#15422: factorization of non-squarefree polynomials over the p-adics
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Reporter: jdemeyer | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-5.13
Component: padics | Resolution:
Keywords: | Merged in:
Authors: Jeroen Demeyer | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #9640 | Stopgaps:
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Description changed by jdemeyer:
Old description:
> 1) The following should be an `ArithmeticError` since whether or not the
> polynomial factors depends on the `O(3^20)` error term (`t^2 - 3^20`
> factors while `t^2 - 3^21` does not):
> {{{
> sage: R.<t> = PolynomialRing(Qp(3))
> sage: (t^2).factor()
> ((1 + O(3^20))*t + (O(3^20)))^2
> }}}
>
> 2) The following should directly call PARI's `factorpadic` without
> coercing the coefficients to `Qp` first:
> {{{
> sage: R.<t> = PolynomialRing(QQ)
> sage: ((t-1)^2).factor_padic(3,5)
> (1 + O(3^5))*t^2 + (1 + 2*3 + 2*3^2 + 2*3^3 + 2*3^4 + O(3^5))*t + (1 +
> O(3^5))
> }}}
New description:
1) The following should be an `ArithmeticError` since whether or not the
polynomial factors depends on the `O(3^20)` error term (`t^2 - 3^20`
factors while `t^2 - 3^21` does not):
{{{
sage: R.<t> = PolynomialRing(Qp(3))
sage: (t^2).factor()
((1 + O(3^20))*t + (O(3^20)))^2
}}}
2) The following should directly call PARI's `factorpadic` without
coercing the coefficients to `Qp` first:
{{{
sage: R.<t> = PolynomialRing(QQ)
sage: ((t-1)^2).factor_padic(3,5)
(1 + O(3^5))*t^2 + (1 + 2*3 + 2*3^2 + 2*3^3 + 2*3^4 + O(3^5))*t + (1 +
O(3^5))
}}}
The attached patch also does some clean-up of the various p-adic
polynomial classes, now `_repr()` and `_factor()` are implemented in
exactly one place. One consequence of this is that `_repr()` for
polynomials over `Zp` has changed: non-exact zeros are now printed.
'''Apply''' [attachment:15422_factorpadic.patch]
--
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Ticket URL: <http://trac.sagemath.org/ticket/15422#comment:9>
Sage <http://www.sagemath.org>
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