×

zbMATH — the first resource for mathematics

Connecting the 3D DGS Calques3D with the CAS Maple. (English) Zbl 1207.68450
Summary: Many (2D) Dynamic Geometry Systems (DGSs) are able to export numeric coordinates and equations with numeric coefficients to Computer Algebra Systems (CASs). Moreover, different approaches and systems that link (2D) DGSs with CASs, so that symbolic coordinates and equations with symbolic coefficients can be exported from the DGS to the CAS, already exist. Although the 3D DGS Calques3D can export numeric coordinates and equations with numeric coefficients to Maple and Mathematica, it cannot export symbolic coordinates and equations with symbolic coefficients. A connection between the 3D DGS Calques3D and the CAS Maple, that can handle symbolic coordinates and equations with symbolic coefficients, is presented here. Its main interest is to provide a convenient time-saving way to explore problems and directly obtain both algebraic and numeric data when dealing with a 3D extension of “ruler and compass geometry”. This link has not only educational purposes but mathematical ones, like mechanical theorem proving in geometry, geometric discovery (hypotheses completion), geometric loci finding \(\dots \) As far as we know, there is no comparable “symbolic” link in the 3D case, except the prototype 3D-LD (restricted to determining algebraic surfaces as geometric loci).

MSC:
68W30 Symbolic computation and algebraic computation
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] L. Bazzotti, G. Dalzotto, L. Robbiano, Remarks on geometric theorem proving, in: J. Richter-Gebert, D. Wang (Eds.), Proceedings of ADG 2000, Springer-Verlag, LNAI 2061, Berlin-Heidelberg, 2001, pp. 104-128. · Zbl 0985.68056
[2] F. Botana, 3D-LD: automatic discovery of 3D loci via the web (Technical Report), Department of Applied Mathematics, University of Vigo, 2002.
[3] Botana, F.; Valcarce, J.L., A dynamic-symbolic interface for geometric theorem discovery, Computers and education, 38, 1-3, 21-35, (2002)
[4] Botana, F.; Valcarce, J.L., A software tool for the investigation of plane loci, Mathematics and computers in simulation, 61, 2, 141-154, (2003) · Zbl 1011.68149
[5] Botana, F.; Valcarce, J.L., Automatic determination of envelopes and other derived curves within a graphic environment, Mathematics and computers in simulation, 67, 1-2, 3-13, (2004) · Zbl 1091.68111
[6] Botana, F., A web-based resource for automatic discovery in plane geometry, International journal of computers for mathematical learning, 8, 1, 109-121, (2003)
[7] Buchberger, B., Applications of Gröbner bases in non-linear computational geometry, (), 59-87
[8] M. Bulmer, D. Fearnley-Sander, T. Stokes, The kinds of truth of geometry theorems, in: J. Richter-Gebert, D. Wang (Eds.), Proceedings of ADG 2000, Springer-Verlag, LNAI 2061, Berlin-Heidelberg, 2001, pp. 129-142. · Zbl 0985.68057
[9] Chou, C., Mechanical geometry theorem proving, (1988), Reidel · Zbl 0661.14037
[10] Chou, S.C.; Gao, X.S.; Ye, Z., Java geometry expert, (), 78-84
[11] P. Conti, C. Traverso, Algebraic and semialgebriac proofs: methods and paradoxes, in: J. Richter-Gebert, D. Wang (Eds.), Proceedings of ADG 2000, Springer-Verlag, LNAI 2061, Berlin-Heidelberg, 2001, pp. 83-103. · Zbl 0985.68075
[12] Corless, R.M., Essential Maple, (1995), Springer-Verlag New York, Berlin, Heidelberg · Zbl 0813.68069
[13] Dolzmann, A.; Sturm, T.; Weispfenning, V., A new approach for automatic theorem proving in real geometry, Journal of automated reasoning, 21, 357-380, (1998) · Zbl 0914.03013
[14] Fuchs, K.; Hohenwarter, M., Combination of dynamic geometry, algebra and calculus in the software system geogebra, ()
[15] Gao, X.S.; Zhang, J.Z.; Chou, S.C., Geometry expert, (1998), Nine Chapters Publishers
[16] Heck, A., Introduction to Maple, (1996), Springer-Verlag New York, Berlin, Heidelberg · Zbl 0861.65001
[17] Jenks, R.D.; Sutor, R.S., Axiom. the scientific computation system, (1992), Springer-Verlag New York, Berlin, Heidelberg · Zbl 0758.68010
[18] Kapur, D.; Mundy, J.L., Wu’s method and its application to perspective viewing, (), 15-36 · Zbl 0664.68102
[19] U. Kortenkamp, Foundations of Dynamic Geometry (PhD. Thesis), Swiss Fed. Inst. Tech. Zurich, 1999.
[20] Kutzler, B., Introduction to DERIVE for windows, (1996), BK-Teachware Hagenberg, Austria
[21] Kutzler, B., Careful algebraic translations of geometry theorems, (), 254-263
[22] Kutzler, B.; Kokol-Voljc, V., DERIVE 5. the mathematical assistant for your PC, (2000), BK-Teachware Hagenberg, Austria
[23] Kutzler, B.; Stifter, S., On the application of buchberger’s algorithm to automated geometry theorem proving, Journal of symbolic computation, 2, 4, 389-397, (1986) · Zbl 0629.68086
[24] MacCallum, M.; Wright, F., Algebraic computing with reduce, (1991), Clarendon Press Oxford
[25] Maplesoft: Maple User Manual, Maplesoft, 2005.
[26] Rayna, G., REDUCE. software for algebraic computation, (1987), Springer-Verlag New York, Berlin, Heidelberg · Zbl 0642.68060
[27] T. Recio, Cálculo Simbólico y Geométrico, Ed. Síntesis, 1998.
[28] T. Recio, F. Botana, Where the truth lies (in automatic theorem proving in elementary geometry), in: A. Laganá, et al. (Eds.), Proceedings of ICCSA 2004, Springer-Verlag, LNCS 3044, Berlin-Heidelberg, 2004, pp. 761-770. · Zbl 1127.68428
[29] Recio, T.; Vélez, M.P., Automatic discovery of theorems in elementary geometry, Journal of automated reasoning, 23, 63-82, (1999) · Zbl 0941.03010
[30] Rich, A., DERIVE user manual, (1994), Soft Warehouse Honolulu
[31] E. Roanes-Lozano, Boosting the geometrical possibilities of dynamic geometry systems and computer algebra systems through cooperation, in: M. Borovcnik, H. Kautschitsch (Eds.), Technology in Mathematics Teaching. Proceedings of ICTMT-5, öbv & hpt, Schrifrenreihe Didaktik der Mathematik 25, Viena, 2002, pp. 335-348.
[32] Roanes-Lozano, E.; Roanes-Macías, E., Automatic theorem proving in elementary geometry with derive 3, The international derive journal, 3, 2, 67-82, (1996)
[33] Roanes-Lozano, E.; Roanes-Macías, E., How dynamic geometry could complement computer algebra systems (linking investigations in geometry to automated theorem proving), () · Zbl 1055.68128
[34] Roanes-Lozano, E.; Roanes-Macías, E.; Villar Mena, M., A bridge between dynamic geometry and computer algebra, Mathematical and computer modelling, 37, 9-10, 1005-1028, (2003) · Zbl 1073.68899
[35] E. Roanes-Lozano, E. Roanes-Macías, A simple geometric theorem with a constructive configuration whose truthfulness depends on the base field considered, International Journal of Computer Information Systems and Industrial Management Applications (IJCISIM) Spec. Vol. 1, 2008, pp. 22-29. URL: www.softcomputing.net/∼ijcisim/.
[36] E. Roanes-Macías, E. Roanes-Lozano, Nuevas Tecnologías en Geometría, Editorial Complutense, Madrid, 1994.
[37] Roanes-Macías, E.; Roanes-Lozano, E., Cálculos matemáticos con Maple V.5, (1999), Rubiños Madrid, (In Spanish)
[38] E. Roanes-Macías, E. Roanes-Lozano, A method for outlining 3D problems in order to study them mechanically. Application to prove the 3D-version of Desargues, in: L. González-Vega, T. Recio (Eds.), Actas de los Encuentros de Álgebra Computacional y Aplicaciones (EACA’2004). Universidad de Cantabria, 2004, pp. 237-242.
[39] E. Roanes-Macías, E. Roanes-Lozano, A Maple package for automatic theorem proving and discovery in 3D-geometry, in: F. Botana, T. Recio (Eds.), Automated Deduction in Geometry, 6th International Workshop, ADG 2006, Springer-Verlag Lecture Notes in Artificial Intelligence 4689, Berlin Heidelberg New York, 2007, pp. 171-188. · Zbl 1195.68095
[40] Roanes-Macías, E.; Roanes-Lozano, E., 3D-extension of Steiner chains problem, Mathematical and computer modelling, 45, 137-148, (2007) · Zbl 1134.65328
[41] Roanes-Macías, E.; Roanes-Lozano, E.; Fernández-Biarge, J., Extensión natural a 3D del teorema de pappus y su configuración completa, Bol. soc. “puig adam”, 80, 38-56, (2008)
[42] Roanes-Macías, E.; Roanes-Lozano, E.; Fernández-Biarge, J., Obtaining a 3D extension of Pascal theorem for non-degenerated quadrics and its complete configuration with the aid of a computer algebra system, RACSAM (revista de la real academia de ciencias exactas, Físicas y naturales, serie A, matemáticas), 103, 1, 93-109, (2009) · Zbl 1179.51001
[43] P. Todd, Geometry Expressions: a constraint based interactive symbolic geometry system, in: F. Botana, T. Recio (Eds.), Automated Deduction in Geometry, 6th International Workshop, ADG 2006, Springer-Verlag Lecture Notes in Artificial Intelligence 4689, Berlin, Heidelberg, New York, 2007, pp. 189-202. · Zbl 1195.68116
[44] D. Wang, GEOTHER 1.1: handling and proving geometric theorems automatically, in: F. Winkler (Ed.), Automated Deduction in Geometry, Lecture Notes in Artificial Intelligence 2930, Springer-Verlag, Berlin, Heidelberg, New York, 2004, pp. 194-215.
[45] Wolfram, S., Mathematica. A system for doing mathematics by computer, (1991), Addison-Wesley Redwood City, CA
[46] Wen-Tsun, W., On the decision problem and the mechanization of theorem-proving in elementary geometry, A.M.S. contemporary mathematics, 29, 213-234, (1984)
[47] Wen-Tsun, W., Some recent advances in mechanical theorem-proving of geometries, A.M.S. contemporary mathematics, 29, 235-242, (1984)
[48] Wen-Tsun, W., The geometer’s sketchpad user guide and reference manual v.3, (1995), Key Curriculum Press Berkeley, CA
[49] Wen-Tsun, W., The geometer’s sketchpad reference manual v.4, (2001), Key Curriculum Press Emeryville, CA
[50] URL: http://www.wolfram.com · Zbl 1107.68324
[51] URL: http://www.maplesoft.com · Zbl 1107.68324
[52] URL: http://education.ti.com/educationportal/sites/US/productDetail/us_derive6.html
[53] URL: http://www.reduce-algebra.com/
[54] URL: http://www.axiom-developer.org/
[55] URL: http://www.mupad.de · Zbl 1107.68324
[56] URL: http://maxima.sourceforge.net/ · Zbl 1107.68324
[57] URL: http://cocoa.dima.unige.it
[58] URL: http://www.singular.uni-kl.de/
[59] URL: http://education.ti.com/educationportal/sites/US/productDetail/us_cabri_geometry.html
[60] URL: http://www.keypress.com/x5521.xml
[61] URL: http://cinderella.de/tiki-index.php
[62] URL: http://www.geogebra.org/cms/
[63] URL: http://www.calques3d.org · Zbl 1107.68324
[64] URL: http://pygeo.sourceforge.net · Zbl 1107.68324
[65] URL: http://www.mmrc.iss.ac.cn/gex/
[66] URL: http://www.cs.wichita.edu/∼ye/
[67] URL: http://www.geometryexpressions.com/ · Zbl 1107.68324
[68] URL: http://www-calfor.lip6.fr/∼wang/epsilon
[69] URL: http://www-calfor.lip6.fr/∼wang/GEOTHER/
[70] URL: http://www.adeptscience.co.uk/products/mathsim/maple/html/OpenMaple.html
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.