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#@local F,F9,TestReadMatEntry,dim,m,v,w,checkShift,testlens,types,vecs,i,j
#@local v1,v2,G
gap> START_TEST("vecmat.tst");
#
# construct finite field of size 9 that is not GF(9)
gap> F9 := AlgebraicExtension(GF(3), CyclotomicPolynomial(GF(3), 4));;
#
# ImmutableVector
#
# zero vector over rationals
gap> F := Rationals;; v := ListWithIdenticalEntries( 3, Zero(F) );
[ 0, 0, 0 ]
gap> w := ImmutableVector( F, v );
[ 0, 0, 0 ]
gap> v = w;
true
gap> IsMutable(w);
false
gap> w := ImmutableVector( F, v, true );
[ 0, 0, 0 ]
gap> v = w;
true
gap> IsMutable(w);
false
# zero vector over GF(2)
gap> F := GF(2);; v := ListWithIdenticalEntries( 3, Zero(F) );
[ 0*Z(2), 0*Z(2), 0*Z(2) ]
gap> w := ImmutableVector( 2, v );
<an immutable GF2 vector of length 3>
gap> v = w;
true
gap> IsMutable(w);
false
gap> w := ImmutableVector( F, v );
<an immutable GF2 vector of length 3>
gap> v = w;
true
gap> IsMutable(w);
false
gap> w := ImmutableVector( F, v, true );
<an immutable GF2 vector of length 3>
gap> v = w;
true
gap> IsMutable(w);
false
# zero vector over GF(9)
gap> F := GF(9);; v := ListWithIdenticalEntries( 3, Zero(F) );
[ 0*Z(3), 0*Z(3), 0*Z(3) ]
gap> w := ImmutableVector( 9, v );
[ 0*Z(3), 0*Z(3), 0*Z(3) ]
gap> v = w;
true
gap> IsMutable(w);
false
gap> w := ImmutableVector( F, v );
[ 0*Z(3), 0*Z(3), 0*Z(3) ]
gap> v = w;
true
gap> IsMutable(w);
false
gap> w := ImmutableVector( F, v, true );
[ 0*Z(3), 0*Z(3), 0*Z(3) ]
gap> v = w;
true
gap> IsMutable(w);
false
# zero vector over GF(9) but not in internal format
gap> F := F9;; v := ListWithIdenticalEntries( 3, Zero(F) );
[ !0*Z(3), !0*Z(3), !0*Z(3) ]
gap> w := ImmutableVector( 9, v );
[ !0*Z(3), !0*Z(3), !0*Z(3) ]
gap> v = w;
true
gap> IsMutable(w);
false
gap> w := ImmutableVector( F, v );
[ !0*Z(3), !0*Z(3), !0*Z(3) ]
gap> v = w;
true
gap> IsMutable(w);
false
gap> w := ImmutableVector( F, v, true );
[ !0*Z(3), !0*Z(3), !0*Z(3) ]
gap> v = w;
true
gap> IsMutable(w);
false
# zero vector over a ring with zero divisors
gap> F := Integers mod 6;; v := ListWithIdenticalEntries( 3, Zero(F) );
[ ZmodnZObj( 0, 6 ), ZmodnZObj( 0, 6 ), ZmodnZObj( 0, 6 ) ]
gap> w := ImmutableVector( F, v );
[ ZmodnZObj( 0, 6 ), ZmodnZObj( 0, 6 ), ZmodnZObj( 0, 6 ) ]
gap> v = w;
true
gap> IsMutable(w);
false
gap> w := ImmutableVector( F, v, true );
[ ZmodnZObj( 0, 6 ), ZmodnZObj( 0, 6 ), ZmodnZObj( 0, 6 ) ]
gap> v = w;
true
gap> IsMutable(w);
false
# empty vectors
gap> v := ImmutableVector( Rationals, [] );
[ ]
gap> IsMutable(v);
false
gap> v := ImmutableVector( GF(2), [] );
[ ]
gap> IsMutable(v);
false
gap> v := ImmutableVector( GF(7), [] );
[ ]
gap> IsMutable(v);
false
gap> v := ImmutableVector( Integers mod 4, [] );
[ ]
gap> IsMutable(v);
false
#
# ImmutableMatrix
#
# identity matrix over rationals
gap> F := Rationals;; m := IdentityMat( 3, F );
[ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ]
gap> w := ImmutableMatrix( F, m );
[ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ]
gap> m = w;
true
gap> IsMutable(w);
false
gap> w := ImmutableMatrix( F, m, true );
[ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ]
gap> m = w;
true
gap> IsMutable(w);
false
# identity matrix over GF(2)
gap> F := GF(2);; m := IdentityMat( 3, F );
[ <a GF2 vector of length 3>, <a GF2 vector of length 3>,
<a GF2 vector of length 3> ]
gap> w := ImmutableMatrix( 2, m );
<an immutable 3x3 matrix over GF2>
gap> m = w;
true
gap> IsMutable(w);
false
gap> w := ImmutableMatrix( F, m );
<an immutable 3x3 matrix over GF2>
gap> m = w;
true
gap> IsMutable(w);
false
gap> w := ImmutableMatrix( F, m, true );
<an immutable 3x3 matrix over GF2>
gap> m = w;
true
gap> IsMutable(w);
false
# identity matrix over GF(9)
gap> F := GF(9);; m := IdentityMat( 3, F );
[ [ Z(3)^0, 0*Z(3), 0*Z(3) ], [ 0*Z(3), Z(3)^0, 0*Z(3) ],
[ 0*Z(3), 0*Z(3), Z(3)^0 ] ]
gap> w := ImmutableMatrix( 9, m );
[ [ Z(3)^0, 0*Z(3), 0*Z(3) ], [ 0*Z(3), Z(3)^0, 0*Z(3) ],
[ 0*Z(3), 0*Z(3), Z(3)^0 ] ]
gap> m = w;
true
gap> IsMutable(w);
false
gap> w := ImmutableMatrix( F, m );
[ [ Z(3)^0, 0*Z(3), 0*Z(3) ], [ 0*Z(3), Z(3)^0, 0*Z(3) ],
[ 0*Z(3), 0*Z(3), Z(3)^0 ] ]
gap> m = w;
true
gap> IsMutable(w);
false
gap> w := ImmutableMatrix( F, m, true );
[ [ Z(3)^0, 0*Z(3), 0*Z(3) ], [ 0*Z(3), Z(3)^0, 0*Z(3) ],
[ 0*Z(3), 0*Z(3), Z(3)^0 ] ]
gap> m = w;
true
gap> IsMutable(w);
false
# identity matrix over GF(9) but not in internal format
gap> F := F9;; m := IdentityMat( 3, F );
[ [ !Z(3)^0, !0*Z(3), !0*Z(3) ], [ !0*Z(3), !Z(3)^0, !0*Z(3) ],
[ !0*Z(3), !0*Z(3), !Z(3)^0 ] ]
gap> w := ImmutableMatrix( 9, m );
[ [ !Z(3)^0, !0*Z(3), !0*Z(3) ], [ !0*Z(3), !Z(3)^0, !0*Z(3) ],
[ !0*Z(3), !0*Z(3), !Z(3)^0 ] ]
gap> m = w;
true
gap> IsMutable(w);
false
gap> w := ImmutableMatrix( F, m );
[ [ !Z(3)^0, !0*Z(3), !0*Z(3) ], [ !0*Z(3), !Z(3)^0, !0*Z(3) ],
[ !0*Z(3), !0*Z(3), !Z(3)^0 ] ]
gap> m = w;
true
gap> IsMutable(w);
false
gap> w := ImmutableMatrix( F, m, true );
[ [ !Z(3)^0, !0*Z(3), !0*Z(3) ], [ !0*Z(3), !Z(3)^0, !0*Z(3) ],
[ !0*Z(3), !0*Z(3), !Z(3)^0 ] ]
gap> m = w;
true
gap> IsMutable(w);
false
# identity matrix over a ring with zero divisors
gap> F := Integers mod 6;; m := IdentityMat( 3, F );
[ [ ZmodnZObj( 1, 6 ), ZmodnZObj( 0, 6 ), ZmodnZObj( 0, 6 ) ],
[ ZmodnZObj( 0, 6 ), ZmodnZObj( 1, 6 ), ZmodnZObj( 0, 6 ) ],
[ ZmodnZObj( 0, 6 ), ZmodnZObj( 0, 6 ), ZmodnZObj( 1, 6 ) ] ]
gap> w := ImmutableMatrix( F, m );;
# these "=" tests contradict the definition of "=" in matobj.gi
# there is no method for IsPlist and IsMatrixObj in general
#gap> m = w;
#true
gap> IsMutable(w);
false
gap> w := ImmutableMatrix( F, m, true );;
#gap> m = w;
#true
gap> IsMutable(w);
false
# empty matrix
gap> m := ImmutableMatrix( Rationals, [] );
[ ]
gap> IsMutable(m);
false
gap> m := ImmutableMatrix( GF(2), [] );
[ ]
gap> IsMutable(m);
false
gap> m := ImmutableMatrix( GF(7), [] );
[ ]
gap> IsMutable(m);
false
gap> m := ImmutableMatrix( Integers mod 4, [] );
[ ]
gap> IsMutable(m);
false
#
# Test matrix access functions (see also listindex.tst)
#
gap> TestReadMatEntry := function(m)
> local dim;
> dim := DimensionsMat(m);
> dim := [ [1..dim[1]], [1..dim[2]] ];
> return ForAll(dim[1], row->ForAll(dim[2], col-> m[row,col] = m[row][col]));
> end;;
#
gap> F := GF(2);; m := IdentityMat( 3, F );;
gap> TestReadMatEntry(m);
true
gap> m[1,4];
Error, List Element: <list>[4] must have an assigned value
gap> m[4,1];
Error, List Element: <list>[4] must have an assigned value
#
gap> m := ImmutableMatrix( 2, m );
<an immutable 3x3 matrix over GF2>
gap> TestReadMatEntry(m);
true
gap> m[1,4];
Error, column index 4 exceeds 3, the number of columns
gap> m[4,1];
Error, row index 4 exceeds 3, the number of rows
#
gap> F := GF(9);; m := IdentityMat( 3, F );;
gap> TestReadMatEntry(m);
true
gap> m[1,4];
Error, List Element: <list>[4] must have an assigned value
gap> m[4,1];
Error, List Element: <list>[4] must have an assigned value
#
gap> m := ImmutableMatrix( 9, m );;
gap> TestReadMatEntry(m);
true
gap> m[1,4];
Error, column index 4 exceeds 3, the number of columns
gap> m[4,1];
Error, row index 4 exceeds 3, the number of rows
#
# some tests for GF(2) rep
#
gap> F := GF(2);;
gap> m := ImmutableMatrix( F, IdentityMat( 3, F ) );
<an immutable 3x3 matrix over GF2>
gap> v := ImmutableVector( F, [1,0,1] * One(F) );
<an immutable GF2 vector of length 3>
gap> m * v = v;
true
gap> v * m = v;
true
gap> v * v;
0*Z(2)
gap> m * m = m;
true
# test greased matrix mult
gap> m := ImmutableMatrix( F, IdentityMat( 150, F ) );
<an immutable 150x150 matrix over GF2>
gap> m * m = m;
true
gap> PROD_GF2MAT_GF2MAT_SIMPLE(m,m) = m;
true
gap> PROD_GF2MAT_GF2MAT_ADVANCED(m,m,8,1) = m;
true
#
#
#
gap> F:=GF(3);;
gap> v:=[ Z(3)^0, Z(3), Z(3)^0, 0*Z(3), Z(3)^0, Z(3)^0, Z(3)^0, Z(3)^0 ];;
gap> vecs:=[
> [ Z(3)^0, 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ],
> [ 0*Z(3), Z(3)^0, 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ],
> [ 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3) ],
> [ 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3) ],
> [ 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3), Z(3)^0, 0*Z(3) ],
> [ 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3), Z(3)^0 ] ];;
gap> AClosestVectorCombinationsMatFFEVecFFE(vecs,F,v,1,1);
[ 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3), Z(3)^0 ]
gap> AClosestVectorCombinationsMatFFEVecFFECoords(vecs,F,v,1,1);
[ [ 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3), Z(3)^0 ],
[ 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0 ] ]
gap> DistancesDistributionMatFFEVecFFE(vecs,F,v);
[ 0, 4, 6, 60, 109, 216, 192, 112, 30 ]
gap> DistancesDistributionVecFFEsVecFFE(vecs,v);
[ 0, 0, 0, 0, 0, 4, 0, 1, 1 ]
#
gap> v1:=[ Z(3)^0, Z(3), Z(3)^0, 0*Z(3), Z(3)^0, Z(3)^0, Z(3)^0, Z(3)^0 ];;
gap> v2:=[ Z(3), Z(3)^0, Z(3)^0, 0*Z(3), Z(3)^0, Z(3)^0, Z(3)^0, Z(3)^0 ];;
gap> DistanceVecFFE(v1,v2);
2
#
gap> checkShift := function(filt, field, length, shift)
> local w;
> w := NewVector(filt, field, List([1..length], x -> Random(field)));
> v := StructuralCopy(w);
> LeftShiftRowVector(v, shift);
> if Length(v) <> Maximum(0, length - shift) then
> Print("failed left shift\n");
> fi;
> if ForAny([1..length-shift], i -> (w[i+shift] <> v[i])) then
> Print("failed left shift\n");
> fi;
> v := StructuralCopy(w);
> RightShiftRowVector(v, shift, Zero(field));
> if Length(v) <> length + shift then
> Print("failed right shift\n");
> fi;
> if ForAny([1..length], i -> (w[i] <> v[i+shift])) then
> Print("failed right shift\n");
> fi;
> if ForAny([1..shift], i -> (v[i] <> Zero(field))) then
> Print("failed right shift\n");
> fi;
> end;;
# Check around powers of two
gap> testlens := [0,1,2,7,8,9,15,16,17,31,32,33,62,63,64,65,66,126,127,128,129];;
gap> for types in [[IsGF2VectorRep, GF(2)],
> [IsPlistVectorRep, Integers],
> [Is8BitVectorRep, GF(2)],
> [Is8BitVectorRep, GF(9)]] do
> for i in testlens do
> for j in testlens do
> checkShift(IsGF2VectorRep, GF(2), i, j);
> od;
> od;
> od;
# Check the change of the base domain.
gap> v:= Vector( IsPlistVectorRep, GF(4), [ 0, 1 ] * Z(2) );;
gap> ImmutableVector( GF(2), v );
<immutable plist vector over GF(2) of length 2>
# ImmutableVector is not allowed to return non-lists when called with lists.
gap> v:= [ 0, 1 ] * Z(5)^0;;
gap> IsList( v );
true
gap> IsList( ImmutableVector( GF(5^6), v ) );
true
gap> ConvertToVectorRep( v );; IsList( v );
true
gap> IsList( ImmutableVector( GF(5^6), v ) );
true
# Check that the vector representations fit in the computation of the
# nice monomorphism.
gap> G:= Group([ [ [ Z(5^6)^6944, 0*Z(5) ], [ 0*Z(5), Z(5^2)^20 ] ] ]);;
gap> Size( G );;
#
gap> STOP_TEST("vecmat.tst");
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