SymPy is a Python library for symbolic mathematical computations. It has a broad range of features, ranging from calculus, algebra, geometry, discrete mathematics, and even quantum physics. It also includes basic plotting functionality and print functions with LaTeX support.
SciPy is a considered to be one of the core packages for scientific computing routines. As a useful expansion of the NumPy core functionality, it contains a broad range of functions for linear algebra, interpolation, integration, clustering, and many more.
NumPy is probably the most fundamental package for efficient scientific computing in Python through linear algebra routines. One of NumPy's major strength is that most operations are implemented as C/C++ and FORTRAN code for efficiency. At its core, NumPy works with multi-dimensional array objects that support broadcasting and lead to efficient, vectorized code.
Theano is an optimizing GPU-meta-programming code generating array oriented optimizing math compiler in Python