Dataset supporting the paper: Truth table invariant cylindrical algebraic decomposition

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ProjectionCAD.mpl

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Section1to7-Maple.mw

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Section1to7-Maple.pdf

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Section1to7-Qepcad.zip

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Section82-ExampleSet.txt

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Section82-ExampleSet.mw

data 795 3 1538 document 795 Section82-ExampleSet.pdf application/pdf 19ef4e7726514f1ca4ffb226782a22b3 MD5 88497 2015-05-18 16:31:30 https://researchdata.bath.ac.uk/76/8/Section82-ExampleSet.pdf 76 8 8 application/pdf other PDF printout of Maple worksheet for experiments in Section 8.2 of the paper en public cc_by_sa

Section82-ExampleSet.pdf

data 796 3 1540 document 796 Section83-Maple.mw application/xml 149c72db32de05355781077a7efde2e6 MD5 59691 2015-05-18 16:31:36 https://researchdata.bath.ac.uk/76/9/Section83-Maple.mw 76 9 9 application/xml other Maple worksheet for Table 3 in the paper en public cc_by_sa

Section83-Maple.mw

data 797 3 1542 document 797 Section83-Maple.pdf application/pdf 2ad483991d8968fcb50ec85d51c8424a MD5 17344 2015-05-18 16:31:40 https://researchdata.bath.ac.uk/76/10/Section83-Maple.pdf 76 10 10 application/pdf other PDF printout of Maple worksheet for Table 3 in the paper en public cc_by_sa

Section83-Maple.pdf

data 798 3 1544 document 798 Section83-Qepcad.zip application/zip 561736482a3dac4103f98b8850602503 MD5 15260 2015-05-18 16:31:43 https://researchdata.bath.ac.uk/76/11/Section83-Qepcad.zip 76 11 11 application/zip other Qepcad-B files for Table 3 in the paper en public cc_by_sa

Section83-Qepcad.zip

data 801 1 1555 document 801 README.txt text/plain 6ac1b7a8dd07eb11684f4f77332874a4 MD5 5279 2015-05-18 16:38:19 https://researchdata.bath.ac.uk/76/12/README.txt 76 12 12 text/plain other en public

README.txt

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indexcodes.txt

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indexcodes.txt

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http://eprints.org/relation/isVersionOf https://researchdata.bath.ac.uk/id/document/795 http://eprints.org/relation/isVolatileVersionOf https://researchdata.bath.ac.uk/id/document/795 http://eprints.org/relation/issmallThumbnailVersionOf https://researchdata.bath.ac.uk/id/document/795 archive 3777 disk0/00/00/00/76 2015-05-19 09:05:55 2026-04-18 04:45:46 2015-05-19 09:05:55 data_collection show Bradford Russell R.J.Bradford@bath.ac.uk 0009-0003-3251-2051 University of Bath FALSE Davenport James J.H.Davenport@bath.ac.uk 0000-0002-3982-7545 University of Bath TRUE England Matthew Matthew.England@coventry.ac.uk 0000-0001-5729-3420 Coventry University TRUE McCallum Scott Scott.McCallum@mq.edu.au 0000-0002-5682-7993 Macquarie University FALSE Wilson David D.J.Wilson@bath.ac.uk University of Bath FALSE Dataset supporting the paper: Truth table invariant cylindrical algebraic decomposition CZ0010 GJ0010 dept_compsci Within the zipped directories Section1to7-Qepcad.zip and Section83-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. Within the file Section82-ExampleSet.txt, the 29 examples are defined in the following syntax, used by the TTICAD algorithm that is the subject of the paper: (a) First a line starting with "#" giving the full example name followed in brackets by the shortened name used in Table 2. (b) Then a second line in which the example is defined as a list of two sublists: (i) The first sublist defines the polynomials used. They are sorted into further lists, one for each formulae in the example. Each of these has two entries. The first is either a polynomial defining an equational constraint (EC); a list of polynomials defining multiple ECs; or an empty list (signalling no ECs). The second is a list of any non ECs. (ii) The second sublist is the variable ordering from highest (eliminate first in projection) to lowest. Note that Maple algorithms use this order by Qepcad-B the reverse. This text file doubles as a Maple function definition. When read into Maple the command GenerateInput is defined which can provide the input in formats suitable for the three Maple algorithms tested. The files in this data set support the paper "Truth table invariant cylindrical algebraic decomposition" by Russel Bradford, James H. Davenport, Matthew England, Scott McCallum and David Wilson. They include the following: 1. A Maple worksheet and library file concerning the Maple results for the worked examples throughout Sections 1-7 of the paper. 2. A zipped directory of files concerning the worked examples from Sections 1-7 of the paper, this time when studied with Qepcad-B. 3. The example set that is the subject of the experiments in Section 8.2 of the paper, whose results were summarised in Table 2, and an example Maple worksheet that uses this set as input. 4. A Maple worksheet that shows how the numbers from Maple in Table 3 in the paper were obtained. 5. A zipped directory of files showing how the numbers from Qepcad-B in Table 3 in the paper were obtained. 2015 University of Bath public RightsHolder University of Bath Engineering and Physical Sciences Research Council https://doi.org/10.13039/501100000266 EP/J003247/1 Real Geometry and Connectedness via Triangular Description The data collection was by recording cell counts and timings of various CAD algorithms. A full explanation can be found in the associated paper. Regarding the example set in Section82-ExampleSet.txt, we note that the timings for Maple reported in the paper were from running Maple in command line mode. The same example set was tested in Qepcad. Here explicit ECs for a parent formula were entered in dynamically as products of the individual sub-formulae ECs, in cases where an explicit EC exists. Finally, the example set was also tested in Mathematica. Mathematica's CAD command does not return cell counts - these were obtained upon request to a Mathematica developer. Hence they are not recreatable using the information here (something outside the control of the present authors). 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 16 (released Spring 2012). It is likely that the same results would be obtained in Maple 17, 18, 2015 and future versions, 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. Qepcad-B is a free piece of software for Linux which can be obtained from http://www.usna.edu/CS/qepcadweb/B/QEPCAD.html. https://doi.org/10.1016/j.jsc.2015.11.002 https://doi.org/10.1007/978-3-662-44199-2_69 https://researchportal.bath.ac.uk/en/publications/d7737767-fef3-4fe7-ba8b-8bdfc6abf21c en 1 10.15125/BATH-00076 https://doi.org/10.1016/j.jsc.2015.11.002 pub open