Evaluate sympy expression from an array of values

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First of all, at the moment SymPy does not guarantee support for numpy arrays which is what you want in this case. Check this bug report http://code.google.com/p/sympy/issues/detail?id=537

Second, If you want to evaluate something numerically for many values SymPy is not the best choice (it is a symbolic library after all). Use numpy and scipy.

However, a valid reason to evaluate something numerically will be that deriving the expression to be evaluated was hard so you derive it in SymPy and then evaluate it in NumPy/SciPy/C/Fortran. To translate an expression to numpy just use

from sympy.utilities.lambdify import lambdify
func = lambdify(x, big_expression_containing_x,'numpy') # returns a numpy-ready function
numpy_array_of_results = func(numpy_array_of_arguments)

Check the docstring of lambdify for more details. Be aware that lambdify still has some issues and may need a rewrite.

And just as a side note, if you want to evaluate the expressions really many times, you can use the codegen/autowrap module from sympy in order to create fortran or C code that is wrapped and callable from python.

EDIT: An updates list of ways to do numerics in SymPy can be found on the wiki https://github.com/sympy/sympy/wiki/Philosophy-of-Numerics-and-Code-Generation-in-SymPy

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