Check equality of Cross arguments after simplifications

sympde/calculus/core.py

@@ -428,6 +428,14 @@ def __new__(cls, arg1, arg2, **options):
             a,b = b,a
             c   = -c
 
+        # after simplifications, the expression can be reduced to 0 in some cases
+        # here's an example;
+        # if b is a Vector and u and v are scalar functions,
+        # we should have the following
+        # cross(b*u,b*v) = u*v*cross(b,b) = 0
+        if a == b:
+            return S.Zero
+
         obj = Basic.__new__(cls, a, b)
 
         return c*obj

sympde/expr/tests/test_expr.py

@@ -1937,6 +1937,12 @@ def test_matrices_vectors():
     assert not A1 == A
     # ...
 
+    # ... some tests on cross operator & vectors
+    assert cross(b,b)     == 0
+    assert cross(b*u,b*u) == 0
+    assert cross(b*u,b*v) == 0
+    # ...
+
     ########################################################################
     #                    SCALAR-FUNCTION CASE
     ########################################################################
@@ -2021,12 +2027,12 @@ def test_matrices_vectors():
     assert is_linear_expression(f(u,v), (v,))
     # ...
 
-#    # ...
-#    f = lambda u,v: cross(b*u, b*v)
-#
-#    assert is_linear_expression(f(u,v), (u,))
-#    assert is_linear_expression(f(u,v), (v,))
-#    # ...
+    # ...
+    f = lambda u,v: cross(b*u, b*v)
+
+    assert is_linear_expression(f(u,v), (u,))
+    assert is_linear_expression(f(u,v), (v,))
+    # ...
 
     # ...
     f = lambda u,v: cross(b*u, grad(v))