Consider the annihilating $D$-ideal of a massless one-loop triangle Feynman integral, appearing in Equation (5.14) in [HPSZ]. In what follows, we write this system of PDEs in connection form.
|
|
|
|
We can check that the ideal has holonomic rank $4$ and compute the standard monomials of the Gröbner basis of $RI$.
|
|
Finally, we can compute the connection matrices.
|
|
|
[HPSZ] J. Henn, E. Pratt, A.-L. Sattelberger, and S. Zoia. $D$-Module Techniques for Solving Differential Equations behind Feynman Integrals. Letters in Mathematical Physics, 114(28), 2024.
The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/ConnectionMatrices/examples.m2:100:0.