Opened 20 months ago

## #19989 new defect

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

Reported by: | dkrenn | Owned by: | |
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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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