Remove SymPy dependency

[Prof Garth Wells]

Using SymPy in FIAT is like using a sledgehammer to crack a peanut.

It's a heavy dependency that imports a lot of files, which can slow import.

Also, the SymPy Debian/Ubuntu packages pull in a lot of very large package dependencies, e.g. texlive. This blows out the size of virtual images and Linux containers.

[Johannes Ring]

It is possible to avoid installing texlive together with SymPy by running apt-get with --no-install-recommends.

[Lawrence Mitchell]

One option may be to use pymbolic (http://mathema.tician.de/software/pymbolic/) which is quite lightweight. The following patch to expansions.py appears to DTRT:

diff --git a/FIAT/expansions.py b/FIAT/expansions.py
index cd22748..ddb3110 100644
--- a/FIAT/expansions.py
+++ b/FIAT/expansions.py
@@ -21,14 +21,19 @@ to allow users to get coordinates that they want."""

 import numpy
 import math
-import sympy
+import pymbolic
 from . import reference_element
 from . import jacobi


-def _tabulate_dpts(tabulator, D, n, order, pts):
-    X = sympy.DeferredVector('x')
+class Differentiator(pymbolic.mapper.differentiator.DifferentiationMapper):
+
+    # Derivative of list is just list of derivative of entries
+    def map_list(self, expr):
+        return [self.rec(x) for x in expr]
+

+def _tabulate_dpts(tabulator, D, n, order, pts):
     def form_derivative(F):
         '''Forms the derivative recursively, i.e.,
         F               -> [F_x, F_y, F_z],
@@ -37,45 +42,10 @@ def _tabulate_dpts(tabulator, D, n, order, pts):
                             [F_zx, F_zy, F_zz]]
         and so forth.
         '''
-        out = []
-        try:
-            out = [sympy.diff(F, X[j]) for j in range(D)]
-        except AttributeError:
-            # Intercept errors like
-            #  AttributeError: 'list' object has no attribute
-            #  'free_symbols'
-            for f in F:
-                out.append(form_derivative(f))
-        return out
-
-    def numpy_lambdify(X, F):
-        '''Unfortunately, SymPy's own lambdify() doesn't work well with
-        NumPy in that simple functions like
-            lambda x: 1.0,
-        when evaluated with NumPy arrays, return just "1.0" instead of
-        an array of 1s with the same shape as x. This function does that.
-        '''
-        try:
-            lambda_x = [numpy_lambdify(X, f) for f in F]
-        except TypeError:  # 'function' object is not iterable
-            # SymPy's lambdify also works on functions that return arrays.
-            # However, use it componentwise here so we can add 0*x to each
-            # component individually. This is necessary to maintain shapes
-            # if evaluated with NumPy arrays.
-            lmbd_tmp = sympy.lambdify(X, F)
-            lambda_x = lambda x: lmbd_tmp(x) + 0*x[0]
-        return lambda_x
-
-    def evaluate_lambda(lmbd, x):
-        '''Properly evaluate lambda expressions recursively for iterables.
-        '''
-        try:
-            values = [evaluate_lambda(l, x) for l in lmbd]
-        except TypeError:  # 'function' object is not iterable
-            values = lmbd(x)
-        return values
+        return [Differentiator(X[j])(F) for j in range(D)]

     # Tabulate symbolically
+    X = pymbolic.primitives.Variable('x')
     symbolic_tab = tabulator(n, X)
     # Make sure that the entries of symbolic_tab are lists so we can
     # append derivatives
@@ -86,10 +56,8 @@ def _tabulate_dpts(tabulator, D, n, order, pts):
         shape = [len(symbolic_tab), len(pts)] + r * [D]
         data[r] = numpy.empty(shape)
         for i, phi in enumerate(symbolic_tab):
-            # Evaluate the function numerically using lambda expressions
-            deriv_lambda = numpy_lambdify(X, phi[r])
-            data[r][i] = \
-                numpy.array(evaluate_lambda(deriv_lambda, pts.T)).T
+            # Evalute numerically, binding 'x' to the required points
+            data[r][i] = numpy.array(pymbolic.evaluate(phi[r], {'x': pts.T})).T
             # Symbolically compute the next derivative.
             # This actually happens once too many here; never mind for
             # now.

[Prof Garth Wells]

Is pymbolic available as a Debian/Ubuntu package, and does it work with Python 3?

[Lawrence Mitchell]

It does, I believe, work with python 3 (at least setup.py claims so). It does not appear to be an ubuntu package in 14.04.

[Martin Sandve Alnæs]

Maybe we can use ufl with some minor extensions.