Algorithms for Pfaffian Systems and Cohomology Intersection Numbers of Hypergeometric Integrals

DOI10.1007/978-3-030-52200-1_7zbMath1503.33014OpenAlexW3041970101MaRDI QIDQ5039557

Saiei-Jaeyeong Matsubara-Heo, Nobuki Takayama

Publication date: 13 October 2022

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-52200-1_7

zbMATH Keywords

Gröbner basisGKZ hypergeometric systemscohomology intersection numbers

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Other hypergeometric functions and integrals in several variables (33C70) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10)

Related Items (4)

AN ALGORITHM OF COMPUTING COHOMOLOGY INTERSECTION NUMBER OF HYPERGEOMETRIC INTEGRALS ⋮ Macaulay matrix for Feynman integrals: linear relations and intersection numbers ⋮ Intersection numbers from higher-order partial differential equations ⋮ Localization formulas of cohomology intersection numbers

Uses Software

• Risa/Asir
• OpenXM

Cites Work

• Unnamed Item
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• A Quick Introduction to Gröbner Bases
• Pfaffian Equations and Contiguity Relations of the Hypergeometric Function of Type (<i>k</i>+1, <i>k</i>+<i>n</i>+2) and Their Applications
• Computing closed form solutions of integrable connections
• Polynomial and rational solutions of holonomic systems

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