPE_LIST_GF2MAT, list );
# else
# ASS_PLIST_DEFAULT( list, pos, val );
# fi;
#end );
#############################################################################
##
#M UNB_LIST( <gf2mat>, <pos> ) . . . . . . unbind a position of a GF2 matrix
##
InstallOtherMethod( UNB_LIST,
"for GF2 matrix",
true,
[ IsList and IsGF2MatrixRep and IsMutable,
IsPosInt ],
0,
UNB_GF2MAT );
InstallOtherMethod( UNB_LIST,
"for GF2 matrix",
true,
[ IsList and IsGF2MatrixRep,
IsPosInt ],
0,
function(m, pos)
if IsMutable(m) then
TryNextMethod();
elif pos <= Length(m) then
Error("Unbind: can't unbind an entry of an immutable GF2 Matrix" );
fi;
end);
#############################################################################
##
#M PrintObj( <gf2mat> ) . . . . . . . . . . . . . . . . print a GF2 matrix
##
InstallMethod( PrintObj,
"for GF2 matrix",
true,
[ IsGF2MatrixRep ],
0,
function( mat )
local i, j;
Print( "\>\>[ \>\>" );
for i in [ 1 .. NrRows(mat) ] do
if 1 < i then Print( "\<,\< \>\>" ); fi;
Print( "\>\>[ \>\>" );
for j in [ 1 .. NrCols(mat) ] do
if 1 < j then Print( "\<,\< \>\>" ); fi;
Print( mat[i,j] );
od;
Print( " \<\<\<\<]" );
od;
Print( " \<\<\<\<]" );
end );
#############################################################################
##
#M ViewObj( <gf2mat> ) . . . . . . . . . . . . . . . . view a GF2 matrix
##
InstallMethod( ViewObj,
"for GF2 matrix",
true,
[ IsMatrix and IsFinite and IsGF2MatrixRep ],
0,
function( mat )
if IsMutable(mat) then
Print("<a ",NrRows(mat),"x",NrCols(mat)," matrix over GF2>");
else
Print( "<an immutable ", NrRows(mat), "x", NrCols(mat),
" matrix over GF2>" );
fi;
end );
#############################################################################
##
#M ShallowCopy( <gf2mat> ) . . . . . . mutable shallow copy of a GF2 matrix
##
BindGlobal("SHALLOWCOPY_GF2MAT",
function(mat)
local copy, i, len;
len := mat![1];
copy := [ len ];
for i in [2..len+1] do
copy[i] := mat![i];
od;
Objectify( TYPE_LIST_GF2MAT, copy );
return copy;
end);
InstallMethod( ShallowCopy,
"for GF2 matrix",
true,
[ IsMatrix and IsGF2MatrixRep ],
0,
SHALLOWCOPY_GF2MAT);
InstallOtherMethod(TransposedMat,"GF2 matrix",true,
[IsMatrix and IsGF2MatrixRep],0,TRANSPOSED_GF2MAT);
InstallOtherMethod(MutableTransposedMat,"GF2 matrix",true,
[IsMatrix and IsGF2MatrixRep],0,TRANSPOSED_GF2MAT);
#############################################################################
##
#M AdditiveInverseOp( <gf2mat> ) . mutable additive inverse of a GF2 matrix
##
InstallMethod( AdditiveInverseOp,
"for GF2 matrix",
true,
[ IsMatrix and IsListDefault and IsGF2MatrixRep ],
0,
function(mat)
local copy, i, len;
len := mat![1];
copy := [ len ];
for i in [2..len+1] do
copy[i] := ShallowCopy(mat![i]);
SetFilterObj(copy[i],IsLockedRepresentationVector);
od;
Objectify( TYPE_LIST_GF2MAT, copy );
return copy;
end);
#############################################################################
##
#M AdditiveInverseSameMutability( <gf2mat> ) . same mutability additive inverse
##
InstallMethod( AdditiveInverseSameMutability,
"for GF2 matrix",
true,
[ IsMatrix and IsListDefault and IsGF2MatrixRep ],
0,
function(mat)
local copy, i, len,r ;
if not IsMutable(mat) then
return mat;
fi;
len := mat![1];
copy := [ len ];
for i in [2..len+1] do
r := mat![i];
if IsMutable(r) then
copy[i] := ShallowCopy(mat![i]);
SetFilterObj(copy[i],IsLockedRepresentationVector);
else
copy[i] := r;
fi;
od;
Objectify( TYPE_LIST_GF2MAT, copy );
return copy;
end);
#############################################################################
##
#M AdditiveInverse( <gf2mat> ) . . . . . . additive inverse of a GF2 matrix
##
InstallMethod( AdditiveInverse,
"for GF2 matrix",
true,
[ IsMatrix and IsListDefault and IsGF2MatrixRep ],
0,
# we are in GF2
Immutable );
#############################################################################
##
#M InverseOp( <gf2mat> ) . . . . . . . . . . mutable inverse of a GF2 matrix
##
InstallMethod( InverseOp,
"for GF2 matrix",
true,
[ IsMultiplicativeElementWithInverse and IsOrdinaryMatrix and
IsSmallList and IsFFECollColl
and IsGF2MatrixRep ],
0,
INV_GF2MAT_MUTABLE );
#############################################################################
##
#M InverseSameMutability( <gf2mat> ) same mutability inverse of a GF2 matrix
##
InstallMethod( InverseSameMutability,
"for GF2 matrix",
true,
[ IsMultiplicativeElementWithInverse and IsOrdinaryMatrix and
IsSmallList and IsFFECollColl
and IsGF2MatrixRep ],
0,
INV_GF2MAT_SAME_MUTABILITY );
#############################################################################
##
#M InverseOp( <list of gf2 vectors> ) . . . mutable inverse of a GF2 matrix
##
InstallMethod( InverseOp,
"for plain list of GF2 vectors",
true,
[ IsPlistRep and IsFFECollColl and IsMatrix],
0,
m->INV_PLIST_GF2VECS_DESTRUCTIVE(List(m, ShallowCopy)) );
#############################################################################
##
#M InverseSameMutability( <list of gf2 vectors> ) . same mutability inverse of a GF2 matrix
##
InstallMethod( InverseSameMutability,
"for plain list of GF2 vectors",
true,
[ IsPlistRep and IsFFECollColl and IsMatrix],
0,
function(m)
local inv,i;
inv := INV_PLIST_GF2VECS_DESTRUCTIVE(List(m, ShallowCopy));
if inv = TRY_NEXT_METHOD then
TryNextMethod();
fi;
if IsMutable(m) then
if not IsMutable(m[1]) then
for i in [1..NrRows(m)] do
MakeImmutable(inv[i]);
od;
fi;
else
MakeImmutable(inv);
fi;
return inv;
end );
#############################################################################
##
#M OneOp( <gf2mat> ) . . . . . . . . . . . . . . mutable identity GF2 matrix
##
## A fully mutable GF2 matrix cannot be in the special compressed rep.
## so return it as a plain list
##
BindGlobal("GF2IdentityMatrix", function(n, imm)
local i,id,line,o;
o := Z(2);
id := [n];
for i in [1..n] do
line := ZERO_GF2VEC_2(n);
line[i] := o;
SetFilterObj(line,IsLockedRepresentationVector);
if imm > 0 then
MakeImmutable(line);
fi;
Add(id, line);
od;
if imm > 1 then
Objectify(TYPE_LIST_GF2MAT_IMM, id);
else
Objectify(TYPE_LIST_GF2MAT, id);
fi;
return id;
end);
InstallMethod( OneOp,
"for GF2 Matrix",
true,
[ IsOrdinaryMatrix and IsGF2MatrixRep and IsMultiplicativeElementWithOne],
0,
function(mat)
local len;
len := NrRows(mat);
if len <> NrCols(mat) then
return fail;
fi;
return GF2IdentityMatrix(len, 0);
end);
#############################################################################
##
#M One( <gf2mat> ) . . . . . . . . . . . . . . . . . . . identity GF2 matrix
##
InstallMethod( One,
"for GF2 Matrix",
true,
[ IsOrdinaryMatrix and IsGF2MatrixRep and IsMultiplicativeElementWithOne],
0,
function(mat)
local len;
len := NrRows(mat);
if len <> NrCols(mat) then
return fail;
fi;
return GF2IdentityMatrix(len, 2);
end );
#############################################################################
##
#M OneSameMutability( <gf2mat> ) . . . . . . . . . . . . identity GF2 matrix
##
InstallMethod( OneSameMutability,
"for GF2 Matrix",
true,
[ IsOrdinaryMatrix and IsGF2MatrixRep and IsMultiplicativeElementWithOne],
0,
function(mat)
local len,row1;
len := NrRows(mat);
if len <> NrCols(mat) then
return fail;
fi;
row1 := mat[1];
if not IsMutable(mat) then
return GF2IdentityMatrix(len, 2);
elif IsMutable(mat) and not IsMutable(row1) then
return GF2IdentityMatrix(len, 1);
else
return GF2IdentityMatrix(len, 0);
fi;
end );
#############################################################################
##
#M ZeroOp( <gf2mat> ) . . . . . . . . . . . . . . . mutable zero GF2 matrix
##
##
InstallMethod( ZeroOp,
"for GF2 Matrix",
true,
[ IsMatrix and IsListDefault and IsGF2MatrixRep ],
0,
function( mat )
local new, zero, i;
new := [ Length(mat) ];
if 0 < new[1] then
for i in [ 1 .. new[1] ] do
zero := ZeroOp(mat[1]);
SetFilterObj(zero, IsLockedRepresentationVector);
Add( new, zero );
od;
fi;
Objectify( TYPE_LIST_GF2MAT, new );
return new;
end );
#############################################################################
##
#M ZeroSameMutability( <gf2mat> ) . . . . . . . . . . . matching mutability
##
InstallMethod( ZeroSameMutability,
"for GF2 Matrix",
true,
[ IsMatrix and IsListDefault and IsGF2MatrixRep ],
0,
function( mat )
local new, zero, i;
new := [ Length(mat) ];
if 0 < new[1] then
if IsMutable(mat![2]) then
for i in [ 1 .. new[1] ] do
zero := ZeroSameMutability(mat![2]);
SetFilterObj(zero, IsLockedRepresentationVector);
Add( new, zero );
od;
else
zero := ZeroSameMutability(mat![2]);
SetFilterObj(zero, IsLockedRepresentationVector);
for i in [ 1 .. new[1] ] do
Add( new, zero );
od;
fi;
fi;
Objectify( TypeObj(mat), new );
return new;
end );
#############################################################################
##
#M Zero( <gf2mat> ) . . . . . . . . . . . . . . . . . . . . zero GF2 matrix
##
InstallMethod( Zero,
"for GF2 Matrix",
true,
[ IsMatrix and IsListDefault and IsGF2MatrixRep ],
0,
function( mat )
local new, zero, i;
new := [ Length(mat) ];
if 0 < new[1] then
zero := Zero(mat[1]);
SetFilterObj(zero, IsLockedRepresentationVector);
for i in [ 1 .. new[1] ] do
Add( new, zero );
od;
fi;
Objectify( TYPE_LIST_GF2MAT_IMM, new );
return new;
end );
#############################################################################
##
#M \+( <gf2mat>, <gf2mat> ) . . . . . sum of a GF2 matrix and a GF2 matrix
##
InstallMethod( \+,
"for GF2 matrix and GF2 matrix",
IsIdenticalObj,
[ IsMatrix and IsListDefault and IsGF2MatrixRep,
IsMatrix and IsListDefault and IsGF2MatrixRep ],
0,
SUM_GF2MAT_GF2MAT );
#############################################################################
##
#M \<( <gf2mat>, <gf2mat> ) . . . . . . . . . . .comparison of GF2 matrices
##
InstallMethod( \<,
"for GF2 matrix and GF2 matrix",
IsIdenticalObj,
[ IsMatrix and IsListDefault and IsGF2MatrixRep,
IsMatrix and IsListDefault and IsGF2MatrixRep ],
0,
LT_GF2MAT_GF2MAT);
#############################################################################
##
#M \=( <gf2mat>, <gf2mat> ) . . . . . . . . . . .comparison of GF2 matrices
##
InstallMethod( \=,
"for GF2 matrix and GF2 matrix",
IsIdenticalObj,
[ IsMatrix and IsListDefault and IsGF2MatrixRep,
IsMatrix and IsListDefault and IsGF2MatrixRep ],
0,
EQ_GF2MAT_GF2MAT);
#############################################################################
##
#M \-( <gf2mat>, <gf2mat> ) . . . . . sum of a GF2 matrix and a GF2 matrix
##
InstallMethod( \-,
"for GF2 matrix and GF2 matrix",
IsIdenticalObj,
[ IsMatrix and IsListDefault and IsGF2MatrixRep,
IsMatrix and IsListDefault and IsGF2MatrixRep ],
0,
# we are in GF2
SUM_GF2MAT_GF2MAT );
#############################################################################
##
#M \*( <gf2vec>, <gf2mat> ) . . . product of a GF2 vector and a GF2 matrix
##
InstallMethod( \*,
"for GF2 vector and GF2 matrix",
true,
[ IsRingElementList and IsRowVector and IsListDefault and IsGF2VectorRep,
IsMatrix and IsListDefault and IsGF2MatrixRep ],
0,
PROD_GF2VEC_GF2MAT );
#############################################################################
##
#M <vec>*<mat> . . . general method for GF2 vector and a matrix
## works fast when the matrix is a plain list
## of compressed GF2 vectors, otherwise falls through
##
InstallMethod(\*, "for a GF2 vector and a compatible matrix",
IsElmsColls, [IsRowVector and IsGF2VectorRep and IsSmallList
and IsRingElementList,
IsRingElementTable and IsPlistRep], 0,
PROD_GF2VEC_ANYMAT);
#############################################################################
##
#M \*( <gf2mat>, <gf2vec> ) . . . product of a GF2 matrix and a GF2 vector
##
InstallMethod( \*,
"for GF2 matrix and GF2 vector",
true,
[ IsMatrix and IsListDefault and IsGF2MatrixRep,
IsRowVector and IsListDefault and IsGF2VectorRep ],
0,
PROD_GF2MAT_GF2VEC );
#############################################################################
##
#M \*( <gf2mat>, <gf2mat> ) . . . product of a GF2 matrix and a GF2 matrix
##
InstallMethod( \*,
"for GF2 matrix and GF2 matrix",
IsIdenticalObj,
[ IsMatrix and IsListDefault and IsGF2MatrixRep,
IsMatrix and IsListDefault and IsGF2MatrixRep ],
0,
PROD_GF2MAT_GF2MAT );
#############################################################################
##
#M \*( <gf2elm>, <gf2mat> ) . . . product of a GF2 element and a GF2 matrix
##
InstallMethod( \*,
"for GF2 element and GF2 matrix",
IsElmsCollColls,
[ IsFFE,
IsMatrix and IsListDefault and IsGF2MatrixRep ],
0,
function(s,m)
if s = Z(2) then
return AdditiveInverseSameMutability(m);
elif IsZero(s) then
return ZeroSameMutability(m);
else
TryNextMethod();
fi;
end);
#############################################################################
##
#M \*( <gf2mat>, <gf2elm> ) . . . product of a GF2 matrix and a GF2 element
##
InstallMethod( \*,
"for GF2 matrix and GF2 element",
IsCollCollsElms,
[ IsMatrix and IsListDefault and IsGF2MatrixRep,
IsFFE ],
0,
function(m,s)
if s = Z(2) then
return AdditiveInverseSameMutability(m);
elif IsZero(s) then
return ZeroSameMutability(m);
else
TryNextMethod();
fi;
end);
#############################################################################
##
#F ConvertToVectorRep(<v>)
##
BindGlobal("LOCAL_COPY_GF2", GF(2));
BindGlobal("SMALL_PRIME_POWERS", Immutable(Filtered([2..256], IsPrimePowerInt)));
InstallGlobalFunction(ConvertToVectorRepNC,function( arg )
local v, q, vc, common, field, q0;
if Length(arg) < 1 then
Error("ConvertToVectorRep: one or two arguments required");
fi;
v := arg[1];
#
# Handle fast, certain cases where there is no work. Microseconds count here
#
if IsGF2VectorRep(v) and (Length(arg) = 1 or arg[2] = 2 or arg[2] = LOCAL_COPY_GF2) then
return 2;
fi;
if Is8BitVectorRep(v) then
q0 := Q_VEC8BIT(v);
if Length(arg) = 1 then
return q0;
fi;
if IsPosInt(arg[2]) then
q := arg[2];
elif IsField(arg[2]) then
q := Size(arg[2]);
else
return fail;
fi;
if q = q0 then
return q;
fi;
if IsLockedRepresentationVector(v) then
Error("Vector is locked over current field");
else
if q = 2 then
CONV_GF2VEC(v);
return 2;
elif q <= 256 then
if not q in SMALL_PRIME_POWERS then
return fail;
fi;
CONV_VEC8BIT(v,q);
return q;
else
if q mod q0 <> 0 then
Error("New field size incompatible with vector entries");
else
PLAIN_VEC8BIT(v);
return q;
fi;
fi;
fi;
fi;
if (Length(v) = 0 and Length(arg) = 1) or
(Length(v) >0 and not IsRowVector(v)) then
return fail;
fi;
# if the representation of v is already locked, then
# we ignore a second arguments and just report on the vector
if IsLockedRepresentationVector(v) then
if IsGF2VectorRep(v) then
q := 2;
elif Is8BitVectorRep(v) then
q := Q_VEC8BIT(v);
else
Error("vector is locked in an unknown representation");
fi;
if not IsInt(arg[2]) then
arg[2] := Size(arg[2]);
fi;
if Length(arg) = 2 and q <> arg[2] then
Info(InfoWarning, 1,
"ConvertToVectorRep: locked vector not converted to different field");
fi;
return q;
fi;
#
# Ask the kernel to check the list for us.
# We have to do this, even in an NC version because the list might contain
# elements of large finite fields
#
if not IS_VECFFE(v) then
if IsFFECollection(v) then
# now we might have some elements in a large field representation
# or possibly a totally bad list
vc := ShallowCopy(v);
common := FFECONWAY.WriteOverSmallestCommonField(vc);
#
# FFECONWAY.WriteOverSmallestCommonField returns an integer or fail.
# When integer is returned, it also may modify entries of vc
#
if common = fail or common > 256 then
#
# vector needs a field > 256, so can't be compressed
# or vector contains non-ffes or no common characteristic
#
return fail;
fi;
# Switching the object below can change the mutability of v, so we
# make sure that if v is immutable it stays immutable.
if not IsMutable(v) then
MakeImmutable(vc);
fi;
# We need to force the switch, because v (and vc) might
# be in the public region, with all caveats that might have.
# ConvertToVectorRep should not be used in HPC-GAP
FORCE_SWITCH_OBJ(v,vc); # horrible hack.
else
return fail;
fi;
else
common := COMMON_FIELD_VECFFE(v);
fi;
#
# see if the user gave us q
#
if Length(arg) > 1 then
field := arg[2];
if IsPosInt(field) then
q := field;
Assert(2,IsPrimePowerInt(q));
elif IsField(field) then
q := Size(field);
else
Error("q not a field or positive integer");
fi;
else
q := fail;
fi;
#
# if there is a field, we go to work
#
if q = fail then
if common = fail then
return fail;
fi;
if not IsPrimeInt(common) then
common := SMALLEST_FIELD_VECFFE(v);
fi;
if common = 2 then
CONV_GF2VEC(v);
return 2;
elif common <= 256 then
CONV_VEC8BIT(v,common);
return common;
else
return fail;
fi;
elif q = 2 then
if common > 2 and common mod 2 = 0 then
common := SMALLEST_FIELD_VECFFE(v);
fi;
if common <> 2 then
Error("ConvertToVectorRepNC: Vector cannot be written over GF(2)");
fi;
CONV_GF2VEC(v); # safe to call this even with an invalid argument
return 2;
elif q <= 256 then
if common <> q then
if IsPlistRep(v) and GcdInt(common,q) > 1 then
common := SMALLEST_FIELD_VECFFE(v);
fi;
if common ^ LogInt(q, common) <> q then
Error("ConvertToVectorRepNC: Vector cannot be written over GF(",q,")");
fi;
fi;
Assert(2, ForAll(v, elm -> elm in GF(q)));
CONV_VEC8BIT(v,q);
return q;
else
return fail;
fi;
end);
#############################################################################
##
#F CopyToVectorRep( <v>, <q> )
##
InstallGlobalFunction(CopyToVectorRep,function( v, q )
local vc, common, res;
# Handle fast, certain cases where there is no work. Microseconds count here
if Length(v) = 0 then
return v;
fi;
if IsGF2VectorRep(v) and q=2 then
if IsMutable(v) then
return(ShallowCopy(v));
else
return v;
fi;
fi;
if Is8BitVectorRep(v) then
if q = Q_VEC8BIT(v) then
if IsMutable(v) then
return(ShallowCopy(v));
else
return v;
fi;
fi;
fi;
# Ask the kernel to check the list for us.
# We have to do this, even in an NC version because the list might contain
# elements of large finite fields.
# Calling IS_VECFFE may force a full inspection of the list.
if not IS_VECFFE(v) then
# TODO: no need of the next 'if' block in the NC-version
if IsFFECollection(v) then
# Now we might have some elements in a large field representation
# or possibly a totally bad list. We will examine the shallow copy
# of v to avoid side effects when CopyToVectorRep modifies v and
# then returns fail
vc := ShallowCopy(v);
common := FFECONWAY.WriteOverSmallestCommonField(vc);
#
# FFECONWAY.WriteOverSmallestCommonField returns an integer or fail.
# When it returns an integer, it may modify individual entries of vc
#
if common = fail or common > 256 then
#
# vector needs a field > 256, so can't be compressed
# or vector contains non-ffes or no common characteristic
#
return fail; # v cannot be written over GF(q)
fi;
if not IsMutable(v) then
MakeImmutable(vc);
fi;
else
return fail; # v cannot be written over GF(q)
fi;
else
common := COMMON_FIELD_VECFFE(v);
vc := v;
fi;
if q = 2 then
Assert(2, ForAll(vc, elm -> elm in GF(2)));
if common > 2 and common mod 2 = 0 then
common := SMALLEST_FIELD_VECFFE(vc);
fi;
if common <> 2 then
Error("CopyToVectorRep: Vector cannot be written over GF(2)");
fi;
res := COPY_GF2VEC(vc);
if not IsMutable(v) then MakeImmutable(res); fi;
return res;
elif q <= 256 then
if common <> q then
Assert(2, ForAll(vc, elm -> elm in GF(q)));
if IsPlistRep(vc) and GcdInt(common,q) > 1 then
common := SMALLEST_FIELD_VECFFE(vc);
fi;
if common ^ LogInt(q, common) <> q then
Error("CopyToVectorRep: Vector cannot be written over GF(",q,")");
fi;
fi;
res := COPY_VEC8BIT(vc,q);
if not IsMutable(v) then MakeImmutable(res); fi;
return res;
else
return fail; # vector cannot be written over GF(q)
fi;
end);
#############################################################################
##
#F CopyToVectorRepNC( <v>, <q> )
##
## This is the NC-version of CopyToVectorRep. It is forbidden to call it
## unless v is a plain list or a row vector, q<=256 is a valid size of a
## finite field, and all elements of v lie in this field.
##
InstallGlobalFunction(CopyToVectorRepNC,function( v, q )
local common, res;
# Handle fast, certain cases where there is no work. Microseconds count here
if Length(v) = 0 then
return v;
fi;
if IsGF2VectorRep(v) and q=2 then
if IsMutable(v) then
return(ShallowCopy(v));
else
return v;
fi;
fi;
if Is8BitVectorRep(v) then
if q = Q_VEC8BIT(v) then
if IsMutable(v) then
return(ShallowCopy(v));
else
return v;
fi;
fi;
fi;
# Calling COMMON_FIELD_VECFFE may force a full inspection of the list.
common := COMMON_FIELD_VECFFE(v);
if common = fail then
common := SMALLEST_FIELD_VECFFE(v);
if common = fail then
Error("CopyToVectorRepNC: Vector cannot be written over GF(",q,").\n",
"You may try to use CopyToVectorRep instead\n");
fi;
fi;
if q = 2 then
Assert(2, ForAll(v, elm -> elm in GF(2)));
if common > 2 and common mod 2 = 0 then
common := SMALLEST_FIELD_VECFFE(v);
fi;
if common <> 2 then
Error("CopyToVectorRepNC: Vector cannot be written over GF(2)");
fi;
res := COPY_GF2VEC(v);
if not IsMutable(v) then MakeImmutable(res); fi;
return res;
elif q <= 256 then
if common <> q then
Assert(2, ForAll(v, elm -> elm in GF(q)));
if IsPlistRep(v) and GcdInt(common,q) > 1 then
common := SMALLEST_FIELD_VECFFE(v);
fi;
if common ^ LogInt(q, common) <> q then
Error("CopyToVectorRepNC: Vector cannot be written over GF(",q,")");
fi;
fi;
res :=COPY_VEC8BIT(v,q);
if not IsMutable(v) then MakeImmutable(res); fi;
return res;
else
Error("CopyToVectorRepNC: Vector cannot be written over GF(",q,")");
fi;
end);
#############################################################################
##
#F ImmutableMatrix( <field>, <matrix> [,<change>] )
##
BindGlobal("DoImmutableMatrix", function(field,matrix,change)
local sf, rep, ind, ind2, row, i,big,l,nr;
if IsMatrixObj(matrix) then
# result is a matrix object iff 'matrix' is
if field=BaseDomain(matrix) then
return Immutable(matrix);
else
return ImmutableMatrix(field,Unpack(matrix));
fi;
elif not (IsPlistRep(matrix) or IsGF2MatrixRep(matrix) or
Is8BitMatrixRep(matrix)) then
# if empty or not list based, simply return `Immutable'.
return Immutable(matrix);
fi;
if IsPosInt(field) then
sf:=field;
elif IsField(field) then
sf:=Size(field);
elif IsZmodnZObjNonprimeCollection(field) then
# slight abuse of ``field'' variable name
sf:=Size(field);
else
# not a field
return Immutable(matrix);
fi;
big:=sf>256 or sf=0 or not IsFFECollColl(matrix);
# the representation we want the rows to be in
if sf=2 then
rep:=IsGF2VectorRep;
elif not big then
rep:=function(v) return Is8BitVectorRep(v) and Q_VEC8BIT(v) = sf; end;
else
rep:=IsPlistRep;
fi;
# cannot use NrRows consistently, as input might be mixed format
if IsList(matrix) then
nr:=Length(matrix);
else
nr:=NrRows(matrix);
fi;
# get the indices of the rows that need changing the representation.
ind:=[]; # rows to convert
ind2:=[]; # rows to rebuild
for i in [1..nr] do
if not rep(matrix[i]) then
if big or IsLockedRepresentationVector(matrix[i])
or (IsMutable(matrix[i]) and not change) then
Add(ind2,i);
else
# wrong rep, but can be converted
Add(ind,i);
fi;
elif (IsMutable(matrix[i]) and not change) then
# right rep but wrong mutability
Add(ind2,i);
fi;
od;
# do we need to rebuild outer matrix layer?
if not IsMutable(matrix) # matrix was immutable
or (IsMutable(matrix) and not change) # matrix was mutable
or (Length(ind2)>0 and # we want to change rows
not IsMutable(matrix)) #but cannot change entries
or (Is8BitMatrixRep(matrix) # matrix is be compact rep
and (Length(ind)>0 or Length(ind2)>0) ) # and we change rows
then
l:=matrix;
matrix:=[];
for i in l do
Add(matrix,i);
od;
fi;
# rebuild some rows
if IsZmodnZObjNonprimeCollection(field) then
big:=true;
elif big then
if sf<>infinity and IsPrimeInt(sf) and sf>MAXSIZE_GF_INTERNAL then
if not (IsMatrixObj(matrix) and not IsMutable(matrix)) then
if field=sf then field:=Integers mod sf;fi;
for i in ind2 do
matrix[i]:=List(matrix[i],j->j); # plist conversion
od;
fi;
else
for i in ind2 do
matrix[i]:=List(matrix[i],j->j); # plist conversion
od;
fi;
else
for i in ind2 do
row := CopyToVectorRep(matrix[i], sf);
if row <> fail then
matrix[i] := row;
fi;
od;
for i in ind do
matrix[i]:=CopyToVectorRep(matrix[i],sf);
od;
fi;
MakeImmutable(matrix);
if not big and sf=2 and not IsGF2MatrixRep(matrix) then
CONV_GF2MAT(matrix);
elif not big and sf>2 and sf<=256 and not Is8BitMatrixRep(matrix) then
CONV_MAT8BIT(matrix,sf);
fi;
return matrix;
end);
InstallOtherMethod( ImmutableMatrix,"general,2",
[IsObject,IsMatrixOrMatrixObj],0,
function(f,m)
return DoImmutableMatrix(f,m,false);
end);
InstallOtherMethod( ImmutableMatrix,"List of vectors",
[IsObject,IsList],0,
function(f,m)
if not ForAll(m,x->IsList(x) or IsVector(x)) then TryNextMethod();fi;
return DoImmutableMatrix(f,m,false);
end);
InstallOtherMethod(ImmutableMatrix,"general,3",[IsObject,IsMatrixOrMatrixObj,IsBool],0,
DoImmutableMatrix);
InstallOtherMethod( ImmutableMatrix,"field,8bit",[IsField,Is8BitMatrixRep],0,
function(f,m)
if Q_VEC8BIT(m[1])<>Size(f) then
TryNextMethod();
fi;
return Immutable(m);
end);
InstallOtherMethod( ImmutableMatrix,"field,gf2",[IsField,IsGF2MatrixRep],0,
function(f,m)
if 2<>Size(f) then
TryNextMethod();
fi;
return Immutable(m);
end);
InstallOtherMethod( ImmutableMatrix,"fieldsize,8bit",[IsPosInt,Is8BitMatrixRep],0,
function(f,m)
if Q_VEC8BIT(m[1])<>f then
TryNextMethod();
fi;
return Immutable(m);
end);
InstallOtherMethod( ImmutableMatrix,"fieldsize,gf2",[IsPosInt,IsGF2MatrixRep],0,
function(f,m)
if 2<>f then
TryNextMethod();
fi;
return Immutable(m);
end);
InstallOtherMethod( ImmutableMatrix,"empty",[IsObject,IsEmpty],0,
function(f,m)
return Immutable(m);
end);
InstallOtherMethod( ImmutableMatrix,"transposed empty",[IsObject,IsList],0,
function(f,m)
if not ForAll(m,i->IsList(i) and Length(i)=0) then
TryNextMethod();
fi;
return Immutable(m);
end);
#############################################################################
##
#F ImmutableVector( <field>, <vector> )
##
InstallMethod( ImmutableVector,"general,2",[IsObject,IsRowVector],0,
function(f,v)
local v2;
if not IsInt(f) then f := Size(f); fi;
# 'IsRowVector' implies 'IsList'.
# We are not allowed to return a non-list,
# thus we are not allowed to call 'Vector'.
# Since there is a method for 'IsVectorObj' as the second argument,
# we do not deal with proper vector objects here.
if f <= 256 then
v2 := CopyToVectorRep(v,f);
if v2 <> fail then v := v2; fi;
fi;
return Immutable(v);
end);
InstallOtherMethod( ImmutableVector,"vectorObj,2",[IsObject,IsVectorObj],0,
function(f,v)
return MakeImmutable( ChangedBaseDomain( v, f ) );
end);
InstallOtherMethod( ImmutableVector,"general,3",[IsObject,IsRowVector,IsBool],0,
function(f,v,change)
local v2;
if not IsInt(f) then f := Size(f); fi;
if f <= 256 then
v2 := CopyToVectorRep(v,f);
if v2 <> fail then v := v2; fi;
fi;
return Immutable(v);
end);
InstallOtherMethod( ImmutableVector,"field,8bit",[IsField,Is8BitVectorRep],0,
function(f,v)
if Q_VEC8BIT(v)<>Size(f) then
TryNextMethod();
fi;
return Immutable(v);
end);
InstallOtherMethod( ImmutableVector,"field,gf2",[IsField,IsGF2VectorRep],0,
function(f,v)
if 2<>Size(f) then
TryNextMethod();
fi;
return Immutable(v);
end);
InstallOtherMethod( ImmutableVector,"fieldsize,8bit",[IsPosInt,Is8BitVectorRep],0,
function(f,v)
if Q_VEC8BIT(v)<>f then
TryNextMethod();
fi;
return Immutable(v);
end);
InstallOtherMethod( ImmutableVector,"fieldsize,gf2",[IsPosInt,IsGF2VectorRep],0,
function(f,v)
if 2<>f then
TryNextMethod();
fi;
return Immutable(v);
end);
InstallOtherMethod( ImmutableVector,"empty",[IsObject,IsEmpty],0,
function(f,v)
return Immutable(v);
end);
#############################################################################
##
#M MultVector( <vl>, <mul>)
##
InstallOtherMethod( MultVector, "for GF(2) vector and char 2 scalar",
IsCollsElms, [IsGF2VectorRep and IsRowVector and IsMutable,
IsFFE], 0,
MULT_VECTOR_GF2VECS_2);
#############################################################################
##
#M PositionNot( <vec>, GF2Zero )
#M PositionNot( <vec>, GF2Zero, 0)
##
InstallOtherMethod( PositionNot, "for GF(2) vector and 0*Z(2)",
IsCollsElms, [IsGF2VectorRep and IsRowVector , IsFFE and
IsZero], 0,
POSITION_NONZERO_GF2VEC);
InstallMethod( PositionNot, "for GF(2) vector and 0*Z(2) and offset",
IsCollsElmsX, [IsGF2VectorRep and IsRowVector , IsFFE and
IsZero, IsInt], 0,
function(v,z,z1)
return POSITION_NONZERO_GF2VEC3(v,z,z1);
end);
#############################################################################
##
#M Append( <vecl>, <vecr> )
##
InstallMethod( Append, "for GF2 vectors",
true, [IsGF2VectorRep and IsMutable and IsList,
IsGF2VectorRep and IsList], 0,
APPEND_GF2VEC);
#############################################################################
##
#M ShallowCopy( <vec> ) . . . for GF2 vectors
##
InstallMethod( ShallowCopy,
"for GF2 vectors",
true, [ IsGF2VectorRep and IsList and IsRowVector ], 0,
SHALLOWCOPY_GF2VEC);
#############################################################################
##
#M PositionNonZero( <vec> )
##
InstallOtherMethod(PositionNonZero, "for GF(2) vector",true,
[IsGF2VectorRep and IsRowVector],0,
# POSITION_NONZERO_GF2VEC ignores the second argument
v-> POSITION_NONZERO_GF2VEC(v,0));
InstallOtherMethod(PositionNonZero, "for GF(2) vector and offset",true,
[IsGF2VectorRep and IsRowVector, IsInt],0,
# POSITION_NONZERO_GF2VEC3 ignores the second argument
function(v, from)
return POSITION_NONZERO_GF2VEC3(v,0,from);
end);
#############################################################################
##
#M PositionNonZero( <vec> )
##
InstallOtherMethod(PositionNonZero,
"General method for a row vector",
true,[IsRowVector],0,
function(vec)
local i,z;
if Length(vec)=0 then return 1;fi;
z:=Zero(vec[1]);
for i in [1..Length(vec)] do
if vec[i]<>z then return i;fi;
od;
return Length(vec)+1;
end);
#############################################################################
##
#M NumberFFVector(<<vec>,<sz>)
##
InstallMethod(NumberFFVector,"GF2-Vector",true,
[IsGF2VectorRep and IsRowVector and IsFFECollection,IsPosInt],0,
function(v,n)
if n<>2 then TryNextMethod();fi;
return NUMBER_GF2VEC(v);
end);
#############################################################################
##
#M NumberFFVector(<vec>,<sz>)
##
InstallMethod(NumberFFVector,"uncompressed vecffe",
[IsRowVector and IsFFECollection,IsPosInt],
function(v,n)
local qels, sy, p, x;
qels:= EnumeratorSorted( GF(n) );
sy := 0;
for x in v do
p := Position(qels, x);
if p = fail then
Info(InfoWarning,2,
"NumberFFVector: Vector not over specified field");
return fail;
fi;
sy := n*sy + (p-1);
od;
return sy;
end);
#############################################################################
##
#M IsSubset(<finfield>,<gf2vec>)
##
InstallMethod(IsSubset,"field, 8bit-vector",IsIdenticalObj,
[ IsField and IsFinite and IsFFECollection,
IsGF2VectorRep and IsRowVector and IsFFECollection],0,
function(F,v)
# the family ensures the field is in the correct characteristic.
return true;
end);
#############################################################################
##
#M DefaultFieldOfMatrix( <ffe-mat> )
##
InstallMethod( DefaultFieldOfMatrix,
"method for a matrix over GF(2)", true,
[ IsMatrix and IsFFECollColl and IsGF2MatrixRep ], 0,
function( mat )
return GF(2);
end );
#############################################################################
##
#M DegreeFFE( <ffe-mat> )
##
InstallOtherMethod( DegreeFFE,
"method for a matrix over GF(2)", true,
[ IsMatrix and IsFFECollColl and IsGF2MatrixRep ], 0,
function( mat )
return 1;
end );
#############################################################################
##
#M DegreeFFE( <vector> )
##
InstallOtherMethod( DegreeFFE, "for GF(2) vectors", true,
[ IsRowVector and IsFFECollection and IsGF2VectorRep ], 0, v->1);
#############################################################################
##
#M LeftShiftRowVector( <vec>, <shift> )
##
InstallMethod( LeftShiftRowVector, "gf2 vector", true,
[IsMutable and IsRowVector and IsGF2VectorRep,
IsPosInt], 0,
SHIFT_LEFT_GF2VEC);
#############################################################################
##
#M RightShiftRowVector( <vec>, <shift>, <zero> )
##
InstallMethod( RightShiftRowVector, "gf2 vector, fill with zeros", IsCollsXElms,
[IsMutable and IsRowVector and IsGF2VectorRep,
IsPosInt,
IsFFE and IsZero], 0,
SHIFT_RIGHT_GF2VEC);
#############################################################################
##
#M ShrinkRowVector( <vec> )
InstallMethod( ShrinkRowVector, "GF2 vector", true,
[IsMutable and IsRowVector and IsGF2VectorRep ],
0,
function(vec)
local r;
r := RIGHTMOST_NONZERO_GF2VEC(vec);
RESIZE_GF2VEC(vec, r);
end);
#############################################################################
##
#M RemoveOuterCoeffs( <vec>, <zero> )
##
InstallMethod( RemoveOuterCoeffs, "gf2vec and zero", IsCollsElms,
[ IsMutable and IsGF2VectorRep and IsRowVector, IsFFE and
IsZero], 0,
function (v,z)
local shift;
shift := POSITION_NONZERO_GF2VEC(v,z) -1;
if shift <> 0 then
SHIFT_LEFT_GF2VEC( v, shift);
fi;
if v <> [] then
RESIZE_GF2VEC(v, RIGHTMOST_NONZERO_GF2VEC(v));
fi;
return shift;
end);
#############################################################################
##
#M ProductCoeffs( <vec>, <len>, <vec>, <len>)
##
##
InstallMethod( ProductCoeffs, "GF2 vectors, kernel method", IsFamXFamY,
[IsGF2VectorRep and IsRowVector, IsInt, IsGF2VectorRep and
IsRowVector, IsInt ], 0,
PROD_COEFFS_GF2VEC);
InstallOtherMethod( ProductCoeffs, "Gf2 vectors, kernel method (2 arg)",
IsIdenticalObj,
[IsGF2VectorRep and IsRowVector, IsGF2VectorRep and
IsRowVector ], 0,
function(v,w)
return PROD_COEFFS_GF2VEC(v, Length(v), w, Length(w));
end);
#############################################################################
##
#M ReduceCoeffs( <vec>, <len>, <vec>, <len>)
##
##
InstallMethod( ReduceCoeffs, "GF2 vectors, kernel method", IsFamXFamY,
[IsGF2VectorRep and IsRowVector and IsMutable, IsInt, IsGF2VectorRep and
IsRowVector, IsInt ], 0,
REDUCE_COEFFS_GF2VEC);
InstallOtherMethod( ReduceCoeffs, "Gf2 vectors, kernel method (2 arg)",
IsIdenticalObj,
[IsGF2VectorRep and IsRowVector and IsMutable, IsGF2VectorRep and
IsRowVector ], 0,
function(v,w)
return REDUCE_COEFFS_GF2VEC(v, Length(v), w, Length(w));
end);
#############################################################################
##
#M PowerModCoeffs( <vec1>, <len1>, <exp>, <vec2>, <len2> )
##
InstallMethod( PowerModCoeffs, "for gf2vectors", IsFamXYFamZ,
[IsGF2VectorRep and IsRowVector, IsInt, IsPosInt,
IsGF2VectorRep and IsRowVector, IsInt], 0,
function( v, lv, exp, w, lw)
local pow, lpow, bits, i;
if exp = 1 then
pow := ShallowCopy(v);
ReduceCoeffs(pow,lv,w,lw);
return pow;
fi;
pow := v;
lpow := lv;
bits := [];
while exp > 0 do
Add(bits, exp mod 2);
exp := QuoInt(exp,2);
od;
bits := Reversed(bits);
for i in [2..Length(bits)] do
pow := PROD_COEFFS_GF2VEC(pow,lpow, pow, lpow);
lpow := Length(pow);
lpow := REDUCE_COEFFS_GF2VEC( pow, lpow, w, lw);
if lpow = 0 then
return pow;
fi;
if bits[i] = 1 then
pow := PROD_COEFFS_GF2VEC(pow, lpow, v, lv);
lpow := Length(pow);
lpow := REDUCE_COEFFS_GF2VEC( pow, lpow, w, lw);
if lpow = 0 then
return pow;
fi;
fi;
od;
return pow;
end);
#############################################################################
##
#M DomainForAction( <pnt>, <acts> )
##
InstallMethod(DomainForAction,"FFE vector/matrix",IsElmsCollCollsX,
# for technical reasons a matrix list is not automatically
# IsMatrixCollection -- thus we cannot use this filter here. AH
#T this method is only installed for finite fields. There ought to be a
#T method for finite rings and there could be one for infinite fields. AH
[IsVector and IsFFECollection,IsList,IsFunction],0,
function(pnt,acts,act)
if (not ForAll(acts,IsMatrix)) or
(act<>OnPoints and act<>OnLines and act<>OnRight
and act<>OnSubspacesByCanonicalBasisConcatenations) or
CollectionsFamily(CollectionsFamily(FamilyObj(pnt)))<>FamilyObj(acts) then
TryNextMethod(); # strange operation, might extend the domain
fi;
return NaturalActedSpace(acts,[pnt]);
# if Length(pnt)=0 or Length(acts)=0 then
# return fail;
# fi;
# l:=Concatenation(acts);
# Add(l,pnt);
# f:=DefaultFieldOfMatrix(l);
# if f = fail then
# return fail;
# fi;
# return f^Length(pnt);
end);
#############################################################################
##
#M DomainForAction( <pnt>, <acts> )
##
InstallMethod(DomainForAction,"matrix/matrix",IsElmsCollsX,
# for technical reasons a matrix list is not automatically
# IsMatrixCollection -- thus we cannot use this filter here. AH
#T this method is only installed for finite fields. There ought to be a
#T method for finite rings and there could be one for infinite fields. AH
[IsMatrix and IsFFECollColl,IsList,IsFunction],0,
function(pnt,acts,act)
local l,f;
if (not ForAll(acts,IsMatrix)) or
(act<>OnPoints and act<>OnSubspacesByCanonicalBasis and act<>OnRight) then
TryNextMethod(); # strange operation, might extend the domain
fi;
l:=NaturalActedSpace(acts,pnt);
f:=Size(LeftActingDomain(l));
l:=Size(l);
return rec(hashfun:=function(b)
local h,i;
h:=0;
for i in b do
h:=h*l+NumberFFVector(i,f);
od;
return h;
end);
end);
InstallMethod(DomainForAction,"vector/permgrp",true,
[IsList,IsList,IsFunction],0,
function(pnt,acts,act)
if (not (ForAll(acts,IsPerm) and ForAll(pnt,IsScalar)))
or (act<>Permuted) then
TryNextMethod(); # strange operation, might extend the domain
fi;
return DefaultField(pnt)^Length(pnt);
end);
#############################################################################
##
#M SemiEchelonMat( <GF2 matrix> )
#M SemiEchelonMatTransformation( <GF2 matrix> )
#M SemiEchelonMatDestructive( <plain list of GF2 vectors> )
#M SemiEchelonMatTransformationDestructive( <plain list of GF2 vectors> )
##
#
#
# This is the rank by which we increase the GF2 kernel methods,
# so that they get tried before the 8bit ones, as they will fall
# through faster.
#
#
BindGlobal("GF2_AHEAD_OF_8BIT_RANK", 10);
#
# If mat is in the GF2 special representation, then we do
# have to copy it, but we know that the rows of the result will
# already be in GF2 special representation, so we skip the conversion
# step in the generic method
#
InstallMethod(SemiEchelonMat, "shortcut method for GF2 matrices",
true,
[ IsMatrix and IsGF2MatrixRep and IsFFECollColl ],
0,
function(mat)
local res;
res := SemiEchelonMatDestructive( List(mat, ShallowCopy) ) ;
ConvertToMatrixRepNC(res.vectors,2);
return res;
end );
InstallMethod(SemiEchelonMatTransformation,
"kernel method for plain lists of GF2 vectors",
true,
[ IsMatrix and IsFFECollColl and IsGF2MatrixRep],
0,
function(mat)
local res;
res := SemiEchelonMatTransformationDestructive( List( mat, ShallowCopy) );
ConvertToMatrixRepNC(res.vectors,2);
ConvertToMatrixRepNC(res.coeffs,2);
ConvertToMatrixRepNC(res.relations,2);
return res;
end );
#
# The real kernel methods, which are destructive and want plain lists
# of GF2 vectors as their arguments, but will try next if they get other
# plain lists
#
InstallMethod(SemiEchelonMatDestructive,
"kernel method for plain lists of GF2 vectors",
true,
[ IsPlistRep and IsMatrix and IsMutable and IsFFECollColl ],
GF2_AHEAD_OF_8BIT_RANK,
SEMIECHELON_LIST_GF2VECS);
InstallMethod(SemiEchelonMatTransformationDestructive,
"kernel method for plain lists of GF2 vectors",
true,
[ IsMatrix and IsPlistRep and IsFFECollColl and IsMutable],
GF2_AHEAD_OF_8BIT_RANK,
SEMIECHELON_LIST_GF2VECS_TRANSFORMATIONS);
#############################################################################
##
#M TriangulizeMat( <plain list of GF2 vectors> )
##
## The method will fall through if the matrix is not a plain list of
## GF2 vectors
InstallMethod(TriangulizeMat,
"kernel method for plain list of GF2 vectors",
true,
[IsMatrix and IsPlistRep and IsFFECollColl and IsMutable],
GF2_AHEAD_OF_8BIT_RANK,
TRIANGULIZE_LIST_GF2VECS);
##
#T Really should sort this one in the kernel
## but this should fix the major inefficiency for now
##
InstallMethod(TriangulizeMat,
"for GF2 matrices",
true,
[IsMatrix and IsMutable and IsFFECollColl and IsGF2MatrixRep],
0,
function(m)
local i,imms;
PLAIN_GF2MAT(m);
imms := [];
for i in [1..Length(m)] do
if not IsMutable(m[i]) then
m[i] := ShallowCopy(m[i]);
imms[i] := true;
else
imms[i] := false;
fi;
od;
TRIANGULIZE_LIST_GF2VECS(m);
for i in [1..Length(m)] do
if not IsMutable(m[i]) then
m[i] := ShallowCopy(m[i]);
imms[i] := true;
else
imms[i] := false;
fi;
od;
CONV_GF2MAT(m);
end);
#############################################################################
##
#M DeterminantMatDestructive ( <plain list of GF2 vectors> )
##
InstallMethod(DeterminantMatDestructive,
"kernel method for plain list of GF2 vectors",
true,
[IsMatrix and IsPlistRep and IsFFECollColl and IsMutable],
GF2_AHEAD_OF_8BIT_RANK,
DETERMINANT_LIST_GF2VECS);
#############################################################################
##
#M RankMatDestructive ( <plain list of GF2 vectors> )
##
InstallOtherMethod(RankMatDestructive,
"kernel method for plain list of GF2 vectors",
[IsMatrix and IsPlistRep and IsFFECollColl and IsMutable],
GF2_AHEAD_OF_8BIT_RANK,
RANK_LIST_GF2VECS);
--> --------------------
--> maximum size reached
--> --------------------
[ Dauer der Verarbeitung: 0.38 Sekunden
(vorverarbeitet)
]
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