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Where can I find the most up-to-date or whatever you consider to be the most useful symmetry-finding package for differential equations? I do not intend to restrict to, but would like to include those, that are designed to work within Mathematica.

I'm looking for something analogous to this for Mathematica (software and documentation) or this for Maple.

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    $\begingroup$ A good place to start is checking papers that cite that one: scholar.google.com/scholar?cites=15595045703323033950 or cite the publication that followed it: scholar.google.com/scholar?cites=12693930071175863924 However, given that it came out in 2009, I wonder why you think there exists a more up-to-date version. $\endgroup$ – Xerxes Feb 28 '13 at 18:12
  • $\begingroup$ Thanks. I did check papers that cite that one. I cannot actually find the SYM package code online (obviously I could e-mail the authors). But, the package not being online usually means there is little to no documentation. So, I thought I'd ask the community if there's some well-known package that I haven't ever heard of since I'm not an expert in this domain. $\endgroup$ – Cameron Smith Feb 28 '13 at 19:42
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    $\begingroup$ You might find references to relevant Mathematica software here. $\endgroup$ – Daniel Lichtblau Mar 1 '13 at 17:43
  • $\begingroup$ Thanks @DanielLichtblau. Software is here. $\endgroup$ – Cameron Smith Mar 1 '13 at 18:56
  • $\begingroup$ I reference your question in this related ask.sagemath.org question. $\endgroup$ – Geremia Mar 6 '17 at 18:32
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I recommend "Introduction to Symmetry Analysis" by Cantwell. It comes with a quite powerful Mathematica package, with numerous examples included.

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    $\begingroup$ Your link to the Mathematica package is dead. $\endgroup$ – Geremia Mar 24 '20 at 20:03
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    $\begingroup$ @Geremia both work for me, perhaps you can’t access the address due to country restrictions? $\endgroup$ – CA Trevillian Mar 24 '20 at 21:30
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    $\begingroup$ @CATrevillian I changed the Mathematica package link that from the author's website. $\endgroup$ – Geremia Mar 24 '20 at 21:52
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Hi all please send me an mail at spawn@math.upatras.gr or visit my web site www.math.upatras.gr/~spawn, although the version on the site is not updated you can find an online version of the help files of the package. Many things have been added since my thesis. Among them, I have added command for the algebraic manipulation of the symmetries (Levi decomposition, ideals, quotient algebras, etc.), contracting conservation laws using the self adjoint property of a Differential equation and the Noether operator and constructing the equivalent algebra and finding the discrete symmetries (following an idea of Hydon in his book). Many things are still in development/testing so i need your feedback!

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See: Hereman's "24 [symmetry-finding] software packages mainly for Mathematica (commercial software), some for Macsyma* (commercial software)."

*Maxima/wxMaxima are free versions.

Gerd Baumann's Symmetry Analysis of Differential Equations with Mathematica® comes with some extra materials that include a Mathematica package called MathLie, freely downloadable here (20.5 MB).

Also: Brian Cantwell's Introduction to Symmetry Analysis's IntroToSymmetry.m.

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The SYM package was developed by Stylianos Dimas and may be found in Appendix A of his thesis at http://nemertes.lis.upatras.gr/jspui/bitstream/10889/1697/1/thesis.pdf

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    $\begingroup$ Because we are an English language site, it would be appropriate (and kind) of you to point out that the entire text of that thesis--including the comments in the code--is in Greek. $\endgroup$ – whuber Feb 28 '13 at 21:25
  • $\begingroup$ @whuber internationalmathematicasymposium.org/IMS2006/IMS2006_CD/… $\endgroup$ – Dr. belisarius Feb 28 '13 at 21:34
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    $\begingroup$ @whuber Yes, that's a bit of a problem. I'm not recommending anybody read the text of the thesis, just grep the relevant Mathematica package out of the appendix. As belisarius points out, there are a few English-language papers in the literature concerning the package. $\endgroup$ – Xerxes Feb 28 '13 at 21:36
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    $\begingroup$ @belisarius Thanks. That seems like a version of the reference supplied by the OP. $\endgroup$ – whuber Feb 28 '13 at 21:36
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    $\begingroup$ Dimas also says in the preface to Appendix A that you can contact him for a copy of the package at spawn@math.upatras.gr According to his most recent paper, that e-mail is still valid (although he's now in Brazil). $\endgroup$ – Xerxes Feb 28 '13 at 21:56

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