#19989: asymptotics for multivariate generating functions: zero division error
on
last coordinate
-------------------------------------+----------------------------
Reporter: dkrenn | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-7.1
Component: asymptotic expansions | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies: #10519
Stopgaps: |
-------------------------------------+----------------------------
{{{
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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Ticket URL: <http://trac.sagemath.org/ticket/19989>
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