Open source mathematical software. - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-18T08:53:55Z http://mathoverflow.net/feeds/question/19046 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/19046/open-source-mathematical-software Open source mathematical software. Cristos A. Ruiz 2010-03-22T18:46:15Z 2012-09-21T09:07:53Z <p>I want some recomendation on which software I should install on my computer, an open source program for general abstract mathematical purposes (as opposed to applied mathematics). </p> <p>I would likely use it for group theory, number theory, algebraic geometry and probably polytopes. </p> <p>The kind of program I have in mind is Mathematica or Matlab. Altough probably those are not designed por abstract mathematics.</p> <p>Any suggestions?</p> http://mathoverflow.net/questions/19046/open-source-mathematical-software/19048#19048 Answer by Alon Amit for Open source mathematical software. Alon Amit 2010-03-22T18:50:30Z 2010-03-22T18:50:30Z <p><a href="http://www.gap-system.org/" rel="nofollow">GAP</a> is fantastic for group theory, combinatorics and and number theory. <a href="http://www.sagemath.org/" rel="nofollow">Sage</a> is becoming very popular and essentially includes GAP as well.</p> http://mathoverflow.net/questions/19046/open-source-mathematical-software/19051#19051 Answer by AlB for Open source mathematical software. AlB 2010-03-22T19:14:14Z 2010-09-13T23:50:30Z <p>Here are some links.</p> <ul> <li><a href="http://www.axiom-developer.org/" rel="nofollow">Axiom</a> and <a href="http://maxima.sourceforge.net/" rel="nofollow">Maxima</a> are good general purpose computer algebra systems.</li> <li><a href="http://www.gap-system.org/" rel="nofollow">GAP</a> is a system for computational discrete algebra (with particular emphasis on computational group theory).</li> <li><a href="http://pari.math.u-bordeaux.fr/" rel="nofollow">PARI/GP</a> is a CAS for fast computations in number theory.</li> <li><a href="http://www.sagemath.org/" rel="nofollow">SAGE</a> is a kind of unified framework for several systems, including GAP, PARI, and Maxima.</li> <li><a href="http://www.gnu.org/software/octave/" rel="nofollow">Octave</a> is a system for numerical computations (it is close to Matlab).</li> <li><a href="http://cadabra.phi-sci.com/" rel="nofollow">Cadabra</a> is a computer algebra system designed for the solution of the field theory problems.</li> <li><a href="http://cocoa.dima.unige.it/" rel="nofollow">CoCoA</a> stands for "Computations in commutative algebra".</li> <li><a href="http://www.math.tu-berlin.de/~kant/kash.html" rel="nofollow">KANT / KASH</a> stands for "Computational Algebraic Number Theory".</li> <li><a href="http://www.math.uiuc.edu/Macaulay2/" rel="nofollow">Macaulay 2</a> is a system for research in commutative algebra and algebraic geometry.</li> <li><a href="http://snap-pari.sourceforge.net/" rel="nofollow">Snap</a> is a computer program for studying arithmetic invariants of hyperbolic 3-manifolds.</li> <li><a href="http://www.algorithm.uni-bayreuth.de/en/research/SYMMETRICA/" rel="nofollow">Symmetrica</a> is an object oriented computer algebra system for representations, combinatorics and applications of symmetric groups.</li> </ul> http://mathoverflow.net/questions/19046/open-source-mathematical-software/19052#19052 Answer by akopyan for Open source mathematical software. akopyan 2010-03-22T19:19:04Z 2010-03-22T19:19:04Z <p>I like <a href="http://edu.kde.org/kig/" rel="nofollow">kig</a>. Very useful software for simple geometric constructions. Also it can help if you want to make a figure for a paper. </p> http://mathoverflow.net/questions/19046/open-source-mathematical-software/19053#19053 Answer by José Figueroa-O'Farrill for Open source mathematical software. José Figueroa-O'Farrill 2010-03-22T19:22:41Z 2010-03-22T19:22:41Z <p>I like <a href="http://www-math.univ-poitiers.fr/~maavl/LiE/" rel="nofollow">LiE</a> for computations with Lie algebras, especially roots and weights computations, plethysms,... It also has a <a href="http://www-math.univ-poitiers.fr/~maavl/LiE/form.html" rel="nofollow">web form</a> interface.</p> http://mathoverflow.net/questions/19046/open-source-mathematical-software/19057#19057 Answer by Jason Polak for Open source mathematical software. Jason Polak 2010-03-22T19:45:29Z 2010-03-22T19:45:29Z <p><a href="http://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo/" rel="nofollow">Kenzo</a> and <a href="http://chomp.rutgers.edu/" rel="nofollow">Chomp</a> are for computing homology. Kenzo for instance can take an arbitrary abstract simplicial complex and compute the simplicial homology groups, and it has various spaces already built in. You can compute the homology of products and other neat things with it.</p> http://mathoverflow.net/questions/19046/open-source-mathematical-software/19058#19058 Answer by Marko Amnell for Open source mathematical software. Marko Amnell 2010-03-22T20:19:36Z 2011-03-16T19:37:41Z <p>Michael Rubinstein's lcalc is a fast and easy-to-use program for calculating values of L-functions including the Riemann zeta function. It can be downloaded from:</p> <p><a href="http://pmmac03.math.uwaterloo.ca/~mrubinst/L_function_public/L.html" rel="nofollow">http://pmmac03.math.uwaterloo.ca/~mrubinst/L_function_public/L.html</a></p> http://mathoverflow.net/questions/19046/open-source-mathematical-software/19059#19059 Answer by mathy for Open source mathematical software. mathy 2010-03-22T20:23:57Z 2010-03-22T20:56:09Z <p><em>The kind of program I have in mind is Mathematica or Matlab. Altough probably those are not designed por abstract mathematics.</em></p> <p>What would be extremely useful to the progress of abstract mathematics would be a library of mathematical algorithms which were <em>formally verified for correctness</em>. Results obtained via such a library could be routinely cited in research papers without any doubt as to their correctness. The authors of SAGE suggest open source software as a means of achieving "research grade" mathematical software in [ <a href="http://www.ams.org/notices/200710/tx071001279p.pdf" rel="nofollow">http://www.ams.org/notices/200710/tx071001279p.pdf</a> ][ <a href="http://wstein.org/mathsoftbio/history.pdf" rel="nofollow">http://wstein.org/mathsoftbio/history.pdf</a> ], but arguably they don't go far enough.</p> <p>None of the "open source" mathematical software mentioned here currently meets this standard; the closest is C-CoRN [ <a href="http://c-corn.cs.ru.nl/" rel="nofollow">http://c-corn.cs.ru.nl/</a> ], a library of constructive mathematics for the Coq proof assistant.</p> <p>Now don't get me wrong, building a <em>comprehensive</em> library of formalized mathematics covering even the undergrad curriculum would be a vast undertaking. But the benefits would be huge, not just for computational mathematics but for all kinds of mathematical practice. The main obstacle is the nature of the work involved, which tends to be tedious and offering little reward to professional mathematicians, if occasionally playful and addictive. Perhaps undergraduate students should be encouraged to take courses in logic and contribute to such efforts.</p> http://mathoverflow.net/questions/19046/open-source-mathematical-software/19060#19060 Answer by Vladimir Dotsenko for Open source mathematical software. Vladimir Dotsenko 2010-03-22T20:45:14Z 2010-03-22T20:45:14Z <p>For all sorts of Groebner bases-related computation (I believe you might need some at least for questions in algebraic geometry), I would recommend Bergman (http://servus.math.su.se/bergman/).</p> http://mathoverflow.net/questions/19046/open-source-mathematical-software/19064#19064 Answer by Mikael Vejdemo-Johansson for Open source mathematical software. Mikael Vejdemo-Johansson 2010-03-22T20:56:44Z 2010-03-22T20:56:44Z <p>For commutative algebra and algebraic geometry, in addition to the already mentioned CoCoA, there is <a href="http://www.singular.uni-kl.de/" rel="nofollow">Singular</a>.</p> http://mathoverflow.net/questions/19046/open-source-mathematical-software/19112#19112 Answer by Harald Schilly for Open source mathematical software. Harald Schilly 2010-03-23T14:43:03Z 2010-03-23T14:43:03Z <p>Rubinstein's lcalc is part of Sage</p> <p><a href="http://www.sagemath.org/doc/reference/sage/lfunctions/lcalc.html" rel="nofollow">http://www.sagemath.org/doc/reference/sage/lfunctions/lcalc.html</a></p> http://mathoverflow.net/questions/19046/open-source-mathematical-software/19115#19115 Answer by Tom Leinster for Open source mathematical software. Tom Leinster 2010-03-23T15:17:47Z 2010-03-23T15:17:47Z <p>The only mathematical software I've learned to use so far is <a href="http://www.gnuplot.info/" rel="nofollow">gnuplot</a>, which does 2D and 3D plots. </p> <p>It's very easy to use, at least for basic tasks such as "plot $x \log(x)$ for $0 \leq x \leq 1$". It comes ready-installed on many Linux distributions. </p> http://mathoverflow.net/questions/19046/open-source-mathematical-software/19417#19417 Answer by Immi Halupczok for Open source mathematical software. Immi Halupczok 2010-03-26T13:10:57Z 2010-03-26T13:10:57Z <p>Oberwolfach recently started a site listing mathematical software, sorted by subject: <a href="http://orms.mfo.de/" rel="nofollow">Oberwolfach References on Mathematical Software</a>.</p> http://mathoverflow.net/questions/19046/open-source-mathematical-software/36609#36609 Answer by sleepless in beantown for Open source mathematical software. sleepless in beantown 2010-08-25T01:56:39Z 2010-08-25T12:37:32Z <p>Scilab (http://www.scilab.org/) is also numerical software which is free and open source, akin to Octave and Matlab. It's been developed at INRIA and ENPC. I also highly recommend Octave for numerical analysis and statistical analysis.</p> <p>Maxima is also on many gnu/linux installations and can be used in a text window or terminal without any graphics. The WxMaxima front end works in a graphical-user-environment and has better visualization of formulas and allows for menu-level interaction, instead of having to have all of the commands memorized.</p> http://mathoverflow.net/questions/19046/open-source-mathematical-software/36667#36667 Answer by Yujia Qiu for Open source mathematical software. Yujia Qiu 2010-08-25T13:09:05Z 2010-08-25T13:09:05Z <p>I am using SAGE for computing over elliptic curves. It is very convenient and has lots of implementations of algorithms. But I have not found a way to instal in under windows environment without virtual box.</p> http://mathoverflow.net/questions/19046/open-source-mathematical-software/38626#38626 Answer by avr-white for Open source mathematical software. avr-white 2010-09-13T23:29:29Z 2010-09-13T23:29:29Z <p>I'll second the votes for <a href="http://en.wikipedia.org/wiki/Sage_%28mathematics_software%29" rel="nofollow">Sage</a>, Macsyma as Maxima and Wxmaxima, Scilab, Octave, <a href="http://en.wikipedia.org/wiki/R_%28programming_language%29" rel="nofollow">R</a>, and GAP.</p> <p>For kids to play with are <a href="http://en.wikipedia.org/wiki/Kig" rel="nofollow">KGeometry KiG</a> (K-interactive-Geometry), letting you draw out geometric relationships and actively move points around, letting all defined subcomponents change with it: e.g. draw three points, define+draw the line segments between the points, define+draw the perpendicular bisectors of these line segments, define+draw a circle that touches the three points of the triangle. Now drag any of the three points of the triangle around and watch all of the defined components move along to remain the bisectors / intersections / circles consistently. It's a great way to play around with geometric constructions.</p> <p>Also, you can't go wrong with using <a href="http://en.wikipedia.org/wiki/Awk" rel="nofollow">awk</a>, <a href="http://en.wikipedia.org/wiki/Sed" rel="nofollow">sed</a>, and bash on the command line.</p> http://mathoverflow.net/questions/19046/open-source-mathematical-software/58716#58716 Answer by matthias beck for Open source mathematical software. matthias beck 2011-03-17T03:03:18Z 2011-03-17T03:03:18Z <p><em>... and probably polytopes.</em></p> <p>I recommend <a href="http://polymake.org/doku.php/start" rel="nofollow">polymake</a> for general polytope computations, <a href="http://www.math.ucdavis.edu/~mkoeppe/latte/" rel="nofollow">LattE</a> for lattice-point enumeration, <a href="http://www.mathematik.uni-osnabrueck.de/normaliz/" rel="nofollow">Normaliz</a> for computations related to lattice polytopes, and <a href="http://www.4ti2.de/" rel="nofollow">4ti2</a> for Gröbner basis computations.</p> http://mathoverflow.net/questions/19046/open-source-mathematical-software/85464#85464 Answer by Predrag Punosevac for Open source mathematical software. Predrag Punosevac 2012-01-12T02:49:53Z 2012-01-12T04:01:07Z <p>I can't believe that Python and its vast scientific application libraries are not mentioned in this thread. Let me be little bit bias and mention projects like <a href="http://www2.gsu.edu/~matrhc/PyDSTool.htm" rel="nofollow">PyDSTool</a>. What makes Maple or Mathematica language simpler than Python? Similarly time proven but proprietary computer algebra system MuPad now a part of MATLAB is not mentioned. FreeMat, the cleanest (other two being GNU Octabe and Scilab) reimplementation of MATLAB API, is also not mentioned. PostScript, page description language (arguably proprietary), is not mentioned. It is wonderful language for teaching geometry and programming pictures.</p> <p>P.S. I was surprised that people even mentioned things like Maple and Mathematica. I personally have not meet a person who had a look at the source code of these two systems. However, I have friends who have worked for MathWorks and have seen the source code of MATLAB.</p> http://mathoverflow.net/questions/19046/open-source-mathematical-software/101550#101550 Answer by PaPiro for Open source mathematical software. PaPiro 2012-07-07T00:36:13Z 2012-07-07T00:36:13Z <p>I recommend <a href="http://www.pascgalois.org/" rel="nofollow">PascGalois Project</a> software for visualizing abstract mathematics. Classroom resources also available.</p> http://mathoverflow.net/questions/19046/open-source-mathematical-software/107756#107756 Answer by Xingdong Zuo for Open source mathematical software. Xingdong Zuo 2012-09-21T09:07:53Z 2012-09-21T09:07:53Z <p>We are taught to use <strong>Sage</strong> to replace Matlab and Mathematica, now it also supports the online version via web browser which is very convenient and cross-platform.</p> <p>In addition, Sage is python based, it's easy to combine python programming which is more and more popular in scientific computation nowadays.</p>