Re: [PARI-2.0.x.beta, x>14] Strange behavior of matdet

[Karim BELABAS <Karim.Belabas@math.u-psud.fr>]

> I have noticed the following (cumbersome) problem with matdet, as the title
> suggests it occurs with all the available versions of PARI-2.0.x, with
> x>14. (see below for the config).
> 
> Set 
> 
> P=[-290,107,0,0,0,0,0;-2713,1001,0,0,0,0,0;0,0,-3, 2, -5, 1, -1;0,0,-1,
> -1, -2, -2, -1;0,0,1 , 1,  3,  10,  2;0,0,33,  0,  1,  32, 5;0,0, 1, 
> 1,  3,  -1,  1];
> 
> then 
> 
> (23:41) gp > matdet(P)
> %2 = -2051114900000   <--- Wrong answer ....

A (bad) typo in det() [forget to divide by a pivot in rare cases], indeed
introduced in 2.0.15. Here's a fix.

  Karim.


Index: src/basemath/alglin1.c
===================================================================
RCS file: /home/megrez/cvsroot/pari/src/basemath/alglin1.c,v
retrieving revision 1.1.1.1
diff -c -r1.1.1.1 alglin1.c
*** src/basemath/alglin1.c	1999/09/09 15:48:45	1.1.1.1
--- src/basemath/alglin1.c	1999/09/15 10:49:46
***************
*** 1944,1950 ****
        ck = (GEN*)a[k]; m = (GEN)ck[i];
        if (gcmp0(m))
        {
!         if (!gcmp1(p))
            for (j=i+1; j<=nbco; j++)
            {
              p1 = gmul(p,ck[j]);
--- 1944,1955 ----
        ck = (GEN*)a[k]; m = (GEN)ck[i];
        if (gcmp0(m))
        {
!         if (gcmp1(p))
!         {
!           if (!gcmp1(pprec))
!             a[k] = (long)gdivexact((GEN)a[k], pprec);
!         }
!         else
            for (j=i+1; j<=nbco; j++)
            {
              p1 = gmul(p,ck[j]);
__
Karim Belabas                    email: Karim.Belabas@math.u-psud.fr
Dep. de Mathematiques, Bat. 425
Universite Paris-Sud             Tel: (00 33) 1 69 15 57 48
F-91405 Orsay (France)           Fax: (00 33) 1 69 15 60 19
--
PARI/GP Home Page: http://hasse.mathematik.tu-muenchen.de/ntsw/pari/