Fix a bug related to elementary matrices, fix the test and add

some additional tests for elementary matrices.

Author: pstaabp

lib/Value/Matrix.pm

@@ -1102,15 +1102,16 @@ Usage:
 generates the matrix:
 
     [ [ 1, 0, 0, 0 ],
-      [ 0, 1, 0, 0 ],
-      [ 0, -3, 1, 0 ],
+      [ 0, 1, -3, 0 ],
+      [ 0, 0, 1, 0 ],
       [ 0, 0, 0, 1 ] ]
 
-or if the matrix C<$A> exists then
+or if the matrix C<$A> exists of size m by n then
 
     $A->E([3, 4], -5);
 
-will generate the elementary matrix of size number of rows of C<$A>, which multiplies row 3 by -5 and adds to row 4.
+will generate the m by m elementary matrix which multiplies row 3 by -5 and adds to row 4. 
+If $A does not have at least 4 rows, an error is raised.
 
 =back
 
@@ -1147,7 +1148,7 @@ sub E {
 		if (@ij == 1) {
 			$row[$i] = $k if ($i == $ij[0]);
 		} elsif (defined $k) {
-			$row[ $ij[1] ] = $k if ($i == $ij[0]);
+			$row[ $ij[0] ] = $k if ($i == $ij[1]);
 		} else {
 			($row[ $ij[0] ], $row[ $ij[1] ]) = ($row[ $ij[1] ], $row[ $ij[0] ]) if ($i == $ij[0] || $i == $ij[1]);
 		}

t/math_objects/matrix.t

@@ -357,8 +357,21 @@ subtest 'Construct an elementary matrix' => sub {
 		'Elementary Matrix with row multiple';
 
 	my $E3 = Value::Matrix->E(4, [ 3, 2 ], -3);
-	is $E3->TeX, Matrix([ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, -3, 1, 0 ], [ 0, 0, 0, 1 ] ])->TeX,
+	is $E3->TeX, Matrix([ [ 1, 0, 0, 0 ], [ 0, 1, -3, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ])->TeX,
 		'Elementary Matrix with row multiple and add';
+
+	my $A = Matrix([ [ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ], [ 9, 10, 11, 12 ], [ 13, 14, 15, 16 ] ]);
+	is $A->E([ 1, 4 ])->TeX,
+		Matrix([ [ 0, 0, 0, 1 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 1, 0, 0, 0 ] ])->TeX,
+		'Elementary Matrix from syntax $A->E an existing matrix with a row swap';
+
+	is $A->E([2], 5)->TeX,
+		Matrix([ [ 1, 0, 0, 0 ], [ 0, 5, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ])->TeX,
+		'Elementary Matrix from syntax $A->E an existing matrix with a row multiple';
+
+	is $A->E([ 2, 4 ], -4)->TeX,
+		Matrix([ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, -4, 0, 1 ] ])->TeX,
+		'Elementary Matrix from syntax $A->E an existing matrix with a row multiple and add';
 };
 
 subtest 'Extract a slice from a Matrix' => sub {