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TestZeroVector := function(filt, ring, len)
local i, vec, vec2;
vec := ZeroVector(filt, ring, len);
Assert(0, filt(vec) = true);
Assert(0, BaseDomain(vec) = ring);
Assert(0, Length(vec) = len);
for i in [1..len] do
if not IsZero(vec[i]) then Error("entry ", i," is ", vec[i], " and not zero"); fi;
od;
vec2 := ZeroVector(len, vec);
if vec <> vec2 then Error("ZeroVector(len, vec) differs"); fi;
vec2 := NewZeroVector(filt, ring, len);
if vec <> vec2 then Error("NewZeroVector(filt, ring, len) differs"); fi;
return vec;
end;
TestZeroMatrix := function(filt, ring, rows, cols)
local i, j, mat, mat2;
mat := ZeroMatrix(filt, ring, rows, cols);
Assert(0, filt(mat) = true);
Assert(0, BaseDomain(mat) = ring);
Assert(0, NrRows(mat) = rows);
Assert(0, NrCols(mat) = cols);
for i in [1..rows] do
for j in [1..cols] do
if not IsZero(mat[i,j]) then Error("entry ", i,",",j," is ", mat[i,j], " and not zero"); fi;
od;
od;
mat2 := ZeroMatrix(rows, cols, mat);
if mat <> mat2 then Error("ZeroMatrix(rows, cols, mat) differs"); fi;
mat2 := NewZeroMatrix(filt, ring, rows, cols);
if mat <> mat2 then Error("NewZeroMatrix(filt, ring, rows, cols) differs"); fi;
return mat;
end;
TestIdentityMatrix := function(filt, ring, degree)
local i, j, mat, mat2;
mat := IdentityMatrix(filt, ring, degree);
Assert(0, filt(mat) = true);
Assert(0, BaseDomain(mat) = ring);
Assert(0, NrRows(mat) = degree);
Assert(0, NrCols(mat) = degree);
for i in [1..degree] do
for j in [1..degree] do
if i<>j and not IsZero(mat[i,j]) then
Error("entry ", i,",",j," is not zero");
elif i=j and not IsOne(mat[i,j]) then
Error("diagonal entry ", i,",",j," is not one");
fi;
od;
od;
mat2 := IdentityMatrix(degree, mat);
if mat <> mat2 then Error("IdentityMatrix(degree, mat) differs"); fi;
mat2 := NewIdentityMatrix(filt, ring, degree);
if mat <> mat2 then Error("NewIdentityMatrix(filt, ring, degree) differs"); fi;
return mat;
end;
TestCompanionMatrix := function(filt, pol, ring)
local degree, mat, i, j, mat2;
degree:= Degree(pol);
mat:= CompanionMatrix(filt, pol, ring);
Assert(0, filt(mat) = true);
Assert(0, BaseDomain(mat) = ring);
Assert(0, NrRows(mat) = degree);
Assert(0, NrCols(mat) = degree);
for i in [1..degree] do
for j in [1..degree-1] do
if i <> j+1 and not IsZero(mat[i,j]) then
Error("entry ", i,",",j," is not zero");
elif i = j+1 and not IsOne(mat[i,j]) then
Error("entry ", i,",",j," is not one");
fi;
od;
od;
mat2 := CompanionMatrix(pol, mat);
if mat <> mat2 then Error("CompanionMatrix(pol, mat) differs"); fi;
mat2 := NewCompanionMatrix(filt, pol, ring);
if mat <> mat2 then Error("NewCompanionMatrix(filt, pol, ring) differs"); fi;
return mat;
end;
TestElementaryTransforms := function(mat, scalar)
local i, j, copy, eq;
Assert(0, NrRows(mat) >= 2);
Assert(0, NrCols(mat) >= 2);
# make an old-fashioned entry-wise copy of this matrix so we can compare
# all changes made there independent of any special properties of the
# matrix representation
copy := [];
for i in [1..NrRows(mat)] do
copy[i] := [];
for j in [1..NrCols(mat)] do
copy[i,j] := mat[i,j];
od;
od;
eq := function()
local i, j;
for i in [1..NrRows(mat)] do
for j in [1..NrCols(mat)] do
if copy[i,j] <> mat[i,j] then
return false;
fi;
od;
od;
return true;
end;
#
#
#
for i in [1..NrRows(mat)] do
MultMatrixRowLeft(mat,i,scalar);
MultMatrixRowLeft(copy,i,scalar);
if not eq() then Error("MultMatrixRowLeft(",i,",",scalar,") failure"); fi;
od;
for i in [1..NrRows(mat)] do
MultMatrixRowRight(mat,i,scalar);
MultMatrixRowRight(copy,i,scalar);
if not eq() then Error("MultMatrixRowRight(",i,",",scalar,") failure"); fi;
od;
for i in [1..NrCols(mat)] do
MultMatrixColumnLeft(mat,i,scalar);
MultMatrixColumnLeft(copy,i,scalar);
if not eq() then Error("MultMatrixColumnLeft(",i,",",scalar,") failure"); fi;
od;
for i in [1..NrCols(mat)] do
MultMatrixColumnRight(mat,i,scalar);
MultMatrixColumnRight(copy,i,scalar);
if not eq() then Error("MultMatrixColumnRight(",i,",",scalar,") failure"); fi;
od;
#
#
#
for i in [1..NrRows(mat)] do
for j in [1..NrRows(mat)] do
AddMatrixRowsLeft(mat,i,j,scalar);
AddMatrixRowsLeft(copy,i,j,scalar);
if not eq() then Error("AddMatrixRowsLeft(",i,",",j,",",scalar,") failure"); fi;
od;
od;
for i in [1..NrRows(mat)] do
for j in [1..NrRows(mat)] do
AddMatrixRowsRight(mat,i,j,scalar);
AddMatrixRowsRight(copy,i,j,scalar);
if not eq() then Error("AddMatrixRowsRight(",i,",",j,",",scalar,") failure"); fi;
od;
od;
for i in [1..NrCols(mat)] do
for j in [1..NrCols(mat)] do
AddMatrixColumnsLeft(mat,i,j,scalar);
AddMatrixColumnsLeft(copy,i,j,scalar);
if not eq() then Error("AddMatrixColumnsLeft(",i,",",j,",",scalar,") failure"); fi;
od;
od;
for i in [1..NrCols(mat)] do
for j in [1..NrCols(mat)] do
AddMatrixColumnsRight(mat,i,j,scalar);
AddMatrixColumnsRight(copy,i,j,scalar);
if not eq() then Error("AddMatrixColumnsRight(",i,",",j,",",scalar,") failure"); fi;
od;
od;
#
#
#
for i in [1..NrRows(mat)] do
for j in [1..NrRows(mat)] do
SwapMatrixRows(mat,i,j);
SwapMatrixRows(copy,i,j);
if not eq() then Error("SwapMatrixRows(",i,",",j,") failure"); fi;
od;
od;
for i in [1..NrCols(mat)] do
for j in [1..NrCols(mat)] do
SwapMatrixColumns(mat,i,j);
SwapMatrixColumns(copy,i,j);
if not eq() then Error("SwapMatrixColumns(",i,",",j,") failure"); fi;
od;
od;
end;
[ Dauer der Verarbeitung: 0.7 Sekunden
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