# Kira - A Feynman Integral Reduction Program

## TL;DR

Kira is a new program implementing an optimized Laporta algorithm for reducing multi-loop integrals in quantum field theory, demonstrating competitive performance against existing tools like Reduze 2 and FIRE 5.

## Contribution

It introduces a novel modular arithmetic-based algorithm to efficiently remove dependent equations and optimizes algebraic manipulations in integral reduction.

## Key findings

- Kira performs competitively with Reduze 2 and FIRE 5.
- The modular arithmetic approach improves equation reduction efficiency.
- Optimizations in back substitution enhance overall performance.

## Abstract

In this article, we present a new implementation of the Laporta algorithm to reduce scalar multi-loop integrals---appearing in quantum field theoretic calculations---to a set of master integrals. We extend existing approaches by using an additional algorithm based on modular arithmetic to remove linearly dependent equations from the system of equations arising from integration-by-parts and Lorentz identities. Furthermore, the algebraic manipulations required in the back substitution are optimized. We describe in detail the implementation as well as the usage of the program. In addition, we show benchmarks for concrete examples and compare the performance to Reduze 2 and FIRE 5. In our benchmarks we find that Kira is highly competitive with these existing tools.