Begin forwarded message:

> From: Genya Zaytman <[EMAIL PROTECTED]>
> Date: March 31, 2008 1:15:21 PM EDT
> To: David Harvey <[EMAIL PROTECTED]>
> Subject: Fwd: Multivariate Polynomial Factoring is Broken
>
>
> Begin forwarded message:
>> From: Genya Zaytman <[EMAIL PROTECTED]>
>> Date: March 31, 2008 1:14:39 PM EDT
>> Subject: Multivariate Polynomial Factoring is Broken
>>
>> sage: version()
>> 'SAGE Version sage-2.11, Release Date: 2008-03-30'
>> sage: q = 1073741789
>> sage: T.<aa, bb> = PolynomialRing(GF(q))
>> sage: f = aa^2 + 12124343*bb*aa + 32434598*bb^2; f
>> aa^2 + 12124343*aa*bb + 32434598*bb^2
>> sage: f.factor()
>> (32434598) * (16373350*aa^2 + 437239695*aa*bb + bb^2)
>> sage: g = (32434598) * (16373350*aa^2 + 437239695*aa*bb + bb^2); g
>> aa^2 - 49344938*aa*bb + 32434598*bb^2
>> sage: f == g
>> False
>>
>


So basically, in the example above, we factor a homogeneous degree 2  
polynomial in two variables, multiply it back out and get a different  
answer.

david


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