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H. Arponen's user avatar
H. Arponen's user avatar
H. Arponen
  • Member for 13 years, 3 months
  • Last seen more than 5 years ago
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ANOTHER Exterior differential system on $SO(3;\mathbb R) \times \mathbb R$
That is absolutely beautiful, thank you Robert!! That's something I need a while to digest, but I'll read your paper (seems it's open access).
accepted
ANOTHER Exterior differential system on $SO(3;\mathbb R) \times \mathbb R$
awarded
 Yearling
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ANOTHER Exterior differential system on $SO(3;\mathbb R) \times \mathbb R$
Jeanne: that is GREAT news, exactly what I was hoping!! Actually I also had a third equation which is a bit simpler than this one but more complicated than the other one, for which I managed to get solutions parametrized by one function of three variables. The result(s) mean that there's an infinite number of asymptotic symmetries of a certain noncompact homogeneous space. The problem is based on this one: arxiv.org/abs/1209.5597
comment
Exterior differential system on $SO(3;\mathbb R) \times \mathbb R$
By the way, I fould your Cartan package for Maple. Will it be able to handle/solve this type of EDSes? I don't have access to Maple right now, but it could be useful in the future...
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ANOTHER Exterior differential system on $SO(3;\mathbb R) \times \mathbb R$
added 378 characters in body
revised
ANOTHER Exterior differential system on $SO(3;\mathbb R) \times \mathbb R$
added 7 characters in body
comment
ANOTHER Exterior differential system on $SO(3;\mathbb R) \times \mathbb R$
I found an appropriate package for REDUCE: reduce-algebra.com/docs/eds.pdf Unfortunately I have virtually no experience with REDUCE...
comment
ANOTHER Exterior differential system on $SO(3;\mathbb R) \times \mathbb R$
Oops, should have been a bit more careful... edited the post accordingly!
revised
ANOTHER Exterior differential system on $SO(3;\mathbb R) \times \mathbb R$
Clarifications as suggested by R.B.
comment
Exterior differential system on $SO(3;\mathbb R) \times \mathbb R$
Jeanne: umm... you don't happen to be able to say something about another (more difficult) problem here? mathoverflow.net/questions/111578/… It seems like this kind of systems would be best solved by a CAS package. I already found you Cartan package for Maple, but I guess it can't handle systems like this?
asked
ANOTHER Exterior differential system on $SO(3;\mathbb R) \times \mathbb R$
awarded
 Commentator
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Exterior differential system on $SO(3;\mathbb R) \times \mathbb R$
Thanks a lot Jeanne!! I guess rather than overthinking it, sometimes it's better to just go ahead and SOLVE that damn thing already! ;) Thanks also for the speed lesson in exterior differentials systems!
accepted
Exterior differential system on $SO(3;\mathbb R) \times \mathbb R$
asked
Exterior differential system on $SO(3;\mathbb R) \times \mathbb R$
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How can one find generators of basic differential forms on homogeneous spaces?
Pardon if I don't really get the language here... what do you mean by "the generators"? Vector fields satisfying the Lie algebra?
revised
Finite dimensional homogeneous spaces of $Diff(S^1)$
edited body; added 41 characters in body; added 12 characters in body
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Finite dimensional homogeneous spaces of $Diff(S^1)$
ah... I read your answer more carefully now... indeed, I thought Cartan was talking about vector fields, when he was talking about the pseudo group...
revised
Finite dimensional homogeneous spaces of $Diff(S^1)$
fixed a typo in the formulae; added 97 characters in body