# Algebraic computation of genetic patterns related to three-dimensional evolution algebras

## TL;DR

This paper applies computational algebraic geometry to classify three-dimensional evolution algebras, representing genetic mutation patterns during cell division, into isotopism and isomorphism classes.

## Contribution

It introduces a method to classify three-dimensional evolution algebras into isotopism and isomorphism classes using algebraic geometry techniques.

## Key findings

- Distribution of three-dimensional evolution algebras into isotopism classes
- Classification of algebras with one-dimensional annihilator into isomorphism classes
- Application of algebraic geometry to genetic pattern analysis

## Abstract

The mitosis process of an eukaryotic cell can be represented by the structure constants of an evolution algebra. Any isotopism of the latter corresponds to a mutation of genotypes of the former. This paper uses Computational Algebraic Geometry to determine the distribution of three-dimensional evolution algebras over any field into isotopism classes and hence, to describe the spectrum of genetic patterns of three distinct genotypes during a mitosis process. Their distribution into isomorphism classes is also determined in case of dealing with algebras having a one-dimensional annihilator.