# The Computational Complexity of Polynomial Subalgebras

## Overview

*On the Computational Complexity of Polynomial Subalgebras*

**arXiv:**TBA

**Abstract.** The computational complexity of polynomial ideals and Gröbner bases has been studied since the 1980’s. In recent years the related topic of polynomial subalgebras and SAGBI bases have gained more and more attention in computational algebra, with a view towards effective algorithms. We investigate the computational complexity of the subalgebra membership problem and degree bounds. We discuss the parallels and differences compared to the ideal world and also look at important subclasses of polynomials such as homogeneous or monomial algebras.

On this page you can find the Macaulay2 code to experiment with the *binary counting homogeneous polynomial algebra*.

Macaulay2 source code

`BinCountAlgebra.m2`

This page is still under construction.

Project page created: 05/02/2024

Project contributors: Leonie Kayser

Corresponding author of this page: Leonie Kayser, kayser@mis.mpg.de

Software used: Macaulay2 (v1.22)

System setup used:

Macaulay2 (v1.22): MacBook Pro with Intel Core i7 processor at 2.6 GHz, 16 GB RAM

License for code of this project page: MIT License (https://spdx.org/licenses/MIT.html)

License for all other content of this project page (text, images, …): CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/)

Last updated 07/02/2024.