# Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA

## TL;DR

This paper introduces CANONICA, a Mathematica package that automates transforming multi-loop Feynman integrals into a canonical basis, simplifying their differential equations, and is the first publicly available tool for multi-scale cases.

## Contribution

The paper presents the first publicly available implementation of an algorithm for transforming multi-scale Feynman integrals into a canonical basis.

## Key findings

- CANONICA automates the transformation process.
- The algorithm's uniqueness of canonical forms is proven.
- The package facilitates solving differential equations of Feynman integrals.

## Abstract

The integration of differential equations of Feynman integrals can be greatly facilitated by using a canonical basis. This paper presents the Mathematica package CANONICA, which implements a recently developed algorithm to automatize the transformation to a canonical basis. This represents the first publicly available implementation suitable for differential equations depending on multiple scales. In addition to the presentation of the package, this paper extends the description of some aspects of the algorithm, including a proof of the uniqueness of canonical forms up to constant transformations.