Dynatomic polynomials in Sage 6.4.1

[David Krumm]

The following code works in Sage 6.2 but does not work in 6.4.1. Could anyone suggest a way to fix this? When I input this code in Sage 6.4.1 I get the message"TypeError: keys do not match self's parent.

K.<c> = FunctionField(QQ)

A.<x> = AffineSpace(K,1)

f = Hom(A,A)([x^2 + c])

f.dynatomic_polynomial(4)

Thanks,

David

[Ben]

Hi David,
It looks like there are two underlying errors that were introduced
when fixing other things. One is in homogenize for affine morphisms,
which will be a trivial fix and I'll do it shortly (as soon as I finish
the ticket I'm currently working on). However, there is also an issue
with FunctionFields, so just switching to projective space does not fix
the issue. I'm not sure of the fix for that one yet.

In the short term, if you just want a symbolic dynatomic polynomial for
x^2+c, this works for polynomial rings

K.<c> = PolynomialRing(QQ)

A.<x> = AffineSpace(K,1)
f = Hom(A,A)([x^2 + c])
f.dynatomic_polynomial(4)

btw, you may be interested that we are currently working on using your
numberfield point algorithm for an enumeration of projective and affine
points and a naive point search for schemes (Trac #17386)

> --
> You received this message because you are subscribed to the Google
> Groups "sage-dynamics" group.
> To unsubscribe from this group and stop receiving emails from it, send
> an email to sage-dynamic...@googlegroups.com
> <mailto:sage-dynamic...@googlegroups.com>.
> To post to this group, send email to sage-d...@googlegroups.com
> <mailto:sage-d...@googlegroups.com>.
> To view this discussion on the web visit
> https://groups.google.com/d/msgid/sage-dynamics/1c77b91d-e44a-4ea4-aea0-c4d34b6a7411%40googlegroups.com
> <https://groups.google.com/d/msgid/sage-dynamics/1c77b91d-e44a-4ea4-aea0-c4d34b6a7411%40googlegroups.com?utm_medium=email&utm_source=footer>.
> For more options, visit https://groups.google.com/d/optout.

[Ben]

This is now tickets 17356 and 17353

On 12/21/2014 12:17 AM, David Krumm wrote:

[David Krumm]

Dear Ben,

Thanks!  I thought I'd also mention a couple things regarding enumeration of points of bounded height. First, I wrote a paper on the case of projective spaces, generalizing the earlier paper for number fields:

http://www.cmc.edu/pages/faculty/DKrumm/research/papers/Pn_bdd_height.pdf

Also, maybe you should ask Charlotte Turner (former student of Cremona) where she got on this problem. If I recall correctly, her thesis was about an algorithm for listing points of bounded height on varieties over number fields, and she had Sage code for that.

-David