From 95b2d3554af942e2a31a552844932cc7f3aa74cc Mon Sep 17 00:00:00 2001
From: Matt Wala <wala1@illinois.edu>
Date: Thu, 23 Feb 2017 18:34:07 -0600
Subject: [PATCH] Fix LineTaylorLocalExpansion to work with SymEngine (still
 needed: tests in sumpy, but that's a long-standing bug: see #2).

---
 sumpy/expansion/local.py | 25 ++++++++++++--------
 sumpy/tools.py           | 49 ++++++++++++++++++++++++++++++++++++++++
 2 files changed, 64 insertions(+), 10 deletions(-)

diff --git a/sumpy/expansion/local.py b/sumpy/expansion/local.py
index bdcd9043..f9ec106a 100644
--- a/sumpy/expansion/local.py
+++ b/sumpy/expansion/local.py
@@ -61,24 +61,29 @@ class LineTaylorLocalExpansion(LocalExpansionBase):
             raise RuntimeError("cannot use line-Taylor expansions in a setting "
                     "where the center-target vector is not known at coefficient "
                     "formation")
-        avec_line = avec + sym.Symbol("tau")*bvec
+
+        tau = sym.Symbol("tau")
+
+        avec_line = avec + tau*bvec
 
         line_kernel = self.kernel.get_expression(avec_line)
 
-        return [
-                self.kernel.postprocess_at_target(
-                    self.kernel.postprocess_at_source(
-                        line_kernel.diff("tau", i),
-                        avec),
-                    bvec)
-                .subs("tau", 0)
+        from sumpy.tools import MiDerivativeTaker, my_syntactic_subs
+        deriv_taker = MiDerivativeTaker(line_kernel, (tau,))
+
+        return [my_syntactic_subs(
+                    self.kernel.postprocess_at_target(
+                        self.kernel.postprocess_at_source(
+                            deriv_taker.diff(i),
+                            avec), bvec),
+                    {tau: 0})
                 for i in self.get_coefficient_identifiers()]
 
     def evaluate(self, coeffs, bvec):
         from pytools import factorial
-        return sum(
+        return sym.Add(*(
                 coeffs[self.get_storage_index(i)] / factorial(i)
-                for i in self.get_coefficient_identifiers())
+                for i in self.get_coefficient_identifiers()))
 
 # }}}
 
diff --git a/sumpy/tools.py b/sumpy/tools.py
index 51cc52be..af125566 100644
--- a/sumpy/tools.py
+++ b/sumpy/tools.py
@@ -385,4 +385,53 @@ class KernelCacheWrapper(object):
 
         return knl
 
+
+def my_syntactic_subs(expr, subst_dict):
+    # Workaround for differing substitution semantics between sympy and symengine.
+    # FIXME: This is a hack.
+    from sumpy.symbolic import Basic, Subs, Derivative, USE_SYMENGINE
+
+    if not isinstance(expr, Basic):
+        return expr
+
+    elif expr.is_Symbol:
+        return subst_dict.get(expr, expr)
+
+    elif isinstance(expr, Subs):
+        new_point = tuple(my_syntactic_subs(p, subst_dict) for p in expr.point)
+
+        import six
+        new_subst_dict = dict(
+            (var, subs) for var, subs in six.iteritems(subst_dict)
+            if var not in expr.variables)
+
+        new_expr = my_syntactic_subs(expr.expr, new_subst_dict)
+
+        if new_point != expr.point or new_expr != expr.expr:
+            return Subs(new_expr, expr.variables, new_point)
+
+        return expr
+
+    elif isinstance(expr, Derivative):
+        new_expr = my_syntactic_subs(expr.expr, subst_dict)
+        new_variables = my_syntactic_subs(expr.variables, subst_dict)
+
+        if new_expr != expr.expr or any(new_var != var for new_var, var in
+                                          zip(new_variables, expr.variables)):
+            # FIXME in SymEngine
+            if USE_SYMENGINE:
+                return Derivative(new_expr, new_variables)
+            else:
+                return Derivative(new_expr, *new_variables)
+
+        return expr
+
+    else:
+        new_args = tuple(my_syntactic_subs(arg, subst_dict) for arg in expr.args)
+        if any(new_arg != arg for arg, new_arg in zip(expr.args, new_args)):
+            return expr.func(*new_args)
+        else:
+            return expr
+
+
 # vim: fdm=marker
-- 
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