On Wednesday, June 1, 2022 at 1:55:45 AM UTC+8 Nils Bruin wrote:
> The "GO" mentioned here should correspond to the O(3;1) (or perhaps O(1;3) > ) mentioned in the wikipedia article. > Do you mean that these two ways of writing are a matter of convention? > > The problem with the "real numbers" is that representing many elements > exactly in it is complicated. For many algebraic questions, you can > probably get away with considering the group over Q (or some finite > extensions). > The Lorentz group is a physical problem, not just a pure algebraic problem, so, I am not sure whether this simplified treatment can meet the needs of the problem in any case. > I'm not entirely sure if the connected component SO^+ is readily > implemented in sage. > > "creation" of a mathematical object (particularly an infinite one) is a > rather relative notion anyway: technically speaking > > class LorentzGroup: > pass > > can be passed off as a class whose instances represent the Lorentz group: > there are just many features that haven't been implemented (yet). It's > probably worth checking if the object described above meets your needs. > You only gave the above two lines of code, so I don't know what you mean here. If not, then describing a little more about what you need might help an > expert in giving you further tips. > Yours, Hongyi > On Tuesday, 31 May 2022 at 08:43:54 UTC+2 hongy...@gmail.com wrote: > >> 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/1ab5e711-df56-4fa2-8d86-75b18c4d650en%40googlegroups.com.
