On Sunday, May 29, 2022 at 6:27:18 PM UTC+8 Nils Bruin wrote:
> It depends a little on what coefficients you want. If you're happy with > rational numbers then this should do the trick: > As far as the Lorentz group is concerned, I think it should be constructed on real numbers filed in general, but I'm not sure if sage math has the corresponding implementation on real numbers filed. > > G = diagonal_matrix(QQ,4,[-1,1,1,1]) > lorentz_group = GO(4,QQ,invariant_form=G) > > which just constructs the group of (in this case QQ-valued) matrices that > preserve the quadratic form -t^2+x^2+y^2+z^2. Depending on what you > actually want to do with it, you may be more interested in SO > SO only includes the part where the determinant is equal to 1 in GO, which is not in line with the requirements of Lorentz group, IMO. or perhaps the construction of its lie group/algebra. > The Lorentz group is *a Lie group of symmetries of the spacetime of special relativity, as described here* [1]. So, I'm not sure if your above code snippet also corresponds to a *Lie group.* [1] https://en.wikipedia.org/wiki/Representation_theory_of_the_Lorentz_group Regards, HZ > > On Thursday, 26 May 2022 at 09:11:55 UTC+2 hongy...@gmail.com wrote: > >> How can I create the Lorentz group, as described here [1], in Sage math? >> >> [1] https://en.wikipedia.org/wiki/Lorentz_group#Basic_properties >> >> Regards, >> HZ >> >> -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/ffb54100-70e8-4aab-9885-b99b2f6d6ca9n%40googlegroups.com.
