I'm interested in the use of heuristics and machine learning to speed up these algebraic processes without affecting the mathematical validity of the results.
Many algebraic algorithms that are proving themselves very useful in areas using applied mathematics, for example, Cylindrical Algebraic Decomposition (CAD), non-uniformal Cylindrical Algebraic Decomposition (nuCAD) or Cylindrical Algebraic Covering (CAC). However, they have a huge complexity (double exponential w.r.t. the number of variables) and therefore some interesting problems can't be solved in a reasonable time.
In these algebraic algorithms some choices must be taken, such as a variable ordering or whether it's worth it to use some extra information that might take some time to compute. These choices can be taken using Machine Learning and they have the ability to affect immensely the resources used to find the answer but they don't affect the mathematical validity of the results. Finding, therefore, a way of helping back the field of Mathematics using Machine Learning.
Investigation on Mathematics, MSc, University of Valladolid
31 Oct 2019 → 23 Jul 2020
Award Date: 23 Jul 2020
Mathematics, Degree, University of Valladolid
5 Sep 2015 → 31 Oct 2019
Award Date: 31 Oct 2019
Erasmus on Mathematics, University of Dundee
5 Sep 2018 → 20 Jun 2019
- QA76 Computer software
- Computational and Applied Algebraic Geometry
- Machine Learning
- Symbolic Computation
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