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Computer algebra system
SageMath (previously Sage or SAGE, "System for Algebra and Geometry Experimentation") is a computer algebra system (CAS) with features covering many aspects
SageMath
SageManifolds (following the styling of SageMath) is an extension fully integrated into SageMath, to be used as a package for differential geometry and
Sage_Manifolds
web site. SageMath comprises a variety of other free packages, with a common interface and language. SageMath is developed in Python. SageMath was initiated
List of open-source software for mathematics
List_of_open-source_software_for_mathematics
Chaotic model of atmospheric convection
The Lorenz system is a set of three ordinary differential equations, first developed by the meteorologist Edward Lorenz while studying atmospheric convection
Lorenz_system
General-purpose programming language
PyTorch Lightning Python-Ogre Qiskit QLattice RDKit RPyC Sage Manifolds SageMath ScientificPython scikit-learn scikit-multiflow SciPy SimpleITK spaCy Sphinx
Python_(programming_language)
Cloud computing and course management platform
tracked using revision control systems like Git. CoCalc is operated by SageMath Inc. The creator and lead developer of CoCalc is William Stein, a former
CoCalc
Mathematical software
Significant systems include Axiom, GAP, Maxima, Magma, Maple, Mathematica, SageMath, and SymPy. In the 1950s, while computers were mainly used for numerical
Computer_algebra_system
Open source data science software
the notebook interface of other programs such as Maple, Mathematica, and SageMath, a computational interface style that originated with Mathematica in the
Project_Jupyter
Programming language for statistics
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
R_(programming_language)
Open-source Python library for scientific computing
open-source mathematical libraries Comparison of statistical packages SageMath SymPy HiGHS optimization solver "Release 1.18.0". 19 June 2026. Retrieved
SciPy
Visual representation of solutions to a differential equation
A slope field (also called a direction field) is a graphical representation of the solutions to a first-order differential equation of a scalar function
Slope_field
Python library for machine learning
PyTorch Lightning Python-Ogre Qiskit QLattice RDKit RPyC Sage Manifolds SageMath ScientificPython scikit-learn scikit-multiflow SciPy SimpleITK spaCy Sphinx
Scikit-learn
Type of functional equation (mathematics)
programs: Maple: dsolve Mathematica: DSolve[] Maxima: ode2(equation, y, x) SageMath: desolve() SymPy: sympy.solvers.ode.dsolve(equation) Xcas: desolve(y'=k*y
Differential_equation
Computer algebra system
SageMath, R, and KAlgebra) The GNU TeXmacs and LyX mathematical editor programs can be used to provide an interactive GUI for Maxima, as can SageMath
Maxima_(software)
and orchestrating multi-agent AI workflows Resolver One – a spreadsheet. SageMath – a combination of more than 20 main opensource math packages and provides
List_of_Python_software
Matrix form in linear algebra
with HermiteForm MATLAB with hermiteForm NTL with HNF PARI/GP with mathnf SageMath with hermite_form "HermiteDecomposition". Wolfram Alpha Site. Hermite normal
Hermite_normal_form
Cloud-based Jupyter Notebook environment
— does Jupyter notebooks, Markdown, LaTeX, RMarkdown, Linux terminal, SageMath, GNU Octave. Dataflow.zone – cloud-based AI and data engineering platform
Google_Colab
Topics referred to by the same term
enterprise management and accounting software Sage 50, accounting software SageMath, formerly known as Sage, free mathematics software SAGE (game engine) Serial
Sage
Python library for data analysis
PyTorch Lightning Python-Ogre Qiskit QLattice RDKit RPyC Sage Manifolds SageMath ScientificPython scikit-learn scikit-multiflow SciPy SimpleITK spaCy Sphinx
Pandas_(software)
April 2022). "RKWard 0.7.3". RKWard News. Retrieved 2022-04-21. "SageMath". sagemath.org. Retrieved 2020-02-15. "Minitab.com description". Minitab. Retrieved
Comparison of statistical packages
Comparison_of_statistical_packages
Statistical analysis software
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
SPSS
Computational software program
Literate programming Mathematical markup language Mathematical software SageMath Wolfram Language Wolfram SystemModeler, a physical modeling and simulation
Wolfram_Mathematica
Python distribution
PyTorch Lightning Python-Ogre Qiskit QLattice RDKit RPyC Sage Manifolds SageMath ScientificPython scikit-learn scikit-multiflow SciPy SimpleITK spaCy Sphinx
Anaconda (Python distribution)
Anaconda_(Python_distribution)
Computer system for mathematical calculation
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
Mathcad
Statistical software
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
SAS_(software)
Statistical analysis software
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
WINKS
Documentation generator
other important Python projects, including Bazaar, SQLAlchemy, MayaVi, SageMath, SciPy, Django and Pylons. It is also used for the Blender user manual[failed
Sphinx (documentation generator)
Sphinx_(documentation_generator)
Function returning one of only two values
2016-01-17. "Boolean functions — Sage 9.2 Reference Manual: Cryptography". doc.sagemath.org. Retrieved 2021-05-01. Tarannikov, Yuriy; Korolev, Peter; Botev, Anton
Boolean_function
Data analysis software
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
PSPP
Data visualization package for R
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
Ggplot2
version 6.0 and later SciPy, and thus SciPy-relied software FuncDesigner, SageMath, PythonXY It appears as a built-in routine (for lu, backslash, and forward
UMFPACK
Suite of computer programs
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
JMP_(statistical_software)
Python web framework
PyTorch Lightning Python-Ogre Qiskit QLattice RDKit RPyC Sage Manifolds SageMath ScientificPython scikit-learn scikit-multiflow SciPy SimpleITK spaCy Sphinx
Flask_(web_framework)
Proprietary language for AI accelerators
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
Mojo_(programming_language)
Statistics software
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
Minitab
Mathematical expression with disputed status
explicitly mentioned that the result of 0**0 is platform-dependent). R, SageMath, and PARI/GP evaluate x0 to 1. Mathematica simplifies x0 to 1 even if no
Zero_to_the_power_of_zero
American professor of mathematics
Varieties’, supervised by Hendrik W. Lenstra. He is the lead developer of SageMath and founder of CoCalc. Stein does computational and theoretical research
William_A._Stein
R software and development tools
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
List_of_R_software_and_tools
Python library for numerical programming
PyTorch Lightning Python-Ogre Qiskit QLattice RDKit RPyC Sage Manifolds SageMath ScientificPython scikit-learn scikit-multiflow SciPy SimpleITK spaCy Sphinx
NumPy
Topic in algebraic number theory
computational solver for S-unit equation is available in the software SageMath. Beukers, F.; Schlickewei, H. (1996). "The equation x+y=1 in finitely generated
S-unit
Library for creating visualizations in Python
online Matplotlib and Python graphs PLplot – Python bindings available SageMath – uses Matplotlib to draw plots List of open-source mathematical libraries
Matplotlib
general purpose CAS. Still alive, as open-sourced and freed in December 2008 SageMath William A. Stein 2005 2005 10.9 5 May 2026 Free GNU GPL Mathematics software
List of computer algebra systems
List_of_computer_algebra_systems
GAP GiNaC Macaulay2 Mathomatic Maxima Normaliz OpenAxiom PARI/GP Reduce SageMath Singular SymbolicC++ SymPy Xcas Yacas Meep Elmer FEM solver Numerical Electromagnetics
List of free and open-source software packages
List_of_free_and_open-source_software_packages
versions for individual workstations and high performance computer clusters. SageMath - a system for algebra and geometry experimentation via Python. Scilab
List of computer simulation software
List_of_computer_simulation_software
Differential equation containing derivatives with respect to only one variable
a high-level language primarily intended for numerical computations. SageMath, an open-source application that uses a Python-like syntax with a wide
Ordinary differential equation
Ordinary_differential_equation
Computer algebra system
develop formal algorithms or use it in other software. Giac is used in SageMath for calculus operations. Among other things, Xcas can solve differential
Xcas
Programming Contest
2007 C++ Perl 2008 Java ML 2009 C++ Java ML 2010 C++, Haskell, Python SageMath 2011 F# Shell and C++ 2012 C++ OCaml Java 2013 Java, C#, C++, PHP, Ruby
ICFP_Programming_Contest
Analytics software suite
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
SAS_Viya
Pseudorandom number generator
Octave, GNU Scientific Library Other: Microsoft Excel, GAUSS, gretl, Stata, SageMath, Scilab, Maple, MATLAB It is also available in Apache Commons, in the standard
Mersenne_Twister
Open-source statistical package
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
LaplacesDemon
Programming tool blending code and documents
Org-mode on emacs (with the built-in babel addon) – GPL R Markdown – GPLv3 SageMath – GPLv3 Anaconda SMath Studio – Freeware, not libre: licensed under Creative
Notebook_interface
Certain constant-recursive integer sequences
P_{k})z^{n}={\frac {k-\sum _{j=1}^{k-1}(k-j)P_{j}z^{j}}{1-\sum _{j=1}^{k}P_{j}z^{j}}}.} SageMath implements U n {\displaystyle U_{n}} and V n {\displaystyle V_{n}} as functions
Lucas_sequence
Algorithm in computational number theory
function qflll Pymatgen as the function analysis.get_lll_reduced_lattice SageMath as the method LLL driven by fpLLL and NTL Isabelle/HOL in the 'archive
Lenstra–Lenstra–Lovász lattice basis reduction algorithm
Lenstra–Lenstra–Lovász_lattice_basis_reduction_algorithm
Selection of items from a set
on 9 October 2022. Retrieved 10 April 2017. "Subsets - Combinatorics". Sagemath.org. Retrieved 10 April 2017. Brualdi 2010, p. 52 Benjamin & Quinn 2003
Combination
Mathematical computing environment
graphing software List of numerical-analysis software Mathematical software SageMath (an open source algebra program) "Maple and MapleSim 2025.2 updates". www
Maple_(software)
Python package
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
Bambi_(software)
Python web framework
PyTorch Lightning Python-Ogre Qiskit QLattice RDKit RPyC Sage Manifolds SageMath ScientificPython scikit-learn scikit-multiflow SciPy SimpleITK spaCy Sphinx
Django_(web_framework)
Statistical software package
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
Stata
PARI is also available as a C library to allow for faster computations. SageMath is an open-source math software, with a unified Python interface which
List of numerical-analysis software
List_of_numerical-analysis_software
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
List_of_statistical_software
Multiprecision integer software library
MPIR: Multiple Precision Integers and Rationals SageMath, a computer algebra system that formerly used MPIR Developers William Hart and the MPIR Team Stable
MPIR_(mathematics_software)
Numerical computing environment and programming language
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
MATLAB
Open-source word processor
front-end to a number of computer algebra systems such as Maxima, FriCAS and SageMath, and can in turn integrate some of their output into its typesetting. TeXmacs
GNU_TeXmacs
Python library for symbolic computation
ASCII/Unicode pretty-printing, LaTeX Code generation: C, Fortran, Python SageMath: an open source alternative to Mathematica, Maple, MATLAB, and Magma (SymPy
SymPy
Programming language
Python creator Guido van Rossum. Of particular note: The free software SageMath computer algebra system depends on Cython, both for performance and to
Cython
Implementation of the S programming language
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
S-PLUS
Python library for graphs and networks
release and its continued evolution within the SciPy ecosystem. In 2008, SageMath, an open source mathematics system, incorporated NetworkX into its package
NetworkX
Statistical software
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
SUDAAN
Methods of calculating definite integrals
Encyclopedia of Mathematics Implementations of many quadrature and cubature formulae within the free Tracker Component Library. SageMath Online Integrator
Numerical_integration
Software for scientific statistics and analysis
make use of Julia, KAlgebra, Lua, Maxima, Octave, Python, Qalculate!, R, SageMath, and Scilab. Cantor provides a consistent interface to these backends;
Cantor_(mathematics_software)
Application of statistical techniques to biological systems
deep-learning, machine-learning SQL databases NoSQL NumPy numerical python SciPy SageMath LAPACK linear algebra MATLAB Apache Hadoop Apache Spark Amazon Web Services
Biostatistics
Programming language
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
IDL_(programming_language)
Mathematical visualization BSD 3-clause Maxima Mathematical visualization GPL SageMath Mathematical visualization GPLv3 SymPy Symbolic arithmetic BSD Wolfram
List of mathematical art software
List_of_mathematical_art_software
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
SYSTAT_(statistics_package)
Software used in mathematical applications
Magma Magnus Maple Mathcad Mathematica Mathomatic Maxima PARI/GP REDUCE SageMath Scilab SMath Studio Symbolic Math Toolbox (MATLAB) SymPy Wolfram Alpha
Mathematical_software
Non-linear statistical modeling software suite
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
ADMB
Dynamic programming language
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
Julia_(programming_language)
Event-driven network programming framework
Twisted extensively. SageMath, an open-source alternative to Mathematica, Maple, Magma, MATLAB, has a web-based interface, SageMath notebook, that runs
Twisted_(software)
Class of mathematical software
tensor calculus on smooth manifolds; all SageManifolds code is included in SageMath since version 7.5; it allows for computations in various vector frames
Tensor_software
Axiom CoCoA FriCAS GAP KAlgebra Mathomatic Maxima PARI/GP Reduce SageMath SymPy Xcas Yacas C.a.R. CaRMetal Cinderella Desmos DrGeo GeoGebra Kig Cantor
List of free educational software
List_of_free_educational_software
Econometric software package
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
OxMetrics
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
LIMDEP
Basic component of symmetric key algorithms
Algebraic Representations — Sage 9.2 Reference Manual: Cryptography". doc.sagemath.org. Retrieved 2021-04-30. Saarinen, Markku-Juhani O. (2012). "Cryptographic
S-box
Technique for speeding up algorithms involving Boolean matrices
library for fast arithmetic with dense matrices over F2. M4RI is used by SageMath and the PolyBoRi library. The algorithm was introduced by V. L. Arlazarov
Method_of_Four_Russians
Mathematical construct in computer algebra
example, of CoCoA, GAP, Macaulay 2, Magma, Maple, Mathematica, SINGULAR, SageMath and SymPy. When F4 is available, it is generally much more efficient than
Gröbner_basis
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
Data_Desk
Statistical software for Bayesian analysis
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
WinBUGS
Ray tracing software
into a number of other open source software packages such as VMD, and SageMath. Tachyon is released under a permissive license (included in the tarball)
Tachyon_(software)
Area of mathematics
Kronecker coefficients are implemented in the computer algebra system SageMath. Given an element w ∈ S n {\displaystyle w\in S_{n}} of cycle-type μ =
Representation theory of the symmetric group
Representation_theory_of_the_symmetric_group
Microsoft Excel add-in
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
XLfit
public domain books Quizlet – freemium online flashcard and study platform SageMath – computer algebra system for computational mathematics Saylor Academy
List of online educational resources
List_of_online_educational_resources
Set of applications and supporting libraries
– worksheet view to other Free Software Math packages. GUI frontend to SageMath, Maxima, R and KAlgebra KAlgebra – a mathematical calculator based on the
KDE_Gear
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
ILNumerics
operations in Python. Pandas, a library for data manipulation and analysis. SageMath is a large mathematical software application which integrates the work
List_of_numerical_libraries
Open-source statistical computer software
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
Gretl
OpenBUGS Orange PSPP Python (statsmodels, PyMC, IPython, IDLE) R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat Freeware BV4.1 XploRe WinBUGS Commercial
Genstat
Overview of and topical guide to Python
Instagram (backend) Dropbox Reddit OpenStack Blender (scripting and plugins) SageMath NumPy Pandas TensorFlow ActiveState — commercial Python distributions and
Outline of the Python programming language
Outline_of_the_Python_programming_language
File format that describes one or more computer files available for download
database. Dofus, a Flash MMORPG uses Metalinks for downloads and so does SageMath, the open-source mathematical software. According to the main metalinker
Metalink
Advanced interactive shell for Python
the notebook interface of other programs such as Maple, Mathematica, and SageMath, a computational interface style that originated with Mathematica in the
IPython
Computer algebra system
Pynac, a fork of GiNaC, provides the backend for symbolic expressions in SageMath. Free and open-source software portal Comparison of computer algebra systems
GiNaC
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SAGEMATH
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SAGEMATH
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