Macaulay Matrix for Feynman Integrals: Programs and Data

Programs to construct Macaulay matrices (tentative version)

  1. linsolv.tar.gz (See install.txt firstly).
  2. tmp-MM.rr . (Files with .rr are program files for Risa/Asir .)


In preparation.

Pfaffian equations

  1. pentagon_pfs_x7_x8_x9_x10_x11.m , 1 loop massless pentagon with one off-shell leg, Pfaffian matrix (Mathematica format).

Programs to generate Macaulay matrices and Pfaffian equations in the paper.

  1. Massless hexagon:
    after loading tmp-MM.rr. The Macaulay matrix is stored in the variable NT_MData.
  2. One-loop Pentagon with one massive leg: program files (for Mathematica with FiniteFlow, Risa/Asir) in zip format, notes for the program files.
  3. For other cases, visit this folder .


  1. V. Chestnov, F. Gasparotto, M. K. Mandal, P. Mastrolia, S.J. Matsubara-Heo, H. J. Munch, N.Takayama, Macaulay matrix for Feynman integrals: Linear Relations and Intersection Numbers, preprint at arxiv.