Opened 11 years ago

Closed 11 years ago

#5573 closed defect (fixed)

[with patch; positive review] genus2reduction interface has at least two problems

Reported by: was Owned by: was
Priority: major Milestone: sage-3.4.1
Component: number theory Keywords:
Cc: Merged in:
Authors: Reviewers:
Report Upstream: Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description (last modified by mabshoff)

On Thu, Mar 19, 2009 at 6:14 PM, ARMAND BRUMER wrote:
> Hi William,
>
> This is my first attempt to use sage. I have OSX 10.4.11 
> and just downloaded it.
>
> I wanted to use liu's program. After trying out your 
> examples and getting the same result, I tried the example 
> I was curious about and here is the output. Can you do better. 
> Did I screw up?
>
> Thanks,
> armand

The code:

sage: genus2reduction(x^3 + x^2 + x,-2*x^5 + 3*x^4 - x^3 - x^2 - 6*x - 2)
--------------------------------------------------------------------------- 
ValueError                                
Traceback (most recent call last)

William replies: You have found a bug in Sage. When I try the above by directly using Liu's program (note that i have to remove the spaces in the polynomials and use an explanation point to run the program), I get the following problem:

sage: !genus2reduction
enter Q(x) : x^3+x^2+x        
enter P(x) : -2*x^5+3*x^4-x^3-x^2-6*x-2
 
factorization CPU time = 5
a minimal equation over Z[1/2] is : 
y^2 = x^6+18*x^3+36*x^2-27
 
factorization of the minimal (away from 2) discriminant : 
[2,1;3,15;53,1]
 
p=2
(potential) stable reduction :  (II), j=1
reduction at p : [I{1-0-0}] page 170, (1), f=1
p=3
(potential) stable reduction :  (I)
reduction at p :   ***   expected character: ',' instead of: mod(y,y^2-3)

I don't know if this ever worked, but I bet it did, and PARI changed from 2004 or whatever, until now, and we just didn't pick up the change because we didn't test genus2reduction enough.

  1. A second problem is that if genus2reduction works once, then fails, then it fails to work again:
    sage: R = genus2reduction(x^3 - 2*x^2 - 2*x + 1, -5*x^5)
    sage: R.conductor
    1416875
    sage: R = genus2reduction(x^3 + x^2 + x,-2*x^5 + 3*x^4 - x^3 - x^2 - 6*x - 2)
    Traceback (most recent call last):
    ValueError: error in input; possibly singular curve? 
    (Q=x^3 + x^2 + x, P=-2*x^5 + 3*x^4 - x^3 - x^2 - 6*x - 2)
    sage: R = genus2reduction(x^3 - 2*x^2 - 2*x + 1, -5*x^5)  # just worked above
    Traceback (most recent call last):
    ...
    ValueError: error in input; possibly singular curve? 
    (Q=x^3 - 2*x^2 - 2*x + 1, P=-5*x^5)
    

When we fix this, we will of course have to write code to run through random curves and verify that genus2reduction works sensibly on millions of inputs.

Liu's program genus2reduction, included with Sage, is a C program that is written to use the Pari C library.

Attachments (1)

trac_5573.patch (1.5 KB) - added by was 11 years ago.

Download all attachments as: .zip

Change History (7)

Changed 11 years ago by was

comment:1 Changed 11 years ago by was

  • Summary changed from genus2reduction interface has at least two problems to [with patch; needs review] genus2reduction interface has at least two problems

comment:2 Changed 11 years ago by was

 Basically you should just do (make sure lines don't break when the shouldn't):

$ sage -f http://sage.math.washington.edu/home/wstein/patches/genus2reduction-0.3.p5.spkg 

$ sage
...
sage: hg_sage.apply('http://trac.sagemath.org/sage_trac/attachment/ticket/5573/trac_5573.patch')
sage: quit

$ sage -br
...

comment:3 Changed 11 years ago by mabshoff

  • Description modified (diff)

comment:4 Changed 11 years ago by mabshoff

Patch looks good, I need to have the changes in the spkg explained to me to review this :). William hinted about a change in the pari library.

Cheers,

Michael

comment:5 Changed 11 years ago by mabshoff

Spkg and patch look good. Positive review. William did explain the mod/Mod change that fixed the issue in the spkg.

Cheers,

Michael

comment:6 Changed 11 years ago by mabshoff

  • Resolution set to fixed
  • Status changed from new to closed
  • Summary changed from [with patch; needs review] genus2reduction interface has at least two problems to [with patch; positive review] genus2reduction interface has at least two problems

Reviewed in Sage 3.4.1.rc1.

Cheers,

Michael

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