On 2015-04-28 20:59, Nils Bruin wrote:
On Tuesday, April 28, 2015 at 11:25:07 AM UTC-7, Joao Alberto de Faria
wrote:
The problem is that this issue also occurs for
R.<x>=Qp(5)[]
f=x^2
f.factor(), I was trying to fiddle with it and accidently copied the
wrong code
its trailing coefficient is 0
No, it's not, the trailing coefficient is O(5^20):
sage: R.<x> = Qp(5)[]
sage: f = x^2
sage: parent(f[0])
5-adic Field with capped relative precision 20
This polynomial could have been an approximation of (x^2 + 5^21), which
is irreducible.
Precisely to avoid these issues, polynomials over QQ have a
factor_padic() method which assumes that the input is exact:
sage: R.<x> = QQ[]
sage: f = x^2
sage: f.factor_padic(5,20)
((1 + O(5^20))*x + (O(5^20)))^2
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