MatrixObj: matrix manipulation ops for IsMatrix

Before this, e.g. `SwapMatrixRows(IdentityMat(10,Integers), 1, 2)`
resulted in a "no method found" error.

In addition, use `InstallEarlyMethod` to provide fast methods for classical
lists-of-list matrices.

Before the new early methods (but after enabling everything for `IsMatrix`):

    gap> mat:=IdentityMat(10,Integers);;
    gap> for i in [1..1000000] do SwapMatrixRows(mat,1,2); od; time;
    874
    gap> for i in [1..1000000] do tmp:=mat[1];mat[1]:=mat[2];mat[2]:=tmp; od; time;
    38
    gap> mat:=IdentityMat(10,GF(2));; ConvertToMatrixRep(mat);; mat;
    <a 10x10 matrix over GF2>
    gap> for i in [1..1000000] do SwapMatrixRows(mat,1,2); od; time;
    137
    gap> for i in [1..1000000] do tmp:=mat[1];mat[1]:=mat[2];mat[2]:=tmp; od; time;
    107

After:

    gap> mat:=IdentityMat(10,Integers);;
    gap> for i in [1..1000000] do SwapMatrixRows(mat,1,2); od; time;
    132
    gap> for i in [1..1000000] do tmp:=mat[1];mat[1]:=mat[2];mat[2]:=tmp; od; time;
    37
    gap> mat:=IdentityMat(10,GF(2));; ConvertToMatrixRep(mat);; mat;
    <a 10x10 matrix over GF2>
    gap> for i in [1..1000000] do SwapMatrixRows(mat,1,2); od; time;
    163
    gap> for i in [1..1000000] do tmp:=mat[1];mat[1]:=mat[2];mat[2]:=tmp; od; time;
    102

Note that `SwapMatrixRows` got slightly slower for the compressed matrix over GF(2),
due to the extra overhead caused by the early method. I think for now this is
acceptable. If we are concerned about this, we could probably get rid of most or
all of it by using a "classic" early method, i.e., a kernel one.

lib/matobj.gi

@@ -1490,59 +1490,77 @@ InstallMethod( \[\,\]\:\=, "for a matrix object, two positions, and an object",
 ############################################################################
 
 InstallMethod( MultMatrixRowLeft, "for a mutable matrix object, a row number, and a scalar",
- [ IsMatrixObj and IsMutable, IsInt, IsObject ],
+ [ IsMatrixOrMatrixObj and IsMutable, IsInt, IsObject ],
  function( mat, row, scalar )
  local i;
- 
+
  for i in [1..NrCols(mat)] do
  mat[row,i] := scalar * mat[row,i];
  od;
-
+
+ end );
+
+InstallEarlyMethod( MultMatrixRowLeft,
+ function( mat, i, scalar )
+ if IsPlistRep(mat) then
+ mat[i] := scalar * mat[i];
+ else
+ TryNextMethod();
+ fi;
  end );
 
 ############################################################################
 
 InstallMethod( MultMatrixColumnRight, "for a mutable matrix object, a column number, and a scalar",
- [ IsMatrixObj and IsMutable, IsInt, IsObject ],
+ [ IsMatrixOrMatrixObj and IsMutable, IsInt, IsObject ],
  function( mat, column, scalar )
  local i;
- 
+
  for i in [1..NrRows(mat)] do
  mat[i,column] := mat[i,column] * scalar;
  od;
- 
+
  end );
 
 ############################################################################
 
 InstallMethod( MultMatrixRowRight, "for a mutable matrix object, a row number, and a scalar",
- [ IsMatrixObj and IsMutable, IsInt, IsObject ],
+ [ IsMatrixOrMatrixObj and IsMutable, IsInt, IsObject ],
  function( mat, row, scalar )
  local i;
- 
+
  for i in [1..NrCols(mat)] do
  mat[row,i] := mat[row,i] * scalar;
  od;
-
+
+ end );
+
+InstallEarlyMethod( MultMatrixRowRight,
+ function( mat, i, scalar )
+ if IsPlistRep(mat) then
+ mat[i] := mat[i] * scalar;
+ else
+ TryNextMethod();
+ fi;
  end );
 
 ############################################################################
 
 InstallMethod( MultMatrixColumnLeft, "for a mutable matrix object, a column number, and a scalar",
- [ IsMatrixObj and IsMutable, IsInt, IsObject ],
+ [ IsMatrixOrMatrixObj and IsMutable, IsInt, IsObject ],
  function( mat, column, scalar )
  local i;
- 
+
  for i in [1..NrRows(mat)] do
  mat[i,column] := scalar * mat[i,column];
  od;
- 
+
  end );
 
 ############################################################################
 
 InstallMethod( AddMatrixRowsLeft, "for a mutable matrix object, two row numbers, and a scalar",
- [ IsMatrixObj and IsMutable, IsInt, IsInt, IsObject ] ,
+ [ IsMatrixOrMatrixObj and IsMutable, IsInt, IsInt, IsObject ] ,
  function( mat, row1, row2, scalar )
  local i;
 
@@ -1551,24 +1569,42 @@ InstallMethod( AddMatrixRowsLeft, "for a mutable matrix object, two row numbers,
  od;
 
  end );
-
+
+InstallEarlyMethod( AddMatrixRowsLeft,
+ function( mat, i, j, scalar )
+ if IsPlistRep(mat) then
+ mat[i] := mat[i] + scalar * mat[j];
+ else
+ TryNextMethod();
+ fi;
+ end );
+
  ############################################################################
 
 InstallMethod( AddMatrixRowsRight, "for a mutable matrix object, two row numbers, and a scalar",
- [ IsMatrixObj and IsMutable, IsInt, IsInt, IsObject ] ,
+ [ IsMatrixOrMatrixObj and IsMutable, IsInt, IsInt, IsObject ] ,
  function( mat, row1, row2, scalar )
  local i;
- 
+
  for i in [1..NrCols(mat)] do
  mat[row1,i] := mat[row1,i] + mat[row2,i] * scalar;
  od;
 
  end );
 
+InstallEarlyMethod( AddMatrixRowsRight,
+ function( mat, i, j, scalar )
+ if IsPlistRep(mat) then
+ mat[i] := mat[i] + mat[j] * scalar;
+ else
+ TryNextMethod();
+ fi;
+ end );
+
 ############################################################################
 
 InstallMethod( AddMatrixColumnsRight, "for a mutable matrix object, two column numbers, and a scalar",
- [ IsMatrixObj and IsMutable, IsInt, IsInt, IsObject ] ,
+ [ IsMatrixOrMatrixObj and IsMutable, IsInt, IsInt, IsObject ] ,
  function( mat, column1, column2, scalar )
  local i;
 
@@ -1578,49 +1614,99 @@ InstallMethod( AddMatrixColumnsRight, "for a mutable matrix object, two column n
 
  end );
 
+InstallEarlyMethod( AddMatrixColumnsRight,
+ function( mat, i, j, scalar )
+ local row;
+ if IsPlistRep(mat) then
+ for row in mat do
+ row[i] := row[i] + row[j] * scalar;
+ od;
+ else
+ TryNextMethod();
+ fi;
+ end );
+
 ############################################################################
 
 InstallMethod( AddMatrixColumnsLeft, "for a mutable matrix object, two column numbers, and a scalar",
- [ IsMatrixObj and IsMutable, IsInt, IsInt, IsObject ] ,
+ [ IsMatrixOrMatrixObj and IsMutable, IsInt, IsInt, IsObject ] ,
  function( mat, column1, column2, scalar )
  local i;
 
  for i in [1..NrRows(mat)] do
- mat[i,column1] := mat[i,column1] + scalar * mat[i,column2] ;
+ mat[i,column1] := mat[i,column1] + scalar * mat[i,column2];
  od;
 
  end );
 
-############################################################################ 
+InstallEarlyMethod( AddMatrixColumnsLeft,
+ function( mat, i, j, scalar )
+ local row;
+ if IsPlistRep(mat) then
+ for row in mat do
+ row[i] := row[i] + scalar * row[j];
+ od;
+ else
+ TryNextMethod();
+ fi;
+ end );
+
+############################################################################
 
 InstallMethod( SwapMatrixRows, "for a mutable matrix object, and two row numbers",
- [ IsMatrixObj and IsMutable, IsInt, IsInt ],
+ [ IsMatrixOrMatrixObj and IsMutable, IsInt, IsInt ],
  function( mat, row1, row2 )
  local temp, i;
- 
+
  if row1 <> row2 then
  for i in [1..NrCols(mat)] do
  temp := mat[row1,i];
  mat[row1,i] := mat[row2,i];
  mat[row2,i] := temp;
- od; 
+ od;
  fi;
 
  end );
 
+InstallEarlyMethod( SwapMatrixRows,
+ function( mat, i, j )
+ local tmp;
+ if IsPlistRep(mat) then
+ tmp := mat[i];
+ mat[i] := mat[j];
+ mat[j] := tmp;
+ else
+ TryNextMethod();
+ fi;
+ end );
+
 ############################################################################
 
 InstallMethod( SwapMatrixColumns, "for a mutable matrix object, and two column numbers",
- [ IsMatrixObj and IsMutable, IsInt, IsInt ],
+ [ IsMatrixOrMatrixObj and IsMutable, IsInt, IsInt ],
  function( mat, column1, column2 )
  local temp, i;
- 
+
  if column1 <> column2 then
  for i in [1..NrRows(mat)] do
  temp := mat[i,column1];
  mat[i,column1] := mat[i,column2];
  mat[i,column2] := temp;
- od; 
+ od;
+ fi;
+
+ end );
+
+InstallEarlyMethod( SwapMatrixColumns,
+ function( mat, i, j )
+ local row, tmp;
+ if IsPlistRep(mat) then
+ for row in mat do
+ tmp := row[i];
+ row[i] := row[j];
+ row[j] := tmp;
+ od;
+ else
+ TryNextMethod();
  fi;
-
  end );

lib/matobj2.gd

@@ -1847,7 +1847,7 @@ DeclareOperation( "[]:=", [ IsMatrixOrMatrixObj, IsPosInt, IsPosInt, IsObject ]
 ## </ManSection>
 ## <#/GAPDoc>
 ##
-DeclareOperation( "MultMatrixRowLeft", [ IsMatrixObj and IsMutable, IsInt, IsObject ] );
+DeclareOperation( "MultMatrixRowLeft", [ IsMatrixOrMatrixObj and IsMutable, IsInt, IsObject ] );
 DeclareSynonym( "MultMatrixRow", MultMatrixRowLeft);
 
 ############################################################################
@@ -1866,7 +1866,7 @@ DeclareSynonym( "MultMatrixRow", MultMatrixRowLeft);
 ## </ManSection>
 ## <#/GAPDoc>
 ##
-DeclareOperation( "MultMatrixRowRight", [ IsMatrixObj and IsMutable, IsInt, IsObject ]);
+DeclareOperation( "MultMatrixRowRight", [ IsMatrixOrMatrixObj and IsMutable, IsInt, IsObject ]);
 
 ############################################################################
 ##
@@ -1889,7 +1889,7 @@ DeclareOperation( "MultMatrixRowRight", [ IsMatrixObj and IsMutable, IsInt, IsOb
 ## </ManSection>
 ## <#/GAPDoc>
 ##
-DeclareOperation( "MultMatrixColumnRight", [ IsMatrixObj and IsMutable, IsInt, IsObject ] );
+DeclareOperation( "MultMatrixColumnRight", [ IsMatrixOrMatrixObj and IsMutable, IsInt, IsObject ] );
 DeclareSynonym( "MultMatrixColumn", MultMatrixColumnRight);
 
 ############################################################################
@@ -1908,7 +1908,7 @@ DeclareSynonym( "MultMatrixColumn", MultMatrixColumnRight);
 ## </ManSection>
 ## <#/GAPDoc>
 ##
-DeclareOperation( "MultMatrixColumnLeft", [ IsMatrixObj and IsMutable, IsInt, IsObject ] );
+DeclareOperation( "MultMatrixColumnLeft", [ IsMatrixOrMatrixObj and IsMutable, IsInt, IsObject ] );
 
 ############################################################################
 ##
@@ -1931,7 +1931,7 @@ DeclareOperation( "MultMatrixColumnLeft", [ IsMatrixObj and IsMutable, IsInt, Is
 ## </ManSection>
 ## <#/GAPDoc>
 ##
-DeclareOperation( "AddMatrixRowsLeft", [ IsMatrixObj and IsMutable, IsInt, IsInt, IsObject ] );
+DeclareOperation( "AddMatrixRowsLeft", [ IsMatrixOrMatrixObj and IsMutable, IsInt, IsInt, IsObject ] );
 DeclareSynonym( "AddMatrixRows", AddMatrixRowsLeft);
 
 ############################################################################
@@ -1950,7 +1950,7 @@ DeclareSynonym( "AddMatrixRows", AddMatrixRowsLeft);
 ## </ManSection>
 ## <#/GAPDoc>
 ##
-DeclareOperation( "AddMatrixRowsRight", [ IsMatrixObj and IsMutable, IsInt, IsInt, IsObject ] );
+DeclareOperation( "AddMatrixRowsRight", [ IsMatrixOrMatrixObj and IsMutable, IsInt, IsInt, IsObject ] );
 
 ############################################################################
 ##
@@ -1973,7 +1973,7 @@ DeclareOperation( "AddMatrixRowsRight", [ IsMatrixObj and IsMutable, IsInt, IsIn
 ## </ManSection>
 ## <#/GAPDoc>
 ##
-DeclareOperation( "AddMatrixColumnsRight", [ IsMatrixObj and IsMutable, IsInt, IsInt, IsObject ] );
+DeclareOperation( "AddMatrixColumnsRight", [ IsMatrixOrMatrixObj and IsMutable, IsInt, IsInt, IsObject ] );
 DeclareSynonym( "AddMatrixColumns", AddMatrixColumnsRight);
 
 ############################################################################
@@ -1992,7 +1992,7 @@ DeclareSynonym( "AddMatrixColumns", AddMatrixColumnsRight);
 ## </ManSection>
 ## <#/GAPDoc>
 ##
-DeclareOperation( "AddMatrixColumnsLeft", [ IsMatrixObj and IsMutable, IsInt, IsInt, IsObject ] );
+DeclareOperation( "AddMatrixColumnsLeft", [ IsMatrixOrMatrixObj and IsMutable, IsInt, IsInt, IsObject ] );
 
 ############################################################################
 ##
@@ -2009,7 +2009,7 @@ DeclareOperation( "AddMatrixColumnsLeft", [ IsMatrixObj and IsMutable, IsInt, Is
 ## </ManSection>
 ## <#/GAPDoc>
 ##
-DeclareOperation( "SwapMatrixRows", [ IsMatrixObj and IsMutable, IsInt, IsInt ] );
+DeclareOperation( "SwapMatrixRows", [ IsMatrixOrMatrixObj and IsMutable, IsInt, IsInt ] );
 
 ############################################################################
 ##
@@ -2026,4 +2026,4 @@ DeclareOperation( "SwapMatrixRows", [ IsMatrixObj and IsMutable, IsInt, IsInt ]
 ## </ManSection>
 ## <#/GAPDoc>
 ##
-DeclareOperation( "SwapMatrixColumns", [ IsMatrixObj and IsMutable, IsInt, IsInt ] );
+DeclareOperation( "SwapMatrixColumns", [ IsMatrixOrMatrixObj and IsMutable, IsInt, IsInt ] );

tst/testinstall/MatrixObj/ElementaryMatrices.tst

@@ -1,5 +1,41 @@
 gap> START_TEST("ElementaryMatrices.tst");
 
+#
+gap> ReadGapRoot("tst/testinstall/MatrixObj/testmatobj.g");
+
+#
+gap> TestElementaryTransforms( [[2,4,5],[7,11,-4],[-3,20,0]], -1 );
+gap> TestElementaryTransforms( Matrix( [[2,4,5],[7,11,-4],[-3,20,0]]), -1 );
+
+#
+gap> F := GF(2);;
+gap> mat := RandomInvertibleMat(4, F);; # list of compressed vectors
+gap> TestElementaryTransforms( mat, PrimitiveRoot(F) );
+gap> ConvertToMatrixRep(mat);; # proper matrix obj
+gap> TestElementaryTransforms( mat, PrimitiveRoot(F) );
+
+#
+gap> F := GF(3);;
+gap> mat := RandomInvertibleMat(4, F);; # list of compressed vectors
+gap> TestElementaryTransforms( mat, PrimitiveRoot(F) );
+gap> ConvertToMatrixRep(mat);; # proper matrix obj
+gap> TestElementaryTransforms( mat, PrimitiveRoot(F) );
+
+#
+gap> F := GF(4);;
+gap> mat := RandomInvertibleMat(4, F);; # list of compressed vectors
+gap> TestElementaryTransforms( mat, PrimitiveRoot(F) );
+gap> ConvertToMatrixRep(mat);; # proper matrix obj
+gap> TestElementaryTransforms( mat, PrimitiveRoot(F) );
+
+#
+gap> F := GF(5);;
+gap> mat := RandomInvertibleMat(4, F);; # list of compressed vectors
+gap> TestElementaryTransforms( mat, PrimitiveRoot(F) );
+gap> ConvertToMatrixRep(mat);; # proper matrix obj
+gap> TestElementaryTransforms( mat, PrimitiveRoot(F) );
+
+##########
 #
 gap> mat := Matrix( [[2,4,5],[7,11,-4],[-3,20,0]]);;
 gap> SwapMatrixRows(mat,1,3);