[sage-support] Symmetric polynomials over a ring of polynomials

Hi all, I am new to sage, so please forgive me if this is a trivial question. I am trying to express certain polynomials, which are symmetric in a subset of the variables, in terms of elementary symmetric polynomials on the symmetric subset (with coefficients that are polynomials in the other

[sage-support] Method to invert the birational map from degree 3 curve to its Weierstrass form?

I was happy to see that Sage gives you the explicit map between your cubic to its Weierstrass form. However, rather than having to do so by hand, I was wondering if Sage is capable of giving the map from the Weierstrass form to the original cubic, since I'd like a quick way of finding rational

[sage-support] Re: Method to invert the birational map from degree 3 curve to its Weierstrass form?

Its a 4:1 map so you can't invert it... On Saturday, May 24, 2014 4:45:11 PM UTC+1, diophan wrote: Defn: Defined on coordinates by sending (x : y : z) to (1/8*x*y - 1/16*y^2 - 1/8*y*z : -x^2 + 1/8*x*y + 3/16*y^2 + x*z + 3/8*y*z : -1/256*y^2) -- You received this message because

[sage-support] Re: Method to invert the birational map from degree 3 curve to its Weierstrass form?

Sorry, early weekend and the brain isn't working yet. The documentation says if morphism=True is passed, then a birational equivalence between F and the Weierstrass curve is returned. If the point happens to be a flex, then this is an isomorphism and I wasn't thinking. If I find the flex point

[sage-support] Re: aleph server down?

Thanks to you, Keith! -- Share_The_Sage! On Saturday, May 24, 2014 1:03:21 AM UTC-3, Keith Clawson wrote: Hi, I fixed the problem (it was an incorrect IP address). Thanks, Keith On Friday, May 23, 2014 3:59:50 PM UTC-7, share the sage wrote: Hi sage community! Right now aleph

[sage-support] Re: Method to invert the birational map from degree 3 curve to its Weierstrass form?

On Saturday, May 24, 2014 9:18:29 AM UTC-7, Volker Braun wrote: Its a 4:1 map so you can't invert it... I would find that surprising. For a general plane cubic, there are good recipes for getting a 9:1 map to a Weierstrass model in general and a 1:1 map when a rational point is specified. A

[sage-support] Re: Method to invert the birational map from degree 3 curve to its Weierstrass form?

Yes I just started looking at this again about an hour ago. It looks like the way Sage gets the map is only by doing linear changes of coordinates on P^2 and a Cremona, as outlined here:

[sage-support] Re: Method to invert the birational map from degree 3 curve to its Weierstrass form?

To get back to the question, did you find the inverse by hand or is there something in Sage to help out? I have potentially a large number of cubics I'd like to carry this out with and if there's a way to avoid doing it by hand each time that'd be great. On Saturday, May 24, 2014 4:38:48 PM

[sage-support] Re: Method to invert the birational map from degree 3 curve to its Weierstrass form?

diophan wrote: To get back to the question, did you find the inverse by hand or is there something in Sage to help out? I have potentially a large number of cubics I'd like to carry this out with and if there's a way to avoid doing it by hand each time that'd be great. Ahem, ever heard of tab

[sage-support] Re: Method to invert the birational map from degree 3 curve to its Weierstrass form?

On Saturday, May 24, 2014 9:38:48 PM UTC+1, Nils Bruin wrote: You'd expect that from a y^2=quartic in x model. Yes, I was thinking about the degree-2 case... which is also implemented btw ;-) -- You received this message because you are subscribed to the Google Groups sage-support group.