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Symbolic computing is an entirely different paradigm in computing compared to the numerical array-based computing introduced in the previous chapter. In symbolic computing software, also known as computer algebra systems (CASs), representations of mathematical objects and expressions are manipulated and transformed analytically. Symbolic computing is mainly about using computers to automate analytical computations that can in principle be done by hand with pen and paper. However, by automating the bookkeeping and the manipulations of mathematical expressions using a computer algebra system, it is possible to take analytical computing much further than can realistically be done by hand. Symbolic computing is a great tool for checking and debugging analytical calculations that are done by hand, but more importantly it enables carrying out analytical analysis that may not otherwise be possible.
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Here it is important to keep in mind the distinction between a Python function, or callable Python object such as sympy.Function, and the symbolic function that a sympy.Function class instance represents.
See also the ufuncity from the sympy.utilities.autowrap module and the theano_function from the sympy.printing.theanocode module. These provide similar functionality as sympy.lambdify, but using different computational back ends.
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- Chapter 3