Formulating problems for real algebraic geometry

M England

Research output: Chapter or section in a book/report/conference proceedingChapter in a published conference proceeding

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We discuss issues of problem formulation for algorithms in real algebraic geometry, focussing on quantifier elimination by cylindrical algebraic decomposition. We recall how the variable ordering used can have a profound effect on both performance and output and summarise what may be done to assist with this choice. We then survey other questions of problem formulation and algorithm optimisation that have become pertinent following advances in CAD theory, including both work that is already published and work that is currently underway.
With implementations now in reach of real world applications and new theory meaning algorithms are far more sensitive to the input, our thesis is that intelligently formulating problems for algorithms, and indeed choosing the correct algorithm variant for a problem, is key to improving the practical use of both quantifier elimination and symbolic real algebraic geometry in general.
Original languageEnglish
Title of host publicationProceedings of XIV Encuentro de Álgebra Computacional y Aplicaciones
Subtitle of host publicationBarcelona, June 18-20 2014
Publication statusPublished - 2014


  • symbolic computation
  • computer algebra
  • problem formulation
  • computational algebraic geometry
  • real algebraic geometry


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