free and open-source Python module for scientific computation; cousin of NumPy

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SciPy, NumPy, matplotlib, and other related Python modules are often packaged together as a stack of quantitative tools. They have evolved under the free and open-source software model. It's not surprising that there is some naming inconsistency and redundancy within the stack (e.g., NumPy's histogram() and matplotlib's hist() are more or less the same.) Their openness also means that, if you think a method is producing incorrect results, you can examine/tweak its source code. (Or even become involved in the project's development!)

The SciPy module in particular offers a wide variety of routines for tasks such as optimization and the numerical solution of differential equations. The basic steps in a numerical integration routine like fourth order Runge–Kutta are straightforward. However, reliable application of such methods is complicated by issues including convergence, stability, and adaptive stepsize. Libraries like SciPy (or the GSL in C/C++) allow researchers use such methods without knowing the implementation details.