The "GO" mentioned here should correspond to the O(3;1) (or perhaps O(1;3)
) mentioned in the wikipedia article.
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).
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. If
not, then describing a little more about what you need might help an expert
in giving you further tips.
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
>>>
>>>
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