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Does anyone have a suggestion for the best computer program to perform calculations in the 2nd Weyl algebra?

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Weyl algebra computations are implemented in Macaulay 2 (package D-modules). Here is a manual.

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I use GAP (http://www.gap-system.org/) with the GBNP package (http://www.win.tue.nl/~amc/pub/grobner/chap0.html). You define Weyl algebra as a quotient of free associative algebra by the ideal $<x_1 x_2 - x_2 x_1 - 1>$. Easy to generalize to arbitrary dimension and can handle Clifford algebras (of arbitrary signatures) in the same setting.

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Singular claims to be wise in the ways of Weyl algebra.

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  • $\begingroup$ Have you used singular? I have been trying to install and I am struggling. $\endgroup$
    – No1729
    Commented Sep 2, 2015 at 11:51
  • $\begingroup$ Struggling in what way? Where are you installing it? $\endgroup$
    – Igor Rivin
    Commented Sep 2, 2015 at 11:53
  • $\begingroup$ I have followed the GUIDED CYGWIN INSTALL instructions on the site you linked. The mirror they suggest doesn't seem to up anymore. I have tried other mirrors but in the end when I try to run Singular out of the Cygwin window I just get error messages. $\endgroup$
    – No1729
    Commented Sep 2, 2015 at 11:56
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    $\begingroup$ If you install Sage, you get a copy of Singular included with it, and the Sage install process is quite carefully tested on a wide range of platforms, so it's possible that this may be easier than installing Singular alone. $\endgroup$
    – David Loeffler
    Commented Sep 30, 2015 at 21:15
  • $\begingroup$ you can run singular on cloud.sagemath.com $\endgroup$
    – Dima Pasechnik
    Commented Oct 1, 2015 at 4:13

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