Galois group when polynomial has too high degree

[jmantysalo]

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.

[jmantysalo]

Tested with 5.10: After trying R.<x>=QQ[]; (x^{23-2).galois_group().order() I can't calculate for example R.<x>=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.

[jmantysalo]

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}

[jmantysalo]

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.

[jmantysalo]

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.

[git]

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

[git]

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

​a755205

Changed the limit from 23 to 21.

[jmantysalo]

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.

[ncohen]

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

Nathann

[jmantysalo]

Replying to ncohen:

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.