SageMath is a free open-source mathematics software system licensed under the GPL.

SageMath builds on top of many existing open-source packages.
   Click to see the list:
  1. ATLAS Automatically Tuned Linear Algebra Software
  2. BLAS Basic Fortan 77 linear algebra routines
  3. boehm_gc The Boehm-Demers-Weiser conservative garbage collector
  4. Boost Free peer-reviewed portable C++ source libraries
  5. bzip2 High-quality data compressor
  6. cddlib Double description method of Motzkin et al.
  7. Cephes Cephes mathematical library
  8. Cliquer Routines for clique searching
  9. conway_polynomials Frank Lübeck's tables of Conway polynomials over finite fields
  10. CVXOPT Convex optimization, linear programming, least squares, etc.
  11. Cython C-Extensions for Python
  12. Docutils Open-source text processing system for processing plaintext documentation into useful formats, such as HTML or LaTeX
  13. ECL Embeddable Common-Lisp, an implementation of the Common Lisp language as defined by the ANSI X3J13 specification
  14. eclib John Cremona's programs for enumerating and computing with elliptic curves defined over the rational numbers
  15. elliptic_curves Cremona's mini tables of elliptic curves
  16. f2c Converts Fortran 77 to C code
  17. FFLAS-FFPACK A LGPL-2.1+ source code library for dense linear algebra over word-size finite fields.
  18. FLINT Fast Library for Number Theory
  19. flintqs William Hart's highly optimized multi-polynomial quadratic sieve for integer factorization
  20. fplll Euclidean lattice reduction
  21. FreeType A free, high-quality, and portable font engine
  22. G95 A stable, production Fortran 95 compiler available for multiple CPU architectures and operating systems
  23. GAP Groups, Algorithms, Programming - a system for computational discrete algebra
  24. gcc GCC, the GNU Compiler Collection
  25. GD Dynamic graphics generation tool
  26. gdmodule A Python interface to the GD library
  27. genus2reduction Curve data computation
  28. GF2X A C/C++ software package containing routines for fast arithmetic in GF(2)[x] (multiplication, squaring, GCD) and searching for irreducible/primitive trinomials.
  29. Gfan Gröbner fans and tropical varieties
  30. Givaro C++ library for arithmetic and algebraic computations
  31. GLPK GNU Linear Programming Kit
  32. GMP-ECM Elliptic curve method for integer factorization
  33. GNU MPC Gnu Mpc is a C library for the arithmetic of complex numbers with arbitrarily high precision and correct rounding of the result.
  34. GNU MPFR C library for multiple-precision floating-point computations with correct rounding
  35. GNU patch Applies diffs and patches to files.
  36. GnuTLS The GNU Transport Layer Security Library
  37. graphs A database of combinatorial graphs
  38. GSL The GNU Scientific Library
  39. IML Integer Matrix Library
  40. IPython Interactive computing environmens with an enhanced interactive Python shell
  41. Jinja State of the art, general purpose template engine; slightly outdated version
  42. Jinja2 State of the art, general purpose template engine; awesome version
  43. Jmol Java viewer for chemical structures in 3D
  44. LAPACK Linear Algebra PACKage written in Fortran
  45. lcalc Michael Rubinstein's L-function calculator
  46. LibGAP LibGAP is essentially a fork of the upstream GAP kernel.
  47. Libgcrypt General purpose cryptographic library based on the code from GnuPG
  48. Libgpg-error A small library that defines common error values for all GnuPG components
  49. libiconv A library to enable different languages with different characters to be handled properly
  50. libpng Bitmap image support
  51. LinBox C++ template library for exact, high-performance linear algebra computation with dense, sparse, and structured matrices over the integers and over finite fields
  52. lrcalc Littlewood-Richardson Calculator
  53. M4RI A library for fast arithmetic with dense matrices over GF(2)
  54. M4RI(e) A library for fast arithmetic with dense matrices over GF(2^e)
  55. matplotlib Python plotting library which produces publication quality figures in a variety of hardcopy formats and interactive environments across platforms
  56. Maxima System for manipulating symbolic and numerical expressions
  57. Mercurial Free, distributed source control management tool
  58. MoinMoin The MoinMoin wiki engine
  59. MPFI Multiple precision interval arithmetic library based on MPFR
  60. MPIR Multiple Precision Integers and Rationals
  61. mpmath Pure Python library for multiprecision floating-point arithmetic
  62. ncurses A library of functions that manage an application's display on character-cell terminals
  63. NetworkX Python package for the creation, manipulation, and study of the structure, dynamics, and functions of complex networks
  64. NTL A library for doing number theory
  65. NumPy Package for scientific computing with Python
  66. OpenCDK Open Crypto Development Kit provides basic parts of the OpenPGP message format
  67. PALP A package for analyzing lattice polytopes
  68. PARI/GP computer algebra system for fast computations in number theory
  69. Pexpect Pure Python module that makes Python a better tool for controlling and automating other programs
  70. PIL Python Imaging Library
  71. PolyBoRi Polynomials over Boolean Rings
  72. polytopes_db Reflexive Polytopes Databases that include lists of 2- and 3-dimensional reflexive polytopes
  73. PPL The Parma Polyhedra Library (PPL) provides numerical abstractions especially targeted at applications in the field of analysis and verification of complex systems.
  74. PyCrypto The Python Cryptography Toolkit
  75. Pygments Generic syntax highlighter
  76. Pynac Symbolic computation with Python objects
  77. Python The Python programming language
  78. python-gnutls Python wrapper for the GNUTLS library
  79. R A free software environment for statistical computing and graphics
  80. Ratpoints Find rational points on hyperelliptic curves
  81. Readline The GNU Readline library provides a set of functions for use by applications that allow users to edit command lines as they are typed in
  82. RPy2 provides a low-level interface to R, a proposed high-level interface, including wrappers to graphical libraries, as well as R-like structures and functions.
  83. Rubik Optimal Rubik's cube solver
  84. SageNB The Sage Notebook server
  85. SageTeX The SageTeX package allows you to embed code, results of computations, and plots from the Sage mathematics software suite into LaTeX documents
  86. SciPy Scientific tools for Python
  87. scipy_sandbox This package builds some of the optional/experimental SciPy packages, currently including arpack and delaunay
  88. SCons An open source software construction tool
  89. setuptools Download, build, install, upgrade, and uninstall Python packages -- easily!
  90. Singular Computer algebra system for polynomial computations, with special emphasis on commutative and non-commutative algebra, algebraic geometry, and singularity theory
  91. Sphinx A tool that makes it easy to create intelligent and beautiful documentation
  92. SQLAlchemy Python SQL toolkit and Object Relational Mapper that gives application developers the full power and flexibility of SQL
  93. SQLite Software library that implements a self-contained, serverless, zero-configuration, transactional SQL database engine
  94. Symmetrica Collection of C routines for representation theory
  95. SYMPOW Package to compute special values of symmetric power elliptic curve L-functions
  96. SymPy Python library for symbolic mathematics
  97. Tachyon Parallel/multiprocessor ray tracing system
  98. Termcap Simplifies the process of writing portable text mode applications
  99. Twisted Event-driven networking engine written in Python
  100. weave Tools for including C/C++ code within Python
  101. zlib Data compression library
  102. zn_poly C library for polynomial arithmetic in Z/nZ[x]
  103. ZODB Native object database for Python

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