On pp. 152-3 of Hydon's Symmetry Methods for Differential Equations (2000 ed.), he lists some computer packages for symmetry-finding. This related Mathematica StackExchange question mentions the SYM Mathematica package and Maple's DEtools/symgen. Does SAGE have anything similar for doing symmetry-finding?
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1$\begingroup$ posted and commented/answered on: math.stackexchange.com/questions/2174816/… $\endgroup$– Carlo BeenakkerCommented Mar 6, 2017 at 21:24
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$\begingroup$ and here : ask.sagemath.org/question/36844/symmetry-finding $\endgroup$– F. C.Commented Mar 6, 2017 at 21:31
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2$\begingroup$ The Sympy library in Python claims it can use Lie's method for solving ODEs. So, it would be in SAGE as well. I don't know how well it is implemented but from experience it seems to be of limited utility. $\endgroup$– Ryan BudneyCommented Mar 6, 2017 at 22:36
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2 Answers
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I have prepared algorithm in SageMath which finds determining equations for infinitesimals of ODE of order 2 and 3. My paper is published on this with title "Determining equations for infinitesimal transformation of second and third-order ODE using algorithm in open-source SageMath" in Malaya Journal of Matematik. The link for paper is https://www.malayajournal.org/selected_article.php?id=1007
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Although not specifically for SAGE (which is a conglomeration of several math packages), Dr. Willy Hereman's "24 [symmetry-finding] software packages" is a continually updated list of software (last updated: March 18, 2020).