Bill Allombert on Fri, 12 Nov 1999 12:12:27 +0100 (MET)

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Re: nfgaloisconj() remark


you snip the bad part of the manual:

  ***   Warning: conjugates list may be incomplete in nfgaloisconj.
%7 = [x, 1/2*x^3 - 1/2*x^2 - 5/2*x + 1]~
nf can be simply a polynomial with flag 0,2 and 4, meaning:
0: use combination of flag 4 and 2, not always complete (but a warning is
issued when the list is not proven complete); 2 & 4: same meaning and
restrictions. Note that only flag 4 can be applied to fields of large degrees
(approx. >= 20).  

? nfgaloisconj(nfinit(x^4-x^3-5*x^2+2*x+4),0)
%2 = [x, 1/2*x^3 - 1/2*x^2 - 5/2*x + 1]~

So there are no bugs, and the result is indeed complete.

The warning is issued because the Van der Waerden-Cebotarev test fails,
because bounds used are much too small.

This will be corrected when fast simplefactmod function will be implemented.

You can patch with 

   nbmax = n + (n >> 1) + 1;
+  if (nbmax < 12) nbmax=13;

in galconj.c:numberofconjugates() , but it is rather a bad fix.