PARI-backed LaurentSeries truncates exact polynomials to default precision

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On 9.5.rc3:

sage: R.<z> = LaurentSeriesRing(QQ, implementation='pari')
sage: z^-2
z^-2 + O(z^18)

This happens because construct_from_pari in power_series_pari.pyx expands all t_RFRAC elements to a power series using the parent ring's default precision (usually 20). However, this needlessly reduces the precision when the t_RFRAC has denominator one, i.e., is actually a polynomial and can therefore be represented exactly as a power series. The fix is very simple: Check if the denominator equals 1.

(This behaviour was identified as the root cause for the following loss of precision:)

sage: E = EllipticCurve(GF(257^2), [5,5])
sage: E.weierstrass_p(prec=50, algorithm='fast')
z^-2 + 256*z^2 + 36*z^4 + 86*z^6 + 107*z^8 + 126*z^10 + 119*z^12 + 4*z^14 + 54*z^16 + 216*z^18 + 212*z^20 + 185*z^22 + 100*z^24 + 85*z^26 + 3*z^28 + 10*z^30 + 53*z^32 + 26*z^34 + 163*z^36 + 144*z^38 + 176*z^40 + 121*z^42 + 163*z^44 + 241*z^46 + 82*z^48 + O(z^50)
sage: E.weierstrass_p(prec=50, algorithm='pari')
z^-2 + 256*z^2 + 36*z^4 + 86*z^6 + 107*z^8 + 126*z^10 + 119*z^12 + 4*z^14 + 54*z^16 + O(z^18)
sage: E.weierstrass_p(prec=50, algorithm='quadratic')
z^-2 + 256*z^2 + 36*z^4 + 86*z^6 + 107*z^8 + 126*z^10 + 119*z^12 + 4*z^14 + 54*z^16 + O(z^18)

Component: algebra

Author: Lorenz Panny

Branch/Commit: 9eb2145

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/33224

[yyyyx4]

Commit: 542ab86

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Author: Lorenz Panny

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Branch: public/33224

[yyyyx4]

New commits:

d27cdc7	keep infinite precision when computation is exact
542ab86	add test for #33224

[sagetrac-git]

Changed commit from 542ab86 to 9eb2145

[sagetrac-git]

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

9eb2145

we should take the denominator of the input, not its type :|

[fchapoton]

Reviewer: Frédéric Chapoton

[fchapoton]

comment:6

ok, looks good enough

[vbraun]

Changed branch from public/33224 to 9eb2145