Dataset for Quantifier Elimination and CAD examples in Maple

746 61 12856 3 37349 document 12856 TarskiFormulaLaTeXTools.mpl text/plain b045893ba0fa617c837900021fb2384b MD5 2129 2019-12-02 16:38:35 https://researchdata.bath.ac.uk/746/4/TarskiFormulaLaTeXTools.mpl 746 4 4 text/plain other A file that can be read into Maple, which having done so will enable Maple to better produce the LaTeX for Tarski formulae, 'TarskiFormula' type enabled by the package 'QuantifierElimination'. Hence the Maple inbuilt 'latex' will produce better LaTeX for such formulae. en public cc_mit

TarskiFormulaLaTeXTools.mpl

code 12896 3 37463 document 12896 QuantifierEliminationConversionTools.mpl text/plain e46a3d945025fbe077d07ca83f7fd8d2 MD5 3641 2019-12-04 16:43:44 https://researchdata.bath.ac.uk/746/10/QuantifierEliminationConversionTools.mpl 746 10 10 text/plain other A file that can be read into Maple, which loads three functions 'convertQEtoRC','convertQEtoSyNRAC', c'onvertQEtoQEPCAD' which will convert a QE example written in 'QuantifierElimination' format to that of RegularChains, SyNRAC, or QEPCAD respectively. Note that the Quantifier Elimination procedure in RegularChains is RegularChains:-SemiAlgebraicSetTools:-QuantifierElimination. Note that these functions require the original problem in prenex form. Note QEPCAD will accept redirection of a problem en public cc_mit

QuantifierEliminationConversionTools.mpl

code 13003 2 38080 document 13003 Example Database Info.pdf application/pdf 3a35873eabca9499189d8d35dfce6a26 MD5 261108 2020-01-24 11:51:40 https://researchdata.bath.ac.uk/746/12/Example%20Database%20Info.pdf 746 12 12 application/pdf other Provides references for sources of all semi-algebraic formulae contained in the files in this repository. en public cc_by

Example Database Info.pdf

documentation 13004 3 38084 document 13004 CADDatabase.mm text/plain b1cd75302de204c9b50f3d47b5a27909 MD5 4558 2020-01-24 11:52:17 https://researchdata.bath.ac.uk/746/13/CADDatabase.mm 746 13 13 text/plain other A file that can be read into Maple loading a table of unquantified semi algebraic expressions called 'CADExamples', and nothing else. No auxillary functions are provided in this file. en public cc_by

CADDatabase.mm

data 13005 2 38087 document 13005 QE Example Bank.mpl text/plain 21612c39a7bbda9bd3f165c3b746768e MD5 95339 2020-01-24 11:53:22 https://researchdata.bath.ac.uk/746/14/QE%20Example%20Bank.mpl 746 14 14 text/plain other A file that can be read into Maple that loads tables containing explicit QE problems, and tables and functions from which QE examples can be built. Also loads auxillary functions that can be used to view or interact with such tables, and a "Help" function explaining how to use everything further. All QE problems produced are of format amenable to usage with the package 'QuantifierElimination', which enables the 'TarskiFormula' type. en public cc_mit

QE Example Bank.mpl

code 13006 2 38092 document 13006 lightbox.jpg image/png 128068b31d63e769913c91635698b721 MD5 20126 2020-01-24 12:01:40 https://researchdata.bath.ac.uk/746/15/lightbox.jpg 746 15 15 image/png other Thumbnails conversion from other to thumbnail_lightbox en public

lightbox.jpg

preview.jpg

medium.jpg

small.jpg

indexcodes.txt

http://eprints.org/relation/isVersionOf https://researchdata.bath.ac.uk/id/document/13003 http://eprints.org/relation/isVolatileVersionOf https://researchdata.bath.ac.uk/id/document/13003 http://eprints.org/relation/isIndexCodesVersionOf https://researchdata.bath.ac.uk/id/document/13003 archive 175 disk0/00/00/07/46 2024-06-25 09:21:16 2024-07-15 10:59:19 2024-06-25 09:21:16 data_collection show Tonks Zak z.p.tonks@bath.ac.uk 0000-0001-6019-1775 University of Bath TRUE Supervisor Davenport James J.H.Davenport@bath.ac.uk 0000-0002-3982-7545 University of Bath Dataset for Quantifier Elimination and CAD examples in Maple dept_compsci Quantifier Elimination, Cylindrical Algebraic Decomposition, Maple, Symbolic Computation, Computer Algebra This dataset provides the following: - 'QE Example Database.mpl': a file that can be read into Maple that loads an interactive database of QE examples, along with functions to build and print them, - 'CADDatabase.mm': a file that can be read into Maple that loads a table of purely unquantified examples for CAD, 'CADExamples', with no auxillary functions. These examples are of various types, but are compatible with the input semantics of 'CylindricalAlgebraicDecompose' for the package 'QuantifierElimination' for Maple. - 'TarskiFormulaLaTeXTools.mpl': a file that can be read into Maple that allows Maple to better format Tarski formulae (type 'TarskiFormula' arising from the package 'QuantifierElimination') for LaTeX when passed into Maple's inbuilt function 'latex'. - 'Example Database Info.pdf': A pdf documenting reference and origin information about all examples from the databases included. All formulae or otherwise semi-algebraic sets produced by usage of these files are in 'RationalTarskiFormula' or 'TarskiFormula' type, for compatibility with 'QuantifierElimination'. They are amenable to usage with Maple packages 'RegularChains' or 'SyNRAC', after some conversion. - 'QuantifierEliminationConversionTools.mpl': a file that can be read into Maple that loads two functions for conversion of Tarski formulae from 'QuantifierElimination' format, 'convertQEtoRC', 'convertQEtoSyNRAC', and 'convertQEtoQEPCAD' which convert to format amenable to 'RegularChains', 'SyNRAC', or 'QEPCAD' respectively. 'QEPCAD' requires bespoke input, so one can write the produced string to a file before redirection into QEPCAD. More information about each file is in the metadata for each file. 2023-07-01 University of Bath public Quantifier Elimination over the reals is a problem in Computer Algebra consisting of quantified boolean formulae of polynomial constraints. This dataset provides a collection of real world examples amalgamated from a range of sources, most not seen together before. This database is useful for the purposes of benchmarking and testing, and in particular is an accompaniment for the future to be released Maple package 'QuantifierElimination'. While the main contribution is the collection of Quantifier Elimination problems, auxillary functions are provided for various other purposes, including viewing and building the examples. Also, examples for pure CAD are provided, ie. just semi-algebraic formulae. Lastly, a document detailing references for sources of these examples is provided. RightsHolder University of Bath Engineering and Physical Sciences Research Council https://doi.org/10.13039/501100000266 EP/EG-CM1146/1 PhD Studentship, Hybrid Techniques in Quantifier Elimination Maplesoft EP/EG-CM1146/1 PhD Studentship, Hybrid Techniques in Quantifier Elimination The CAD and QE examples contained in the relevant database come from a wide range of sources, documented in the contained pdf. Where appropriate, these may have been reformatted into Maple format, eg. from Mathematica format for the economics examples. Many of the examples arise from David Wilson's CAD database (reference found in the .pdf), and where appropriate they have been reformatted as the relevant QE problem for the QE database. Otherwise, they may have had some slight reformatting such that they form lists of relations, or sets of polynomials. Maple 2019.0 or newer is sufficient to view the examples. Previous versions of Maple may suffice, although cannot be guaranteed. The examples are all written to be directly compatible for functions contained in the package 'QuantifierElimination' for Maple, to be released. Conversion for usage with Maple packages 'RegularChains' or 'SyNRAC' is available by the included conversion routines. A version of 'RegularChains' is included with any consumer version of Maple, but the newest version is also available online. 'SyNRAC' is only available online. en 1 10.15125/BATH-00746 https://doi.org/10.1007/978-3-030-41258-6_13 pub https://researchportal.bath.ac.uk/en/studentTheses/poly-algorithmic-techniques-in-real-quantifier-elimination thesis https://doi.org/10.1145/3597066.3597090 pub https://doi.org/10.1109/SYNASC61333.2023.00013 pub open