Computational study demonstrates an efficient bipartite-matching algorithm to compute Puiseux-series solutions for determinantal equations, indicating improved speed via network-flow methods.
Let A(t,x) = (Aᵢⱼ (t,x)) be a square matrix with Aᵢⱼ being a polynomial in t and x. This paper proposes an algorithm for computing the Puiseux (= fractional power) series solutions $x = x(t)$ to the equation detA(t, x) = 0. The algorithm is based on an observation which links the Newton diagram (polygon) for det detA(t, x) with the perfect matchings of a bipartite graph associated with A. The algorithm is efficient, making full use of available fast network-type algorithms.
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Kazuo Murota (1990) studied this question.
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