Opened 14 months ago

#19989 new defect

asymptotics for multivariate generating functions: zero division error on last coordinate

Reported by: dkrenn Owned by:
Priority: major Milestone: sage-7.1
Component: asymptotic expansions Keywords:
Cc: Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: #10519 Stopgaps:

Description

    sage: R.<x,y,t> = PolynomialRing(QQ)
    sage: FFPD = FractionWithFactoredDenominatorRing(R)
    sage: H = (1 - y) * (1 + x^2) * (1 - t*(1 + x^2 + x*y^2))
    sage: G = (1 + x) * (1 + x^2 - x*y^2)
    sage: Hfac = H.factor()
    sage: G = G / Hfac.unit()
    sage: F = FFPD(G, Hfac); F
    (-x^2*y^2 + x^3 - x*y^2 + x^2 + x + 1,
     [(y - 1, 1), (x^2 + 1, 1), (x*y^2*t + x^2*t + t - 1, 1)])
    sage: p = {x: 1, y: 1, t: 1/3}
    sage: alpha = [1, 1, 1]
    sage: F.asymptotics_multiple(p, alpha, 1, var('r'))

gives a divison by zero, since the direction is normalized by the last coordinate.

This is a follow-up of #10519.

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