Fix IsUpperTriangularMat for non-square matrices; add tests

lib/matrix.gi

@@ -189,8 +189,8 @@ InstallMethod( IsUpperTriangularMat,
     function( mat )
     local  i, j, z;
     z:=ZeroOfBaseDomain(mat);
-    for i  in [ 1 .. NrRows( mat ) ]  do
-        for j  in [ 1 .. i-1]  do
+    for j  in [ 1 .. NrCols( mat ) ]  do
+        for i  in [ j+1 .. NrRows( mat ) ]  do
             if mat[i,j] <> z  then
                 return false;
             fi;

tst/testinstall/matrix.tst

@@ -0,0 +1,47 @@
+#
+gap> IsDiagonalMat(NullMat(3, 3));
+true
+gap> IsDiagonalMat(NullMat(1, 3));
+true
+gap> IsDiagonalMat(NullMat(3, 1));
+true
+gap> IsDiagonalMat(IdentityMat(3));
+true
+gap> IsDiagonalMat([[1,1],[1,1]]);
+false
+gap> IsDiagonalMat([[1,0],[1,1]]);
+false
+gap> IsDiagonalMat([[1,1],[0,1]]);
+false
+
+#
+gap> IsUpperTriangularMat(NullMat(3, 3));
+true
+gap> IsUpperTriangularMat(NullMat(1, 3));
+true
+gap> IsUpperTriangularMat(NullMat(3, 1));
+true
+gap> IsUpperTriangularMat(IdentityMat(3));
+true
+gap> IsUpperTriangularMat([[1,1],[1,1]]);
+false
+gap> IsUpperTriangularMat([[1,0],[1,1]]);
+false
+gap> IsUpperTriangularMat([[1,1],[0,1]]);
+true
+
+#
+gap> IsLowerTriangularMat(NullMat(3, 3));
+true
+gap> IsLowerTriangularMat(NullMat(1, 3));
+true
+gap> IsLowerTriangularMat(NullMat(3, 1));
+true
+gap> IsLowerTriangularMat(IdentityMat(3));
+true
+gap> IsLowerTriangularMat([[1,1],[1,1]]);
+false
+gap> IsLowerTriangularMat([[1,0],[1,1]]);
+true
+gap> IsLowerTriangularMat([[1,1],[0,1]]);
+false