conversion of power series with zero bigoh to polynomials

[rwst]

sage: R.<x> = PowerSeriesRing(ZZ)
sage: P.<x> = ZZ[]
sage: r=R([1,1,1,1])
sage: r
1 + x + x^2 + x^3
sage: P(r)
TypeError: unable to coerce <type 'sage.rings.power_series_poly.PowerSeries_poly'> to an integer

Sage power series can have zero bigoh term, and such series are identical to polynomials, so coercion should be no problem.

If we should allow zero bigoh in power series is another matter.

Component: algebra

Author: Ralf Stephan

Branch/Commit: u/rws/ticket/15707 @ 4ea4963

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/15707

[pjbruin]

comment:2

This should be fixed, probably also for series with finite precision, i.e. that do have an O(xⁿ) term. There is already the method r.polynomial() which returns exactly the desired result; we just have to tell P(r) to use this.

[nbruin]

comment:4

Note that this is a conversion problem, not a coercion problem. There should be no coercion from PowerSeriesRing to PolynomialRing at all.
In fact, it may even be acceptable to let conversion from PowerSeriestoPolynomials` simply be truncation: conversion is allowed to just be best effort (this is all completely compatible with Peter's comment above).

[rwst]

comment:7

Agree, after sleeping over it and rereading the documentation.

[rwst]

Branch: u/rws/ticket/15707

[sagetrac-git]

Commit: 22058aa

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

22058aa

Trac #15707: convert power series to polynomial by truncation

[tscrim]

comment:11

I agree with this as well (and it's coherent with what we do with real fields to QQ), but could you add an doctest showing this is fixed?

Thanks,

Travis

[sagetrac-git]

Changed commit from 22058aa to 4ea4963

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

4ea4963

trac #15707: doctest

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:13

LGTM

[tscrim]

Author: Ralf Stephan