#858 fix simplify bug, fix expression tree notebook

examples/notebooks/expression_tree/expression-tree.ipynb

@@ -64,7 +64,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We can also calculate the expression tree representing the gradient of the equation with respect to $t$ (which is of course simply the scalar value 1),"
+    "We can also calculate the expression tree representing the gradient of the equation with respect to $t$,"
    ]
   },
   {
@@ -84,7 +84,7 @@
     "![](expression_tree2.png)\n",
     "\n",
     "\n",
-    "...and evaluate this expression, which will again give 1."
+    "...and evaluate this expression,"
    ]
   },
   {
@@ -95,7 +95,7 @@
     {
      "data": {
       "text/plain": [
-       "1.0"
+       "array([[-11.]])"
       ]
      },
      "execution_count": 4,
@@ -104,7 +104,7 @@
     }
    ],
    "source": [
-    "diff_wrt_equation.evaluate(1, np.array([2]))"
+    "diff_wrt_equation.evaluate(t=1, y=np.array([2]), y_dot=np.array([2]))"
    ]
   },
   {
@@ -202,6 +202,13 @@
     "\n",
     "After the third stage, our expression tree is now able to be evaluated by one of the solver classes. Note that we have used a single equation above to illustrate the different types of expression trees in PyBaMM, but any given models will consist of many RHS or algebraic equations, along with boundary conditions. See [here](https://github.com/pybamm-team/PyBaMM/blob/master/examples/notebooks/add-model.ipynb) for more details of PyBaMM models."
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
@@ -220,7 +227,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.3"
+   "version": "3.6.7"
   }
  },
  "nbformat": 4,

pybamm/expression_tree/binary_operators.py

@@ -252,6 +252,10 @@ def _binary_simplify(self, left, right):
         if is_scalar_zero(right):
             return pybamm.Scalar(1)
 
+        # zero to the power of anything is zero
+        if is_scalar_zero(left):
+            return pybamm.Scalar(0)
+
         # anything to the power of one is itself
         if is_scalar_one(right):
             return left

pybamm/expression_tree/symbol.py

@@ -635,6 +635,8 @@ def evaluate_ignoring_errors(self, t=0):
             # (there is a e.g. StateVector in the tree)
             if error.args[0] == "StateVector cannot evaluate input 'y=None'":
                 return None
+            elif error.args[0] == "StateVectorDot cannot evaluate input 'y_dot=None'":
+                return None
             else:
                 raise error
         except ValueError as e:

tests/unit/test_expression_tree/test_operations/test_simplify.py

@@ -16,6 +16,7 @@ def test_symbol_simplify(self):
         d = pybamm.Scalar(-1)
         e = pybamm.Scalar(2)
         g = pybamm.Variable("g")
+        gdot = pybamm.VariableDot("g'")
 
         # negate
         self.assertIsInstance((-a).simplify(), pybamm.Scalar)
@@ -175,6 +176,18 @@ def myfunction(x, y):
         self.assertIsInstance(expr.children[1], pybamm.Negate)
         self.assertIsInstance(expr.children[1].children[0], pybamm.Parameter)
 
+        expr = (e * g * b).simplify()
+        self.assertIsInstance(expr, pybamm.Multiplication)
+        self.assertIsInstance(expr.children[0], pybamm.Scalar)
+        self.assertEqual(expr.children[0].evaluate(), 2.0)
+        self.assertIsInstance(expr.children[1], pybamm.Variable)
+
+        expr = (e * gdot * b).simplify()
+        self.assertIsInstance(expr, pybamm.Multiplication)
+        self.assertIsInstance(expr.children[0], pybamm.Scalar)
+        self.assertEqual(expr.children[0].evaluate(), 2.0)
+        self.assertIsInstance(expr.children[1], pybamm.VariableDot)
+
         expr = (e + (g - c)).simplify()
         self.assertIsInstance(expr, pybamm.Addition)
         self.assertIsInstance(expr.children[0], pybamm.Scalar)