Hi,
This is about a bug I found in PARI's Hermite Normal Form when testing my new
Hermite Normal Form, and a fix from them.
William
---------- Forwarded message ----------
From: Karim Belabas <[EMAIL PROTECTED]>
Date: Feb 18, 2008 2:49 AM
Subject: Re: Bug#741: Fwd: bug in PARI's mathnf function
To: William Stein <[EMAIL PROTECTED]>, [EMAIL PROTECTED]
* William Stein [2008-02-16 23:47]:
> Package: pari
> Version: 2.3.3
[...]
> PARI sometimes puts negative numbers in the *output* of mathnf(a, 1)[0],
> which is a bug.
Indeed.
> * I didn't use mathnf(b) directly (the default option), since
> already for a 20x18 matrix it
> is too slow to be useful.
As documented.
[ Actually, I am going to change this: I don't see the point in defaulting
to a slow routine; let mathnf choose depending on the matrix size.
It should either call matdetint + mathnfmod, or mathnf(,1) ]
> * I'm guessing maybe mathnf(b, 1) uses the modular hnf modulo the
> determinant.
Actually, no; mathnfmod does that.
> If not, maybe you just need to add mutliples of rows until everything
> is correctly normalized.
We do that, with one optimization too many which sometimes cancelled the
normalization step ( when the kernel is non trivial and we are "lucky":
a coefficient which we want to set to 0 is already 0 ).
It is fixed in both stable and unstable branches. I am attaching the
(trivial) patch.
Thanks for your report !
K.B.
--
Karim Belabas Tel: (+33) (0)5 40 00 26 17
IMB, Universite Bordeaux 1 Fax: (+33) (0)5 40 00 69 50
351, cours de la Liberation http://www.math.u-bordeaux.fr/~belabas/
F-33405 Talence (France) http://pari.math.u-bordeaux.fr/ [PARI/GP]
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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Index: src/basemath/alglin2.c
===================================================================
--- src/basemath/alglin2.c (revision 9574)
+++ src/basemath/alglin2.c (working copy)
@@ -3082,11 +3082,9 @@
for (i=h[j]; i; i--)
{
a = gcoeff(A,i,j);
- if (!signe(a)) continue;
-
k = c[i];
- ZV_elem(a,gcoeff(A,i,k), A,B, j,k);
- ZM_reduce(A,B, i,k);
+ if (signe(a)) ZV_elem(a,gcoeff(A,i,k), A,B, j,k);
+ ZM_reduce(A,B, i,k); /* ensure non-negative entries, even if a = 0 */
if (low_stack(lim, stack_lim(av1,1)))
{
if (DEBUGMEM>1) pari_warn(warnmem,"hnfall[3], j = %ld", j);
