SymPy

SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible. SymPy is written entirely in Python.

[SymPy]

Jupyter

Open source, interactive data science and scientific computing across over 40 programming languages.
Project Jupyter was born out of the IPython Project in 2014 as it evolved to support interactive data science and scientific computing across all programming languages.

[Jupyter]

IPython

IPython provides a rich architecture for interactive computing with:
-A powerful interactive shell.
-A kernel for Jupyter.
-Support for interactive data visualization and use of GUI toolkits.
-Flexible, embeddable interpreters to load into your own projects.
-Easy to use, high performance tools for parallel computing.
IPython clients
To get started with IPython in the Jupyter Notebook, see our official example collection. Our notebook gallery is an excellent way to see the many things you can do with IPython while learning about a variety of topics, from basic programming to advanced statistics or quantum mechanics.
To learn more about IPython, you can watch our videos and screencasts, download our talks and presentations, or read our extensive documentation. IPython is open source (BSD license), and is used by a range of other projects; add your project to that list if it uses IPython as a library, and please don’t forget to cite the project.
IPython supports Python 2.7 and 3.3 or newer. Our older 1.x series supports Python 2.6 and 3.2.

[IPython]

Matplotlib

matplotlib is a python 2D plotting library which produces publication quality figures in a variety of hardcopy formats and interactive environments across platforms. matplotlib can be used in python scripts, the python and ipython shell (ala MATLAB®* or Mathematica®†), web application servers, and six graphical user interface toolkits.
matplotlib tries to make easy things easy and hard things possible. You can generate plots, histograms, power spectra, bar charts, errorcharts, scatterplots, etc, with just a few lines of code. For a sampling, see the screenshots, thumbnail gallery, and examples directory
For simple plotting the pyplot interface provides a MATLAB-like interface, particularly when combined with IPython. For the power user, you have full control of line styles, font properties, axes properties, etc, via an object oriented interface or via a set of functions familiar to MATLAB users.

[Matplotlib]

SciPy

SciPy
SciPy (pronounced “Sigh Pie”) is a Python-based ecosystem of open-source software for mathematics, science, and engineering. In particular, these are some of the core packages:
NumPy. Base N-dimensional array package
SciPy library. Fundamental library for scientific computing
Matplotlib. Comprehensive 2D Plotting
IPython. Enhanced Interactive Console
Sympy. Symbolic mathematics
Pandas. Data structures & analysis

[SciPy]