Galois group when polynomial has too high degree

[jm58660]

In 5.4, with KASH installed:

NumberField(x^21-2, 'a').galois_group(type="pari").order()

gives answer 252, but with

NumberField(x^22-2, 'a').galois_group(type="pari").order()

I got

Error, the variable '_s_' must have a value

I guess this relates to kash interface.

Component: number fields

Author: Jori Mäntysalo

Branch/Commit: a755205

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/13810

[jm58660]

comment:1

Tested with 5.10: After trying R.=QQ[]; (x^23-2).galois_group().order() I can't calculate for example R.=QQ[]; (x^20-2).galois_group().order(). It seems that internal(?) kash instance fails and Sage don't notice it. User must restart worksheet to get this running again.

[jm58660]

comment:4

In 5.13beta1 with kash package

NumberField(x^15-2, 'a').galois_group(type="pari").order()

gives

ValueError: Index n must be in {1,..,None}

[jm58660]

comment:7

With sage-6.3 this is slightly more buggy: Trying to with 23. degreee polynomial sage says "Kash crashed -- automatically restarting." but system does not restart kash.

[jm58660]

Branch: u/jmantysalo/galois_group_when_polynomial_has_too_high_degree

[jm58660]

Commit: cbc8acd

[jm58660]

comment:9

There has been some other modifications on src/sage/rings/polynomial/polynomial_rational_flint.pyx that conflicts with this patch.

In any case, http://page.math.tu-berlin.de/~kant/.3a6ca5.html clearly says that polynomials up to degree 23 are supported. But just changing given example x_O:=MaximalOrder(X^2+5); Galois(x_O); to have x^23+5 gives segfault and degree 22 get stuck. So I suggests trying KASH only when degree <= 21.

---

New commits:

cbc8acd

Changed limit of using KASH from <=23 to <=21.

[sagetrac-git]

Changed commit from cbc8acd to f9ab830

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

a755205

Changed the limit from 23 to 21.

[sagetrac-git]

Changed commit from f9ab830 to a755205

[jm58660]

comment:12

As also the web page http://page.math.tu-berlin.de/~kant/kash.html has been changed to "polynomials over Q up to degree 21" (from 23), I think this is clearly the right thing to do.

[jm58660]

Author: Jori Mäntysalo

[nathanncohen]

comment:13

I am getting tired of your adding me in Cc of your ticket every single time you want a review.

Nathann

[jm58660]

comment:14

Replying to @nathanncohen:

I am getting tired of your adding me in Cc of your ticket every single time you want a review.

OK, I'll stop doing that. Sorry.

[fchapoton]

Reviewer: Frédéric Chapoton

[vbraun]

Changed branch from u/jmantysalo/galois_group_when_polynomial_has_too_high_degree to a755205