# A Macaulay2 package for computations with rational maps

## TL;DR

This paper introduces a Macaulay2 package called Cremona that enables efficient computation of degrees, projective degrees, and Segre classes of rational maps between projective varieties, supporting both deterministic and probabilistic methods.

## Contribution

The paper presents new algorithms and implementations in Macaulay2 for computing invariants of rational maps without theoretical limitations, including probabilistic approaches.

## Key findings

- Computes degrees and projective degrees of rational maps.
- Provides a method to compute push-forward of Segre classes.
- Supports both deterministic and probabilistic computations.

## Abstract

The Macaulay2 package Cremona performs some computations on rational and birational maps between irreducible projective varieties. For instance, it provides methods to compute degrees and projective degrees of rational maps without any theoretical limitation, from which is derived a general method to compute the push-forward to projective space of Segre classes. Moreover, the computations can be done both deterministically and probabilistically. We give here a brief description of the methods and algorithms implemented.