#5236: [with patch, needs review] x^(-pm) in ramified extensions of Qp
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Reporter: roed | Owner: roed
Type: defect | Status: new
Priority: major | Milestone: sage-4.0
Component: basic arithmetic | Keywords: padics, exponentiation
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Description changed by roed:
Old description:
> This is probably a problem with some of the shifting code in
> pow_computer_ext, since it only occurs when raising an element to a power
> that's a negative multiple of p. pow_computer_ext needs cleaning up and
> doctesting anyway.
> {{{
> sage: W.<w> = Qp(5,6).ext(x^2+5)
> sage: (5+w)^-4
> w^-4 + 4*w^-3 + 3 + 2*w + 3*w^2 + 3*w^5 + w^6 + O(w^8)
> sage: (5+w)^-5
> RuntimeError: ZZ_p: division by non-invertible element
> sage: W(5)^-5
> 4*w^-10 + w^-8 + O(w^2)
> sage: w^-5
> w^-5 + O(w^7)
> sage: (1+w)^-5
> RuntimeError: ZZ_p: division by non-invertible element
> sage: (1+w)^5
> 1 + 4*w^3 + 3*w^4 + O(w^12)
> sage: (1+w)^-7
> 1 + 3*w + 3*w^2 + 3*w^3 + 3*w^6 + 3*w^7 + 2*w^8 + w^9 + 3*w^10 + O(w^12)
> sage: (1+w)^-10
> RuntimeError: ZZ_p: division by non-invertible element
> }}}
New description:
Depends on 5105 and 5778.
{{{
sage: W.<w> = Qp(5,6).ext(x^2+5)
sage: (5+w)^-4
w^-4 + 4*w^-3 + 3 + 2*w + 3*w^2 + 3*w^5 + w^6 + O(w^8)
sage: (5+w)^-5
RuntimeError: ZZ_p: division by non-invertible element
sage: W(5)^-5
4*w^-10 + w^-8 + O(w^2)
sage: w^-5
w^-5 + O(w^7)
sage: (1+w)^-5
RuntimeError: ZZ_p: division by non-invertible element
sage: (1+w)^5
1 + 4*w^3 + 3*w^4 + O(w^12)
sage: (1+w)^-7
1 + 3*w + 3*w^2 + 3*w^3 + 3*w^6 + 3*w^7 + 2*w^8 + w^9 + 3*w^10 + O(w^12)
sage: (1+w)^-10
RuntimeError: ZZ_p: division by non-invertible element
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5236#comment:10>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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