bug in is_square over number fields

[JohnCremona]

A bug in pari 2.7.1 causes this:

sage: K.<a> = QuadraticField(22)
sage: u = 42*a - 197 # fundamental unit
sage: D = u^14
sage: D.is_square()
MemoryError: Unable to allocate 327680000000 bytes for the PARI stack
(instead, allocated 262144000000 bytes)

This was reported upstream: http://pari.math.u-bordeaux.fr/archives/pari-users-1406/msg00006.html

Upstream fixed this in their git master:

Not a memory issue indeed. The low-level function from the polroots
module that (sharply) estimates the largest modulus of a polynomial
T can't handle the case T(0) = 0 (nor the case where T is constant,
but that's not the issue here...).

It never occurs in the original context of polroots(), but it can occur
in the context of nfroots / nffactor that call it with T := the image
through the successive complex embeddings of our algebraic polynomial.

Fixed in master (2.8.*). Thanks for your report !

Upstream: Fixed upstream, but not in a stable release.

CC: @jdemeyer

Component: packages: standard

Author: Jeroen Demeyer

Branch: dbe9fb5

Reviewer: John Cremona

Issue created by migration from https://trac.sagemath.org/ticket/16894

[jdemeyer]

Description changed:

--- 
+++ 
@@ -8,9 +8,9 @@
 MemoryError: Unable to allocate 327680000000 bytes for the PARI stack
 (instead, allocated 262144000000 bytes)
 ```
-This was reported upstream (to Karim Belabas) who fixed it in pari's main development branch 2.8.*.  It would be good to get the bug fix into Sage sooner.
+This was reported upstream: [http://pari.math.u-bordeaux.fr/archives/pari-users-1406/msg00006.html](http://pari.math.u-bordeaux.fr/archives/pari-users-1406/msg00006.html)
 
-From Karim's email:
+Upstream fixed this in their git master:
 
 ```
 Not a memory issue indeed. The low-level function from the polroots

[jdemeyer]

Author: Jeroen Demeyer

[jdemeyer]

Description changed:

--- 
+++ 
@@ -1,4 +1,4 @@
-A precision bug in pari 2.7.1 causes this:
+A bug in pari 2.7.1 causes this:
 
 ```
 sage: K.<a> = QuadraticField(22)

[jdemeyer]

Branch: u/jdemeyer/ticket/16894

[jdemeyer]

Commit: dbe9fb5

[jdemeyer]

comment:4

This patch fixes the bug, but it causes another doctest failure...

sage -t --long src/sage/rings/number_field/number_field.py
**********************************************************************
File "src/sage/rings/number_field/number_field.py", line 5172, in sage.rings.number_field.number_field.NumberField_generic.?
Failed example:
    Z = K.zeta_function()
Exception raised:
    Traceback (most recent call last):
      File "/usr/local/src/sage-config/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 480, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/usr/local/src/sage-config/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 843, in compile_and_execute
        exec compiled in globs
      File "<doctest sage.rings.number_field.number_field.NumberField_generic.?[1]>", line 1, in <module>
        Z = K.zeta_function()
      File "/usr/local/src/sage-config/local/lib/python2.7/site-packages/sage/rings/number_field/number_field.py", line 5198, in zeta_function
        max_asymp_coeffs=max_asymp_coeffs)
      File "/usr/local/src/sage-config/local/lib/python2.7/site-packages/sage/lfunctions/dokchitser.py", line 342, in init_coeffs
        self._gp_eval(pari_precode)
      File "/usr/local/src/sage-config/local/lib/python2.7/site-packages/sage/lfunctions/dokchitser.py", line 243, in _gp_eval
        raise RuntimeError("Unable to create L-series, due to precision or other limits in PARI.")
    RuntimeError: Unable to create L-series, due to precision or other limits in PARI.
**********************************************************************

---

New commits:

dbe9fb5

Trac #16894: fix PARI nffactor() bug

[jdemeyer]

comment:5

False alarm, the doctest failure was because I forgot to run make.

[JohnCremona]

comment:6

Thanks, Jeroen. I will test this.

[jdemeyer]

Reviewer: John Cremona