FORM Version 5.0

TL;DR

FORM 5 addresses the growing demands of large-scale symbolic computations in theoretical physics by integrating a GRACE-based diagram generator, enabling arbitrary precision floating point arithmetic, and supporting numeric evaluation of multiple zeta values and Euler sums. The release unifies high-performance polynomial arithmetic through a Flint interface and improves robustness with a strengthened test suite, while preserving compatibility with FORM 4.3.1 where feasible. Additional enhancements include memory management controls, zstd-based compression for sorting data, read-only tablebases, and a new diagnostic toolkit (e.g., -vv) for transparency of features and libraries. Collectively, these advances expand FORM’s applicability to complex, high-precision, diagrammatic calculations and improve reliability, performance, and reproducibility for the high-energy physics community.

Abstract

We present FORM 5, a major release of the symbolic-manipulation system FORM. Version 5 introduces an integrated diagram generator, based on the GRACE graph-generator, to produce Feynman diagrams directly from FORM scripts. This release also adds support for arbitrary precision floating point coefficients, together with statements for the numerical evaluation of common mathematical functions as well as multiple zeta values and Euler sums. In addition, FORM 5 provides an interface to the FLINT library, offering substantially faster polynomial arithmetic. Various further functions and commands have been added alongside these major features, as well as performance improvements for TFORM and improved compression of FORM's temporary files. Compatibility with the previous release, FORM 4.3.1, is retained except where prior behaviour contradicted the manual or was experimental.