Dynatomic polynomials

[David Krumm]

I'm trying to compute dynatomic polynomials over QQ in such a way that they can be coerced to have GF(p) coefficients, the idea being that I'll do this for many primes p so I only want to compute the polynomial once. When I use the following code I don't see how to change the base ring. Any ideas on how to get around this?

K.<c> = FunctionField(QQ)

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

H=Hom(A,A)

f=H([x^2+c])

f.dynatomic_polynomial(3)

[Vincent Delecroix]

Hi,

There are several weirdness there. First of all there are several ways
to deal with function field. One is with FunctionField as you did and
the other one with

sage: R = PolynomialRing(QQ, 'c')
sage: K = R.fraction_field()
sage: c = K.gen()

the method above seems to work better with coercion as you will see.
Then you can repeat what you did

sage: A.<x> = AffineSpace(K,1)
sage: H=Hom(A,A)
sage: f=H([x^2+c])
sage: g = f.dynatomic_polynomial(3)
sage: g.parent()
Fraction Field of Univariate Polynomial Ring in x over Fraction Field
of Univariate Polynomial Ring in c over Rational Field

For the coercion you can then do

sage: K13 = PolynomialRing(GF(13), 'c').fraction_field()
sage: FF13 = PolynomialRing(K13,'x').fraction_field()
sage: FF13(g)
x^6 + x^5 + (3*c + 1)*x^4 + (2*c + 1)*x^3 + (3*c^2 + 3*c + 1)*x^2 +
(c^2 + 2*c + 1)*x + c^3 + 2*c^2 + c + 1

The last line above does not work if you use FunctionField instead...

This might not be the best solution but I hope it helps,
Vincent

2014-08-11 15:35 UTC, David Krumm <david...@gmail.com>:

> --
> 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.
> To post to this group, send email to sage-d...@googlegroups.com.
> To view this discussion on the web visit
> https://groups.google.com/d/msgid/sage-dynamics/cac1fead-83fa-44d6-8ae6-89b053ba401e%40googlegroups.com.
> For more options, visit https://groups.google.com/d/optout.
>

[David Krumm]

That works for me. Thanks!