# Dataset supporting the paper: Improving the use of equational constraints in cylindrical algebraic decomposition

This is a set of files from which the experimental results reported in the following paper can be derived: Matthew England, Russell Bradford and James H. Davenport. "Improving the use of equational constraints in cylindrical algebraic decomposition." 2015. See the file README.txt or the abstract below for full details.

The files in this dataset support the following paper: ########################################################################################## Improving the use of equational constraints in cylindrical algebraic decomposition Matthew England, Russell Bradford and James H. Davenport. University of Bath http://opus.bath.ac.uk/42451/ ########################################################################################## Please find included the following: ############################## 1a) A Maple worksheet: EBD15-Section2Example-Maple.mw 1b) A pdf printout of the worksheet: EBD15-Section2Example-Maple.pdf 1c) A Maple Library file: ProjectionCAD.mpl These files detail the examples in Section 2 of the paper run in Maple. 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, is required. To use it we need to read the Maple Library file as follows: > read("ProjectionCAD.mpl") > with(ProjectionCAD) More details on this Maple package are available in the technical report at http://opus.bath.ac.uk/43911/ and in the following publication: M. England, D. Wilson, R. Bradford and J.H. Davenport. Using the Regular Chains Library to build cylindrical algebraic decompositions by projecting and lifting. Proc ICMS 2014 (LNCS 8593). DOI: 10.1007/978-3-662-44199-2_69 If you do not have a copy of Maple you can still read the pdf printout of the worksheet. ############################## 2) A zipped directory EBD15-Section2Example-Qepcad.zip Within this directory are files concerning those examples from Section 2 of the paper run in Qepcad-B. Qepcad-B is a free piece of software for Linux which can be obtained from: http://www.usna.edu/CS/qepcadweb/B/QEPCAD.html All the files in the zipped directory 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. To verify the output readers should use the following bash command to run a Qepcad input file "Ex-in.txt" and record the output in "Ex-out.txt". qepcad +N500000000 +L200000 < Ex-in.txt > Ex-out.txt ############################## 3a) A Maple worksheet: EBD15-Section4Example-NewApproach.mw 3b) A pdf printout of the worksheet: EBD15-Section4Example-NewApproach.pdf Concerns the example in Section 4 solved using the new ideas of this paper. See notes for files (1) above. ############################## 4) A zipped directory EBD15-Section4Example-Qepcad.zip Concerns the example in Section 4 when solved with Qepcad. See notes for files (2) above. To run all tests at once use the bash script "RunAll.sh". ############################## 5) A zipped directory EBD15-Section4Example-OtherMaple.zip These files concern 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. The folder contains text files for running the maple code for each of these. An individual one can be executed in command line via > maple < FileName.txt > output.txt To run all tests at once use the bash script "RunTests.sh". ############################## The very last experiment detailed in (5) was also run in the Development Version of Maple giving a different result, as we 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.

Cite this dataset as:

England, M.,
Bradford, R.,
Davenport, J.,
2015.
*Dataset supporting the paper: Improving the use of equational constraints in cylindrical algebraic decomposition.*
University of Bath.
https://doi.org/10.15125/BATH-00071.

### Export

### Data

EBD15-Section2Example-Maple.mw

application/xml (77kB)

Creative Commons: Attribution-Share Alike 4.0

EBD15-Section2E ... ample-Maple.pdf

application/pdf (797kB)

Creative Commons: Attribution-Share Alike 4.0

EBD15-Section2E ... mple-Qepcad.zip

application/zip (5kB)

Creative Commons: Attribution-Share Alike 4.0

EBD15-Section4E ... -NewApproach.mw

application/xml (1MB)

Creative Commons: Attribution-Share Alike 4.0

EBD15-Section4E ... NewApproach.pdf

application/pdf (2MB)

Creative Commons: Attribution-Share Alike 4.0

EBD15-Section4E ... -OtherMaple.zip

application/zip (3MB)

Creative Commons: Attribution-Share Alike 4.0

EBD15-Section4E ... mple-Qepcad.zip

application/zip (23kB)

Creative Commons: Attribution-Share Alike 4.0

ProjectionCAD.mpl

text/plain (225kB)

Creative Commons: Attribution-Share Alike 4.0

Maple (commercial Computer Algebra System)

ProjectionCAD Version 3 (Maple package)

Qepcad-B (free command line interface for quantifier elimination)

### Creators

Matthew England

University of Bath

Russell Bradford

University of Bath

James Davenport

University of Bath

### Documentation

Data collection method:

The data collection was by recording cell counts of CAD algorithms in various computer algebra systems. For a full explanation see the paper this data set supports: ########################################################################################## Improving the use of equational constraints in cylindrical algebraic decomposition Matthew England, Russell Bradford and James H. Davenport. University of Bath ##########################################################################################

Data processing and preparation activities:

The numbers reported in the paper were cell counts taken from running the code provided in this dataset.

### Documentation Files

README.txt

text/plain (4kB)

### Funders

Engineering and Physical Sciences Research Council (EPSRC)

https://doi.org/10.13039/501100000266

Real Geometry and Connectedness via Triangular Description

EP/J003247/1

### Publication details

Publication date: 2015

by: University of Bath

Version: 1

DOI: https://doi.org/10.15125/BATH-00071

URL for this record: https://researchdata.bath.ac.uk/id/eprint/71

### Related articles

England, M. and Bradford, R. and Davenport, J. H., 2015. Improving the Use of Equational Constraints in Cylindrical Algebraic Decomposition. In: *Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '15*ACM Press. Available from: https://doi.org/10.1145/2755996.2756678.

### Contact information

Please contact the Research Data Service in the first instance for all matters concerning this item.

Contact person: Matthew England

Faculty of Science

Computer Science