Merge pull request sympy#2637 from Tempel/matrix_is_zero

MatrixBase.is_zero supporting None results.

sympy/matrices/immutable.py

@@ -90,6 +90,9 @@ def __setitem__(self, *args):
     __neg__ = MatrixBase.__neg__
     __div__ = MatrixBase.__div__
     __truediv__ = MatrixBase.__truediv__
+# This is included after the class definition as a workaround for issue 4114.
+# See http://code.google.com/p/sympy/issues/detail?id=4114
+ImmutableMatrix.is_zero = DenseMatrix.is_zero
 
 
 class ImmutableSparseMatrix(Basic, SparseMatrix):

sympy/matrices/matrices.py

@@ -1962,16 +1962,19 @@ def is_zero(self):
 
         A matrix is zero if every element is zero.  A matrix need not be square
         to be considered zero.  The empty matrix is zero by the principle of
-        vacuous truth.
+        vacuous truth.  For a matrix that may or may not be zero (e.g.
+        contains a symbol), this will be None
 
         Examples
         ========
 
         >>> from sympy import Matrix, zeros
+        >>> from sympy.abc import x
         >>> a = Matrix([[0, 0], [0, 0]])
         >>> b = zeros(3, 4)
         >>> c = Matrix([[0, 1], [0, 0]])
         >>> d = Matrix([])
+        >>> e = Matrix([[x, 0], [0, 0]])
         >>> a.is_zero
         True
         >>> b.is_zero
@@ -1980,8 +1983,13 @@ def is_zero(self):
         False
         >>> d.is_zero
         True
+        >>> e.is_zero
         """
-        return not list(self.values())
+        if any(i.is_zero == False for i in self):
+            return False
+        if any(i.is_zero == None for i in self):
+            return None
+        return True
 
     def is_nilpotent(self):
         """Checks if a matrix is nilpotent.

sympy/matrices/tests/test_matrices.py

@@ -1980,6 +1980,13 @@ def test_is_zero():
     assert Matrix([[0, 0], [0, 0]]).is_zero
     assert zeros(3, 4).is_zero
     assert not eye(3).is_zero
+    assert Matrix([[x, 0], [0, 0]]).is_zero == None
+    assert SparseMatrix([[x, 0], [0, 0]]).is_zero == None
+    assert ImmutableMatrix([[x, 0], [0, 0]]).is_zero == None
+    assert ImmutableSparseMatrix([[x, 0], [0, 0]]).is_zero == None
+    assert Matrix([[x, 1], [0, 0]]).is_zero == False
+    a = Symbol('a', nonzero=True)
+    assert Matrix([[a, 0], [0, 0]]).is_zero == False
 
 
 def test_rotation_matrices():