SageMath
opensource mathematics software system
Mathematicians, scientists, researchers, and students need a powerful tool for their work or study. SageMath is a freely available opensource mathematical software system bundling the functionality of many software libraries, exposing their features in a common interface and extending on top of this with its own powerful algorithms. By leveraging the flexibility and universality of the underlying Python interpreter, SageMath is able to accommodate for a vast range of their requirements.
The mission of SageMath is to create a viable opensource alternative to all major proprietary mathematical software systems.
Python is the main programming language inside the SageMath library and also the language of choice for all interactions with the builtin objects and functions for expressing mathematical concepts and calculations. Besides a commandline and programminglibrary interface, its primary user interface is a dynamic selfhosted website. From the perspective of a user, the interface language is Python, but with a thin extension built directly on top of it.
Almost all areas of mathematics are represented in SageMath, at various levels of sophistication. This includes symbolic calculus, 2D and 3D graphics, polynomials, graph theory, group theory, abstract algebra, combinatorics, cryptography, elliptic curves and modular forms, numerical mathematics, linear algebra and matrix calculations (over various rings), support for parallel computing, and a powerful coercion framework to “mix” elements from different sets for calculations. SageMath’s features also expand into neighboring fields like Statistics and Physics.
SageMath 2021 Projects

Thomas Hagelmayer
Add support for error terms with explicit constants to AsymptoticRingAn asymptotic expression typically contains exact terms and Oterms, for example n3 + 2n2 + O(n). The basic framework for this asymptotic ring is... 
Alexander Galarraga
Dynamics Algorithmic ImprovementsWe aim to improve several computations in dynamics and also implement new features. Improvements include optimizing the automorphic group... 
Trevor Karn
Ginvariants of the OrlikSolomon and OrlikTerao algebrasFor a finitedimensional algebra A equipped with the action of a group G, the invariant algebra A^G has many useful interpretations in topology and... 
Alexis Newton
Implement Small GroupsThe goal of this project is to improve the conversation between Sage and GAP (the SmallGrp package). We want to create convenient ways for... 
David Ayotte
Implementation of the graded ring of quasimodular formsThe goal of this project is twofold: first, we wish to implement the graded ring of quasimodular forms and, second, we wish to implement the... 
Tejasvi Chebrolu
Lazy Formal Power SeriesA formal power series is a (potentially) infinite sequence of coefficients. It turns out to be practical to denote it as an infinite series, although... 
Linden DisneyHogg
Rigorous integration and the AbelJacobi mapRiemann surfaces are key objects in many areas of maths, from mathematical physics to algebraic and arithmetic geometry. As such there is...