[sage-support] decomposition of fractional ideals (converting PARI to SAGE)

[Chan-Ho]

Hi All,

This is a continuation of the question
http://www.mail-archive.com/sage-s...@googlegroups.com/msg16973.html

I am trying to decompose a fractional ideal into primes in a number
field (I use online SAGE.)

I have a Number Field in a2 with defining polynomial
x^6 - 15*x^5 - 514*x^4 + 5312*x^3 + 83552*x^2 - 422208*x - 4272768
and want to decompose Fractional ideal (3).
(SAGE can check this is not a prime ideal.)
However, "factor()" or "prime_above()" did not work because of the
Minkowski bound error.

Thus, I tried to compute this using the following code:

K_f2_bnf = gp(K_f2.pari_bnf()) ; K_f2_bnf ;
ideal = K_f2_bnf.idealprimedec(3) ; ideal ;
ideal1 = K_f2_bnf.idealprimedec(3)[1] ; ideal1 ;
ideal2 = K_f2_bnf.idealprimedec(3)[2] ; ideal2 ;
ideal3 = K_f2_bnf.idealprimedec(3)[3] ; ideal3 ;
ideal4 = K_f2_bnf.idealprimedec(3)[4] ; ideal4

I think that this code does not make errors, and the output was the
following.

[3, [215, 8, 2, 2, 0, 2]~, 1, 2, [0, -1, -1, -1, 0, -1]~]

To change this output (PARI ideals) to SAGE (SAGE ideals), I used

from sage.rings.number_field.number_field_ideal import
convert_from_idealprimedec_form ;
convert_from_idealprimedec_form(K_f2, ideal1)

But the Minkowski error occured again here.
This means that the Minkowski error comes from the translation between
PARI and SAGE?
Is there a better method to compute this in SAGE?

Cheers,

Chan-Ho

--
To post to this group, send email to sage-s...@googlegroups.com
To unsubscribe from this group, send email to sage-support...@googlegroups.com
For more options, visit this group at http://groups.google.com/group/sage-support
URL: http://www.sagemath.org

[Chan-Ho]

Hi All,

I am now at the SAGE22 workshop and directly asked William Stein
concerning this.
He showed me a line

proof.number_field(False)

Then we can turn off the certification process and the decomposition
may work.

Thanks,

Chan-Ho

On May 7, 10:20 am, Chan-Ho <chanho.m...@gmail.com> wrote:
> Hi All,
>

> This is a continuation of the questionhttp://www.mail-archive.com/sage-s...@googlegroups.com/msg16973.html