Repository of data supporting the thesis "Poly-algorithmic Techniques in Real Quantifier Elimination"

Dataset of various files (as a .zip) supporting the PhD thesis "Poly-algorithmic Techniques in Real Quantifier Elimination" by Zak Tonks, University of Bath. The PhD thesis is in the area of Quantifier Elimination over the Reals (QE) in Computer Algebra. The PhD thesis concerns implementation of algorithms in Quantifier Elimination, which largely culminates in the package QuantifierElimination for the Computer Algebra software Maple. Much of this repository is output of the benchmarking of this package against various other packes in Maple and otherwise. Otherwise there are some auxiliary tools and files to assist with working with QE in Maple, converting between various formats, and understanding case studies and the package QuantifierElimination via software demoes as Maple worksheets.

An overview of the contents of this repository (as a .zip file, which contains subdirectories described in the README):

• The example databases contributed from the project, as files that can be read into Maple defining tables of examples, and associated functions to build or examine various examples,
• A pdf file providing the references for all examples from the example databases, and typesetting of the examples as associated QE problems,
• The benchmarking data produced from the benchmarking of the project as csv (comma separated value) files, and the Excel workbooks (xlsx files) processing said data into survival plots for the thesis,
• Copies of the survival plots themselves as .png files,
• The bash and Maple scripts used to generate the raw benchmarking data, that can be reused, including documentation how to do so in the associated README,
• Other auxiliary tools allowing for conversion of QE formulae between formats (such as that of SyNRAC, RegularChains, QuantifierElimination (amongst packages in Maple), and QEPCAD B.
• Maple worksheets and the associated exported pdf files used in software demos at conferences to demonstrate features of QuantifierElimination.
• Some pdf files demonstrating early case studies on Lazard curtains generated from an early development build of QuantifierElimination.

Lastly, there is a README with more detail on the files of the repository further. To emulate the benchmarking of the thesis, an understanding of bash and potentially Maple is assumed, but the raw data from the project is provided here. Before QuantifierElimination's official release, the source code and/or Maple package as an .mla file is available for interested parties upon request to the author Zak Tonks (zak.p.tonks@bath.edu). Any other queries about this data or associated work should be directed to this email address. The author's PhD supervisor's email address is J.H.Davenport@bath.ac.uk.