7 citations · 14 across the 8 of their papers we have counts for
9 papers
Flat coordinates of Frobenius prepotentials related with the reflection groups of types and
Rei Aradachi, Hiromasa Nakayama, Jiro Sekiguchi
In this article, we first explain a group theoretic interpretation of the derivation of the relation between the flat coordinates of the polynomial prepotential and those o…
Comprehensive Restriction Algorithm for Hypergeometric Systems
Hiromasa Nakayama, Nobuki Takayama
An algorithm computing the restriction of a holonomic D-module to a linear subspace was given by T.Oaku in 1997. We consider a problem of computing the restriction for a given holo…
Groebner basis and singular locus of Lauricella's hypergeometric differential equations
Hiromasa Nakayama
We derive Groebner bases for Lauricella's hypergeometric differential equations with respect to a monomial order. By using these Groebner bases, we determi…
The Holonomic Rank of the Fisher-Bingham System of Differential Equations
Tamio Koyama, Hiromasa Nakayama, Kenta Nishiyama +1
The Fisher-Bingham system is a system of linear partial differential equations satisfied by the Fisher-Bingham integral for the -dimensional sphere . The system is given in…
Holonomic Gradient Descent for the Fisher-Bingham Distribution on the -dimensional Sphere
Tamio Koyama, Hiromasa Nakayama, Kenta Nishiyama +1
We propose an accelerated version of the holonomic gradient descent and apply it to calculating the maximum likelihood estimate (MLE) of the Fisher-Bingham distribution on a -di…
Computing Differential Equations for Integrals Associated to Smooth Fano Polytopes
Hiromasa Nakayama, Nobuki Takayama
We give an approximate algorithm of computing holonomic systems of linear differential equations for definite integrals with parameters. We show that this algorithm gives a correct…