Sage is a free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages: NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more.
Access their combined power through a common, Python-based language or directly via interfaces or wrappers. → Tour, Tutorial, Documentation
Mission: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab.
SageMathCloud™ is still in Beta Test.
Work with Sage, or run Python, R, GAP, M2 and more in the Cloud.

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other: Sagenb, KAIST, SageCell

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Random Link: SageTeX - embedding Sage code inside LaTeX documents.