On Sun, Apr 5, 2009 at 9:49 PM, ARMAND BRUMER <bru...@fordham.edu> wrote:
> Hi William,
>
> I just did everything as you suggested and got no errors.
>
> Still the following polynomials caused problems with genus2reduction(0,f).
> So the pari connection is not fixed...
>
>
> f1=x^6 + 4*x^5 - 24*x^4 - 16*x^3 - 52*x^2 - 48*x
> f2=x^6 + 4*x^5 + 24*x^4 + 32*x^3 + 56*x^2 + 48*x + 24
> f3=24*x^5 + 56*x^4 + 76*x^3 + 33*x^2 - 4*x - 20
> f4=-3*x^6 + 6*x^5 - 25*x^4 + 36*x^3 - 69*x^2 + 38*x - 39
>
> Good night from this end!
>
This is a bug in genus2reduction that doesn't have anything to do with
the pari problem that I *did* fix. Calling genus2reduction directly
yields "bug28", which looks serious:
------------------------------------------
sage: !genus2reduction
enter Q(x) : 0
enter P(x) : x^6+4*x^5-24*x^4-16*x^3-52*x^2-48*x
factorization CPU time = 7
a minimal equation over Z[1/2] is :
y^2 = 729*x^6+2268*x^5+2664*x^4+1520*x^3+428*x^2+48*x
factorization of the minimal (away from 2) discriminant :
[2,34;3,16;5,1]
p=2
(potential) stable reduction : (V), j1+j2=0, j1*j2=0
p=3
(potential) stable reduction : (VII)
reduction at p : bug28
------------------------------------------
This could be very hard to fix, except maybe for Qing Liu, who isn't
looking at this stuff anymore.
> The improvement is that sage is willing to do another example,
> interactively, after running into one of these. Of course, a program running
> into such examples would stop!
Sage has a something called "exception handling", which you might like
very much. You can write scripts that will *never* stop even if they
hit almost arbitrary errors in Sage. Watch this (note that the
indentation is important):
Run this code:
R.<x> = ZZ[]
data = []
for i in range(300):
f = R.random_element(degree=6)
try:
data.append((f,genus2reduction(0,f)))
except Exception, msg:
data.append((f, 'fail'))
Then:
sage: len(data)
300
sage: len([z for z in data if z[1] != 'fail'])
276
Read more about try/except here:
http://docs.python.org/tutorial/errors.html
William
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