DOI: 10.15125/bath-00071
title: Dataset supporting the paper: Improving the use of equational constraints in cylindrical algebraic decomposition

description: The files in this dataset support the paper "Improving the use of equational constraints in cylindrical algebraic decomposition" by Matthew England, Russell Bradford and James H. Davenport. They include the following:

1. A Maple worksheet and library file detailing the examples in Section 2 of the paper.
2. A zipped directory of files concerning those examples from Section 2 of the paper run in Qepcad-B.
3. A Maple worksheet concerning the example in Section 4 solved using the new ideas of the paper.
4. A zipped directory of files concerning the example in Section 4 of the paper when solved with Qepcad-B.
5. A zipped directory of files concerning the other CAD implementations in Maple for the example in Section 4. These are
    - Sign-invariant CAD by our own package ProjectionCAD;
    - Sign-invariant CAD by the RegularChains package (two variants);
    - CAD using single EC (four variants) in our own package;
    - CAD using multiple ECs in Regular Chains.
description: The data collection was by recording cell counts of CAD algorithms in various computer algebra systems. A full explanation can be found in the paper this data set supports.
description: The numbers reported in the paper were cell counts taken from running the code provided in this dataset.
description: To run the Maple worksheet you will need a copy of the commercial computer algebra software Maple. This is currently available from http://www.maplesoft.com/products/maple/. The examples were run in Maple 18 (released Spring 2014). It is likely that the same results would be obtained in Maple 17 and 16 as well as future versions of Maple, but this cannot be guaranteed.

An additional code package, developed at the University of Bath and included in this dataset as `ProjectionCAD.mpl`, is required.

If you do not have a copy of Maple you can still read the PDF printout of the worksheets.

The very last experiment detailed in EBD15-Section4Example-OtherMaple.zip was also run in the Development Version of Maple giving a different result, as reported in the paper. The Development Version of Maple is not publicly available. However, it is likely the new algorithm within will be available in the next public Maple release (2015.0).

Qepcad-B is a free piece of software for Linux which can be obtained from http://www.usna.edu/CS/qepcadweb/B/QEPCAD.html.

Bash scripts are provided for running all available tests at once.
description: Within the zipped directories EBD15-Section2Example-Qepcad.zip and EBD15-Section4Example-Qepcad.zip, all the files end in either "-in.txt" or "-out.txt". The former give input for Qepcad and the latter record output. Hence readers without access to Qepcad (e.g. on a Windows system) can still observe the output in the latter files.
description: Further relevant documentation may be found in the following resources.

   England, M., Bradford, R., and Davenport, J. H.,  2015.   Improving the Use of Equational Constraints in Cylindrical Algebraic Decomposition.     In:  Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation.      ACM.  Available from: https://doi.org/10.1145/2755996.2756678.  

   England, M., Wilson, D., Bradford, R., and Davenport, J. H.,  2014.   Using the Regular Chains Library to Build Cylindrical Algebraic Decompositions by Projecting and Lifting.     In:  Mathematical Software – ICMS 2014.      Springer Berlin Heidelberg, 458-465.  Available from: https://doi.org/10.1007/978-3-662-44199-2_69.  

   England, M., and Wilson, D.,  2015.   An Implementation of Sub-CAD in Maple.         Bath U.K.: Department of Computer Science, University of Bath.   Available from: https://researchportal.bath.ac.uk/en/publications/an-implementation-of-sub-cad-in-maple.