On Sun, Dec 19, 2010 at 9:39 PM, John H Palmieri wrote:
> On Dec 19, 7:01 pm, Alex Raichev wrote:
>> Hi all:
>>
>> I get differently formatted answers using factor() multiple times on
>> the same polynomial. I wouldn't call it a bug, but it sure is
>> annoying when doctesting.
>>
>> Alex
>>
>> --
>> | Sage Version 4.6, Release Date: 2010-10-30 |
>> | Type notebook() for the GUI, and license() for information. |
>> --
>> sage: R.= PolynomialRing(QQ)
>> sage: H= x^2*y^4 +y^6 +2*x^3*y^2 +2*x*y^4 -7*x^4 +7*x^2*y^2 +14*y^4
>> +6*x^3 +6*x*y^2 +47*x^2 +47*y^2
>> sage: for k in range(20):
>> : print H.factor()
>> :
>> (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47)
>> (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47)
>> (x^2 + y^2) * (y^4 + 2*x*y^2 - 7*x^2 + 14*y^2 + 6*x + 47)
>> (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47)
>> (x^2 + y^2) * (y^4 + 2*x*y^2 - 7*x^2 + 14*y^2 + 6*x + 47)
>> (x^2 + y^2) * (y^4 + 2*x*y^2 - 7*x^2 + 14*y^2 + 6*x + 47)
>> (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47)
>> (x^2 + y^2) * (y^4 + 2*x*y^2 - 7*x^2 + 14*y^2 + 6*x + 47)
>> (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47)
>> (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47)
>> (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47)
>> (x^2 + y^2) * (y^4 + 2*x*y^2 - 7*x^2 + 14*y^2 + 6*x + 47)
>> (x^2 + y^2) * (y^4 + 2*x*y^2 - 7*x^2 + 14*y^2 + 6*x + 47)
>> (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47)
>> (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47)
>> (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47)
>> (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47)
>> (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47)
>> (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47)
>> (x^2 + y^2) * (y^4 + 2*x*y^2 - 7*x^2 + 14*y^2 + 6*x + 47)
>
> Well, you could do
>
> sage: all([H==H.factor().prod() for k in range(20)])
> True
>
> to doctest it. (I'm assuming that the "prod" method just does basic
> multiplication, and so its implementation has nothing to do with that
> of "factor", so "H==H.factor().prod()" actually tests something
> meaningful.)
+1
Probably worth noting the number of factors as well, e.g.
sage: factorization = H.factor()
sage: len(factorization)
2
sage: prod(factorization) == H
True
- Robert
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