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Evolution of mathematical software

Numerical analysis and symbolic computation had been in most important place of the subject, but other kind of them is also growing now. A useful mathematical knowledge of such as algorism which exist before the invention of electronic computer, helped to mathematical software developing. On the other hand, by the growth of computing power (such as seeing on Moore's law), the new treatment (for example, a new kind of technique such as data assimilation which combined numerical analysis and statistics) needing conversely the progress of the mathematical science or applied mathematics. The progress of mathematical information presentation such as TeX or MathML² will demand to evolution form formula manipulation language to true mathematics manipulation language (notwithstanding the problem that whether mathematical theory is inconsistent or not). And popularization of general purpose mathematical software, special purpose mathematical software³ so called one purpose software which used special subject will alive with adapting for environment progress at normalization of platform. So the diversity of mathematical software will be kept.

Solvers

This section is an excerpt from Solver.[edit]

A solver is a piece of mathematical software, possibly in the form of a stand-alone computer program or as a software library, that 'solves' a mathematical problem. A solver takes problem descriptions in some sort of generic form and calculates their solution. In a solver, the emphasis is on creating a program or library that can easily be applied to other problems of similar type.

Software calculator

Main article: Software calculator

A software calculator allows the user to perform simple mathematical operations, like addition, multiplication, exponentiation and trigonometry. Data input is typically manual, and the output is a text label.

Computer algebra systems

Main article: List of computer algebra systems

Many mathematical suites are computer algebra systems that use symbolic mathematics. They are designed to solve classical algebra equations and problems in human readable notation.

Cryptography

• Comparison of cryptography libraries

Statistics

See also: List of statistical software, Data mining and machine learning software, Data analysis software, and Comparison of statistical packages

Theorem provers and proof assistants

Main articles: List of theorem provers and List of proof assistants

Optimization software

Main article: List of optimization software

Geometry

Main articles: List of interactive geometry software and List of information graphics software

Numerical analysis

See also: List of numerical-analysis software, List of numerical analysis programming languages, Comparison of numerical-analysis software, and List of optimization software

The Netlib repository contains various collections of software routines for numerical problems, mostly in Fortran and C. Commercial products implementing many different numerical algorithms include the IMSL, NMath and NAG libraries; a free alternative is the GNU Scientific Library. A different approach is taken by the Numerical Recipes library, where emphasis is placed on clear understanding of algorithms.

Many computer algebra systems (listed above) can also be used for numerical computations.

Music mathematics software

Main article: List of music software

See also: Music and mathematics

Music mathematics software utilizes mathematics to analyze or synthesize musical symbols and patterns.

• Musimat (by Gareth Loy)⁴

Physics

See also: Physics software, Open-source physics software, List of cosmological computation software, List of software for Monte Carlo molecular modeling, and Computational physics

Plotting and charting

See also: Plotting software, Free plotting software, List of information graphics software, List of charting software, Comparison of JavaScript charting libraries, and Diagramming software

Websites

A growing number of mathematical software is available in web browsers, without the need to download or install any code.⁵

Desmos GeoGebra Jupyter Notebook Kaggle KaTeX

OpenPlaG Overleaf SageMath - CoCalc Symbolab WolframAlpha

Biomathematics

See also: Computational Biology and Biophysics

• List of bioinformatics software
• Biostatistics software
• List of systems biology modeling software
• List of systems biology visualization software

Mathematical chemistry

• List of quantum chemistry and solid-state physics software
• Comparison of software for molecular mechanics modeling

Mathematical modeling and simulations

See also: List of computer simulation software

Programming libraries

See also: List of numerical libraries, Comparison of linear algebra libraries, and List of automated theorem provers

Low-level mathematical libraries intended for use within other programming languages:

• GNU Multiple Precision Arithmetic Library (GMP), for high-performance arbitrary-precision arithmetic.
• Class Library for Numbers, a high-level C++ library for arbitrary-precision arithmetic.
• AMD Core Math Library, a software development library released by AMD
• Boost, for C++

List of mathematical software

See also: Comparison of software calculators, List of open-source software for mathematics, and List of charting software

Desmos GeoGebra GNU Octave gnuplot KCalc Maple (software) Mathematica Mathcad Maxima (software) Microsoft Mathematics

MuPAD MATLAB R (programming language) SageMath SciPy Matlab Simulink SymPy TeX TI-Nspire Wolfram Alpha

Mathematical notation software

See also: Mathematical notation, Typesetting, and Comparison of TeX editors

AUCTeX Authorea Apache OpenOffice Math AsciiMath Calligra Words - Formula editor CoCalc GeoGebra GNOME LaTeX GNU TeXmacs Gummi KaTeX Kile LaTeX LibreOffice Math LyX MathJax MathML

MathType Notepad++ Overleaf Scientific WorkPlace TeX Texmaker TeXnicCenter TeXShop TeXstudio TeXworks Verbosus Vim Visual Studio Code - LaTeX Workshop WinEdt WinFIG WinShell

Mathematical art software

Main article: List of mathematical art software

Apophysis Electric Sheep Fractint Fyre Mandelbulb MilkDrop openPlaG Ultra Fractal XaoS R / R Mandelbrot sets Sterling Bryce Picogen Terragen GeoGebra Desmos

Grapher Winplot Processing Grasshopper 3D P5.js matplotlib gnuplot Inkscape spirograph Wolfram Mathematica Houdini MATLAB TouchDesigner Unity (with math plugins)678910 LaTeX (PGF/TikZ, PGFPlots) Manim D3.js

See also

• Computational mathematics
• Computer-Based Math and computer-based mathematics education
• Comparison of formula editors
• Gödel's incompleteness theorems
• List of information graphics software
• Manim - open-source Python mathematical animation and visualisation software
• Mathlete
• Mathethon
• Plot (graphics)
• Time complexity

External links

• Calcular Database on mathematical software

References

1. See, e.g., the editorial charter of the ACM Transactions on Mathematical Software or the problem taxonomy of the National Institute of Standards and Technology Guide to Available Mathematical Software (both retrieved 2015-02-15). http://toms.acm.org/Charter.html ↩

2. Both MathML and TeX may be only simple a kind of computer language which enable also to present the mathematical formula. However they also may be the mathematical software if the term of software interpreted as whole technology on how to use computer, at most wide sense. ↩

3. Included your written script code on the general purpose mathematical software. ↩

4. Musimathics website, freeware download http://www.musimat.com/ ↩

5. Internet Accessible Mathematical Computation, Institute for Computational Mathematics, Kent State University, retrieved 2015-02-15. http://icm.mcs.kent.edu/research/iamc.html ↩

6. https://assetstore.unity.com/packages/tools/utilities/ultimate-math-library-228481 https://assetstore.unity.com/packages/tools/utilities/ultimate-math-library-228481 ↩

7. https://assetstore.unity.com/packages/tools/gui/math-equation-writer-199520 https://assetstore.unity.com/packages/tools/gui/math-equation-writer-199520 ↩

8. https://assetstore.unity.com/packages/tools/game-toolkits/mathplus-library-72197 https://assetstore.unity.com/packages/tools/game-toolkits/mathplus-library-72197 ↩

9. https://www.evilwizardstudios.com/smithy/ https://www.evilwizardstudios.com/smithy/ ↩

10. https://assetstore.unity.com/packages/3d/environments/neurofractals-pack-124436 https://assetstore.unity.com/packages/3d/environments/neurofractals-pack-124436 ↩