bug with polynomials over power series

[kedlaya]

The first computation of z^2 is incorrect, whereas the second is correct:

sage: C.<t> = PowerSeriesRing(ZZ)
sage: D.<s> = PolynomialRing(C)
sage: z = (1 + O(t)) + t*s^2
sage: z^2
 t^2*s^4 + 1 + O(t)
sage: z._mul_generic(z)
 t^2*s^4 + (2*t + O(t^2))*s^2 + 1 + O(t)

CC: @burcin

Component: basic arithmetic

Keywords: polynomials, power series, Karatsuba

Issue created by migration from https://trac.sagemath.org/ticket/3056

[kedlaya]

Changed keywords from none to polynomials, power series, Karatsuba

[kedlaya]

comment:1

A bit of experimentation by David Harvey suggests that _mul_karatsuba is at fault.

[kedlaya]

comment:2

In my previous example:

sage: (z^2).list()
 [1 + O(t), O(t^1), O(t^1), 0, t^2]

so the output is not actually incorrect, just less precise than it should be. So maybe we should not use Karatsuba for polynomials over an inexact ring? (We already don't for polynomials over a p-adic ring.)