# Computing denumerants in numerical 3-semigroups

## TL;DR

This paper introduces a new algorithm capable of computing denumerants for numerical 3-semigroups with medium to large input data, overcoming limitations of existing computer algebra packages.

## Contribution

A novel algorithm is developed for computing denumerants in numerical 3-semigroups, efficiently handling medium to large input data sizes.

## Key findings

- Successfully computes denumerants for medium input data
- Handles large input data in some cases
- Outperforms existing algorithms in efficiency

## Abstract

As far as we know, usual computer algebra packages can not compute denumerants for almost medium (about a hundred digits) or almost medium--large (about a thousand digits) input data in a reasonably time cost on an ordinary computer. Implemented algorithms can manage numerical $n$--semigroups for small input data. Here we are interested in denumerants of numerical $3$--semigroups which have almost medium input data. A new algorithm for computing denumerants is given for this task. It can manage almost medium input data in the worst case and medium--large or even large input data in some cases.