On Tuesday, 11 September 2012 20:03:43 UTC+8, John Cremona wrote:
> I think this is a great idea. Volker's invariants are maps from the > space of binary forms over some ring R into the coefficient ring, for > example the discriminant will always be one. So I would have thought > to put them into the polynomials code (note that is_homogeneous() is > defined in rings/polynomial/multi_polynomial_libsingular.pyx).
> Volker, will you also include what I call seminvariants?
Yes, it's great, but I would rather like to see it packaged as invariants of a representation of SL(2,C), not
as invariants of a binary form. I CC this to sage-combinat, where they might have better ideas about where this should fit...
(and they actually might have some stuff in this direction already)
> On 11 September 2012 12:55, Volker Braun <vbrau...@gmail.com <javascript:>> > wrote: > > By "classical invariant theory", I mean invariant under the SL(n,C) > action > > and not just under a discrete subgroup. I believe the group theory stuff > > handles only the finite group case, right?
> > On Tuesday, September 11, 2012 12:40:01 PM UTC+1, David Joyner wrote:
> >> There are some invariant theory commands that Simon King and I added > into > >> one of the group theory modules. Maybe you are doing something > different?
> > -- > > You received this message because you are subscribed to the Google > Groups > > "sage-devel" group. > > To post to this group, send email to sage-...@googlegroups.com<javascript:>.
But I need the classical invariants / covariants with their conventional names and normalizations in the literature. I'm not trying to do the most general SL(n,C) representation theory here.
On 11 September 2012 13:16, Volker Braun <vbraun.n...@gmail.com> wrote:
> But I need the classical invariants / covariants with their conventional
> names and normalizations in the literature. I'm not trying to do the most
> general SL(n,C) representation theory here.
I agree (for my own applications). Of course I do not mind if the
functionality is provided by some more general framework, but you must
admit that (for example) binary forms do have quantities associated
with them called invariants, which users should be able to get their
hands on. I don't think we would be very popular if it was not
possible to get the discriminant of a polynomial without constructing
a representation!
> On Tuesday, September 11, 2012 1:12:57 PM UTC+1, Dima Pasechnik wrote:
>> Yes, it's great, but I would rather like to see it packaged as invariants
>> of a representation of SL(2,C), not
>> as invariants of a binary form.
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On Tuesday, 11 September 2012 20:16:37 UTC+8, Volker Braun wrote:
> But I need the classical invariants / covariants with their conventional > names and normalizations in the literature.
I don't think that 98% of Grace and Young (http://archive.org/details/algebraofinvaria00graciala) belong to core Sage. I'd say it might be an optional package. I don't mind discriminants and other bits of the classical invariant theory which went on to live their lives in the modern maths, but, say, catalecticants, minimal systems of invariants for 5-ics, etc, please, give me a break...
Dima, you have just insulted my favourite word (catalecticant)! They
play an important role in 2-descent on elliptic curves! I will be
happy when search_src("catalecticant") returns a result.
> On Tuesday, 11 September 2012 20:16:37 UTC+8, Volker Braun wrote:
>> But I need the classical invariants / covariants with their conventional
>> names and normalizations in the literature.
> I don't think that 98% of Grace and Young
> (http://archive.org/details/algebraofinvaria00graciala) belong to core Sage.
> I'd say it might be an optional package.
> I don't mind discriminants and other bits of the classical invariant theory
> which went on to live their lives in the modern maths, but, say,
> catalecticants, minimal systems of invariants for 5-ics, etc, please, give
> me a break...
>> I'm not trying to do the most general SL(n,C) representation theory here.
>> On Tuesday, September 11, 2012 1:12:57 PM UTC+1, Dima Pasechnik wrote:
>>> Yes, it's great, but I would rather like to see it packaged as invariants
>>> of a representation of SL(2,C), not
>>> as invariants of a binary form.
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On Tuesday, 11 September 2012 21:09:39 UTC+8, John Cremona wrote:
> Dima, you have just insulted my favourite word (catalecticant)!
oops, sorry, I didn't mean getting personal. Please give my regards to catalecticants. :–)
The 1st year of my 1st postdoc was wasted on implementing stuff from Grace and Young, in C+gmp, (as my then boss wished) and I didn't enjoy it at all. And the place I was at didn't do the proper work permit paperwork, and it was Pasechnik vs. State of the Netherlands, with the latter willing to deport me, for most of that bloody year...
> On 11 September 2012 14:03, Dima Pasechnik <dim...@gmail.com <javascript:>> > wrote:
> > On Tuesday, 11 September 2012 20:16:37 UTC+8, Volker Braun wrote:
> >> But I need the classical invariants / covariants with their > conventional > >> names and normalizations in the literature.
> > I don't think that 98% of Grace and Young > > (http://archive.org/details/algebraofinvaria00graciala) belong to core > Sage. > > I'd say it might be an optional package. > > I don't mind discriminants and other bits of the classical invariant > theory > > which went on to live their lives in the modern maths, but, say, > > catalecticants, minimal systems of invariants for 5-ics, etc, please, > give > > me a break...
> >> I'm not trying to do the most general SL(n,C) representation theory > here.
> >> On Tuesday, September 11, 2012 1:12:57 PM UTC+1, Dima Pasechnik wrote:
> >>> Yes, it's great, but I would rather like to see it packaged as > invariants > >>> of a representation of SL(2,C), not > >>> as invariants of a binary form.
> > -- > > You received this message because you are subscribed to the Google > Groups > > "sage-devel" group. > > To post to this group, send email to sage-...@googlegroups.com<javascript:>.
