Machine Learning to Improve Groebner Basis Construction

Machine Learning to Improve Groebner Basis Construction

Eligibility: UK/EU/International graduates with the required entry requirements

Duration: Full-Time – between three and three and a half years fixed term

Application deadline: This opportunity will remain open until a suitable candidate is identified. Early application is therefore recommended

Interview date: Will be confirmed to shortlisted candidates

Start date: Either September 2020 or Jan 2021 dependent upon applicant status and subject to discussion and agreement

For further details contact: Dr Matthew England


The Research Centre for Computational Science and Mathematical Modelling (CSM) is based in the Faculty of Engineering, Environment and Computing (EEC) of Coventry University.  It provides a hub to develop cutting edge research in the areas of Artificial Intelligence, Data Science and Future Computing Technologies. The centre has a vocation to push the boundaries of both fundamental science and practical applications. 

We are offering a new project applying Machine Learning Technology to improve a key algorithm of Computer Algebra Systems.

About the project

Machine Learning (ML) refers to artificial intelligence techniques that employ a combination of statistics and big data to solve problems.  A prominent example is the classification of images according to search terms.

A Computer Algebra Systems (CAS) is a piece of software that performs symbolic mathematical computations with exact precision, as a human mathematician would by hand.  Prominent examples include Maple and the web interface Wolfram Alpha. 

This project will improve the performance of a CAS using ML. The focus is on Groebner Bases (GB): an object routinely used to study the exact solutions of a system of polynomial equations.  The algorithm to produce GB is at once a generalisation of Euclid's algorithm and Gaussian elimination.  Implementations exist in many systems.  However, the algorithm requires choices of the user or implementer.  This project will explore how ML could best make these decisions. 

A CAS prizes exact results above all else while ML tools are inherently probabilistic.  Their combination here is possible because the ML will take decisions which do not affect whether the CAS output is mathematically correct or not.  However, the decisions do have a huge effect on the computational resources needed and the way the output is presented.


This project is offered on a self-funded or externally funded basis. We particular welcome applications from candidates with funding from their home governments or sponsorship from companies.

For the academic year 2020/21:  English, Welsh and EU students can apply to borrow up to £26,445 to help cover the cost of their PhD.  Find out more about PHD Loans.


The successful candidate will receive comprehensive research training including technical, personal and professional skills.  All researchers at Coventry University (from PhD to Professor) are part of the Doctoral College which provides support with career development activities.

The candidate for this project will work in the Centre for Computational Science and Mathematical Modelling amongst other researchers employing similar data science techniques to a wide variety of problems and applications.  With access to cutting edge techniques and high performance computing resources, the Centre for Computational Science and Mathematical Modelling is an ideal place to pursue a PhD in Machine Learning.

In particular, training in machine learning techniques can be provided through modules on our Data Science and Computational Intelligence MSc programme.  The Director of Studies is an international researcher in Computer Algebra, on the Committee of the Association for Computing Machinery Special Interest Group on Symbolic and Algebraic Manipulation (ACM SIGSAM) and the current Program Committee Chair of the annual International Workshop on Computer Algebra in Scientific Computing (CASC).

Entry requirements

  • A minimum of a 2:1 first degree in a relevant discipline/subject area with a minimum 60% mark in the project element or equivalent with a minimum 60% overall module average. 


  • the potential to engage in innovative research and to complete the PhD within a 3.5 years
  • a minimum of English language proficiency (IELTS overall minimum score of 7.0 with a minimum of 6.5 in each component)

How to apply

All applications should include degree certificates and full transcripts of results.  Candidates should also upload a covering letter summarising the candidate’s prior study of mathematics and computer science, existing programming skills, and any other expertise relevant to the project.

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