By Ronan Lamy

Symbolic computation is using algorithms and software program to accomplish unique calculations on symbolic mathematical expressions. It has routinely been the safeguard of monolithic computing device algebra platforms. SymPy places its energy inside effortless achieve of all Python programmers, simply an import assertion away.

Instant SymPy Starter is an advent to the fascinating international of symbolic computation in Python. With hands-on examples and sensible recommendation, you are going to study every thing you want to combine SymPy into your workflow and to make the simplest use of its functionalities.

This booklet will consultant you in your trip with SymPy, from establishing your improvement atmosphere to integrating SymPy into your workflow, with many beneficial assistance. one can find the way to manage a strong setting for either symbolic and numerical computations inside of IPython workstation, and the best way to successfully hire symbolic computation on your numerical calculations. you could stick with the examples alongside by yourself procedure as all of the code comes in downloadable IPython notebooks. in case you have by no means used IPython prior to, you need to think of this because the ideal party to start.

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Example text

Floating point numbers are approximations. Symbolic calculations work best when all objects involved are known exactly. For this reason, you should avoid letting Float objects appear in your expressions. Instead, perform your calculations with Rational and other symbolic objects and convert only the final result to a numeric value. This is done with the N() function. It takes an optional second argument, 'n', specifying the number of digits of precision of the result. By default, the result has 15 digits of precision, which is roughly as much as can be encoded in a Python float.

Hence, if the variable is a real Symbol object, only real solutions are returned, but if it is complex, then all solutions in the complex plane are returned (subject to the aforementioned restriction on returning infinite solution sets). This difference is readily apparent when solving polynomials, as the following example demonstrates: >>> solve(x**2 + 1, x) [] >>> solve(z**2 + 1, z) [-I, I] 35 Instant SymPy Starter There is no restriction on the number of variables appearing in the expression.

The result can be returned in one of two forms, depending on the mathematical structure of the input: either as a list of tuples, where each tuple contains the values for the variables in the order given to solve, or a single dictionary, suitable for use in subs(), mapping variables to their values. As you can see in the following example, it can be hard to predict what form the result will take: >>> solve([exp(x**2) - y, y - 3], x, y) [(-sqrt(log(3)), 3), (sqrt(log(3)), 3)] >>> solve([x**2 - y, y - 3], x, y) [(-sqrt(3), 3), (sqrt(3), 3)] >>> solve([x - y, y - 3], x, y) {y: 3, x: 3} This variability in return types is fine for interactive use, but for library code, more predictability is required.

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