Tuesday 24th March 2015.
Matthew England
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These files comprise the data set supporting the following paper:

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Improving the use of equational constraints in cylindrical algebraic decomposition 
Matthew England, Russell Bradford and James H. Davenport.
University of Bath
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Please find included the following:

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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.

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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

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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.

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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".

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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".

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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.

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