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

Abstract

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-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 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.