Re: the minimal polynomial over the composite field

[macsyma <macsyma@yahoo.co.jp>]

----- Original Message -----

> From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>
> To: macsyma <macsyma@yahoo.co.jp>
> Cc: "pari-users@pari.math.u-bordeaux.fr" <pari-users@pari.math.u-bordeaux.fr>
> Date: 2019/10/9, Wed 21:33
> Subject: Re: the minimal polynomial over the composite field
> 
> On Wed, Oct 09, 2019 at 12:46:15PM +0900, macsyma wrote:
>>  Factoring by galoisfixedfield(,,2) is attractive, 
>>  but it seems time-consuming to put together preparations for that.
> 
> This is true. galoissplittinginit is doing much more initialization
> that what you need. You need much smaller bound.
> 
>>  > Also your example x^n-2 are very sparse which make computation
>>  > faster compared to generic example.
>>  How about 2*(1+x)^n-x^n (dense and having an isomorphic splitting field) ? 
> 
> This is not a good idea: polredbest will reduce it to x^25-2 in 104ms.
> 
> I think you should allow for the number field discriminant to get
> larger, not the model.
> 
> I am concerned that optimizing the program for such easy case will
> make it slower when trying large example.
> 
> I suggest you try polynomial from Klüners-Malle database:
> <http://galoisdb.math.upb.de >
> You can search for the property 'is solvable'.
> 
> Cheers,
> Bill.
> 

Thank you for the information.
> <http://galoisdb.math.upb.de >
I often use this site, its links, and GAP's libraries, 
of course your GALPOL, as useful sample resources.

By the way, is this a bug ?

for(d=2,50,
  for(i=1,galoisgetpol(d),printf([d,i]);
    galoissplittinginit(galoisgetpol(d,i)[1])));

[2,1][3,1][4,1][4,2][5,1][6,1][6,2][7,1]
  ***   at top-level: ...sgetpol(d),printf([d,i]);galoissplittinginit(g
  ***                                             ^---------------------
  *** galoissplittinginit: the PARI stack overflows !

macsyma