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Artificial Intelligence in Computer Algebra, especially Real Geometry

  • Full or part time
  • Application Deadline
    Monday, April 01, 2019
  • Competition Funded PhD Project (European/UK Students Only)
    Competition Funded PhD Project (European/UK Students Only)

Project Description

Computer Algebra is the art/science of using computer systems to do algebra: generally calculations too great for humans, and often close to the limit of feasibility for machines. In particular, we can use computer algebra to ask about the real (or even real and positive) solutions of a system of equations. These questions arise in areas as diverse as systems biology [1], where the existence of multiple steady states gives the possibility of signalling and memory, and economics [4], where we need to check the existence of real (or real positive) solutions to ensure the validity of a particular theory.

However, these computations stretch the limits of current systems, and currently require substantial human expertise to formulate correctly in order to be soluble. Such expertise is rare, and also fallible. Hence we would like to use Artificial Intelligence techniques to “package” such expertise, and make it available to more users. This is particularly important, as users currently have access, via systems such as Maple, Mathematica and SageMath, to the underlying algorithms, but not the expertise, and therefore rapidly reach the conclusion that their problems are intractable, whereas in fact they are merely intractable if approached naïvely.

A start was made in [2], where we showed that machine learning did better than any known heuristic for the choice of variable ordering. In [3] we showed that machine learning could decide when to use a preconditioning technique. But these are isolated results, and the field would benefit from a systematic approach by a dedicated researcher.

This project is associated with the UKRI CDT in Accountable, Responsible and Transparent AI (ART-AI), which is looking for its first cohort of at least 10 students to start in September 2019. Students will be fully funded for 4 years (stipend, UK/EU tuition fees and research support budget). Further details can be found at:

Desirable qualities in candidates include intellectual curiosity, a strong background in maths and programming experience.

Applicants should hold, or expect to receive, a First Class or good Upper Second Class Honours degree. A master’s level qualification would also be advantageous.

Informal enquiries about the project should be directed to Prof James Davenport: .

Enquiries about the application process should be sent to .

Formal applications should be made via the University of Bath’s online application form for a PhD in Computer Science:

Start date: 23 September 2019.

Funding Notes

ART-AI CDT studentships are available on a competition basis for UK and EU students for up to 4 years. Funding will cover UK/EU tuition fees as well as providing maintenance at the UKRI doctoral stipend rate (£15,009 per annum for 2019/20) and a training support fee of £1,000 per annum.

We also welcome all-year-round applications from self-funded candidates and candidates who can source their own funding.


[1] Bradford,R.J., Davenport,J.H., England,M., Errami,H., Gerdt,V., Grigoriev,D., Hoyt,C., Košta,M., Radulescu,O., Sturm,T. & Weber,A., Identifying the Parametric Occurrence of Multiple Steady States for some Biological Networks.

To appear in J. Symbolic Computation. .

[2] Huang,Z., England,M., Wilson,D., Davenport,J.H., Paulson,L.C. & Bridge,J., Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition.

Proc. CICM 2014, Springer Lecture Notes in Computer Science 8543, 2014, pp. 92-107. .

[3] Huang,Z., England,M., Davenport,J.H. & Paulson,L.C., Using Machine Learning to Decide When to Precondition Cylindrical Algebraic Decomposition With Groebner Bases.
Proc. SYNASC 2016, IEEE Press, 2016, pp. 45-52. .

[4] Mulligan,C.B., Davenport,J.H. & England,M., TheoryGuru: A Mathematica Package to Apply Quantifier Elimination Technology to Economics.

Proc. Mathematical Software --- ICMS 2018, Springer Lecture Notes in Computer Science 10931, Springer, Cham, 2018, pp. 369-378. .

How good is research at University of Bath in Computer Science and Informatics?

FTE Category A staff submitted: 24.00

Research output data provided by the Research Excellence Framework (REF)

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