What is GCLC? GCLC ((c) Predrag Janicic 1996-2009) (from "Geometry Constructions->LaTeX converter") is a tool for visualizing and teaching geometry, and for producing mathematical illustrations. GCLC provides easy-to-use support for many geometrical constructions, isometric transformations, conics, parametric curves, flow control, automated theorem proving, etc. The basic idea behind GCLC is that constructions are formal procedures, rather than drawings. Thus, in GCLC, producing mathematical illustrations is based on "describing figures" rather than of "drawing figures". Figures can be displayed and exported to LaTeX and other formats. WinGCLC is the Windows version of GCLC and provides a range of additional functionalities.

Downloads

• DOS/Windows: GCLC 9.0/WinGCLC 2009 (c); command line version (GCLC) and Windows version (WinGCLC) with a graphical, multi-document interface, support for animations, traces, etc. The archive includes manual files, sample files, additonal tools etc. (available since Sept 7, 2009) 

• Linux: GCLC 9.0 (c); command line version, manual files, sample files, etc. (available since Sept 7, 2009) 

• Slides, examples, and exercises for tutorial on intelligent geometrical software and GCLC (Spring School on Geometry and Visualization, April 2008) 

The main purposes of GCLC/WinGCLC:

• producing digital mathematical illustrations of high quality;

• use in teaching geometry;

• use in studying geometry and as a research tool.

The main features of GCLC/WinGCLC:

• support for a range of elementary and compound constructions, isometric transformations, and other geometrical devices;

• support for symbolic expressions, second order curves, parametric curves, flow control, user-defined functions, etc;

• user-friendly interface, interactive work, animations, tracing points, watch window ("geometry calculator''), and other tools;

• easy drawing of trees and graphs;

• built-in theorem provers, capable of proving many complex theorems (in traditional geometry style or in algebraic style);

• very simple, very easy to use, very small in size;

• export of high quality figures into LaTeX (simple LaTeX format, PSTricks format, TikZ format), bitmap, EPS (Encapsualted PostScript), SVG (Scalable Vector Graphics) format;

• command line versions for DOS/Windows and Linux and the MS Windows version;

• import from JavaView JVX format;

• freely available (from http://www.matf.bg.ac.rs/~janicic/gclc and from EMIS (The European Mathematical Information Service) servers: http://www.emis.de/misc/software/gclc/).

WinGCLC screenshot

References: More on the background of GCLC/WinGCLC can be found in:

• P.Janicic and I. Trajkovic: WinGCLC --- a Workbench for Formally Describing Figures. In Proceedings of the 18th spring conference on Computer graphics (SCCG 2003), pages 251--256, Budmerice, Slovakia, April, 24-26 2003. ACM Press, New York, USA.

• M.Djoric and P.Janicic. Constructions, instructions, interactions. Teaching Mathematics and its Applications, 23(2):69--88, 2004.

• P. Quaresma and P. Janicic. Framework for the Constructive Geometry. Technical Report TR2006/001, Center for Informatics and Systems of the University of Coimbra, 2006.

• P. Quaresma and P. Janicic. Integrating dynamic geometry software, deduction systems, and theorem repositories. In J. Borwein and W. Farmer, editors, Mathematical Knowledge Management (MKM-2006), volume 4108 of Lecture Notes in Arti cial Intelligence, pages 280-294. Springer-Verlag, 2006.

• P. Janicic and P. Quaresma. System description: GCLCprover + GeoThms. In U. Furbach and N. Shankar, editors, International Joint Conference on Automated Reasoning (IJCAR-2006), volume 4130 of Lecture Notes in Artificial Intelligence, pages 145-150. Springer-Verlag, 2006.

• P. Janicic. GCLC - A Tool for Constructive Euclidean Geometry and More than That. In N. Takayama, A. Iglesias, and J. Gutierrez, editors, Proceedings of International Congress of Mathematical Software (ICMS 2006), volume 4151 of Lecture Notes in Computer Science, pages 58-73. Springer-Verlag, 2006.

• Predrag Janicic. Geometry Constructions Language, Journal of Automated Reasoning, 2009.

Acknowledgements

I am grateful to

• Prof. Mirjana Djoric for the initial discussion which led to the first version of GCLC (1996);

• Prof. Neda Bokan and other members of the Group for geometry, education and visualization with applications (mostly based at the Faculty of Mathematics, University of Belgrade) for their invaluable support in developing the WinGCLC package (2003);

• EMIS (The European Mathematical Information Service) for mirroring this page at http://www.emis.de/misc/software/gclc/ ) and other EMIS locations;

• Ivan Trajkovic, the main author of the graphical interface in WinGCLC (2003);

• Aleksandar Samardzic for his advices in making Linux release of GCLC (2003/2005);

• James Fry (New Albany, Indiana, USA) for careful revision of the GCLC/WinGCLC manual file and many useful insights and comments (2005);

• DAAD (Germany) for funding my visit to Konrad Polthier's group at Mathematical Institute of TU Berlin (2003), which I used for making a JavaView->GCLC converter. I also thank Konrad Polthier and Klaus Hildebrandt for their hospitality and their collaboration in developing this converter;

• CIM/CISUC (University of Coimbra, Portugal) for funding my visit to the Department of Mathematics, University of Coimbra (2005), which I used for developing the geometry theorem prover built into GCLC. I also thank prof. Pedro Quaresma for his warm hospitality and his collaboration in developing this prover;

• Prof. Pedro Quaresma (University of Coimbra), Jelena Tomasevic, and Milena Vujosevic-Janicic, coauthors of the xml support for GCLC (2006);

• Prof. Bruno Buchberger (RISC, University of Linz, Austria), for kindly inviting me to visit RISC and to present GCLC there (2006).

• Goran Predovic (University of Belgrade, Serbia and The Microsoft Development Center Serbia) - the main author of the theorem provers based on the Wu's methods and on the Groebner bases method (2008);

• Luka Tomasevic (University of Belgrade), the main author of the support for graph drawing (2008);

• Prof. Stefano Marchiafava (University "La Sapienza", Rome, Italy), for kindly inviting me to visit the University "La Sapienza" and to present GCLC there (2008).

• Colleagues which gave contributions and suggestions in earlier stages of development of WinGCLC: Nenad Dedic, Milos Utvic, Nikola Begovic, Ivan Elcic, Jelena Grmusa, Aleksandra Nenadic, Marijana Lukic, Goran Terzic, Milica Labus, Srdjan Vukmirovic, and Aleksandar Gogic (1999/2003);

• Vladimir Baltic (University of Belgrade), Konrad Polthier (TU Berlin), Zach (Temple University, USA), Hristos Bitos (Greece), Aleksandar Gogic (DTA, Belgrade), Bob Schumacher (Cedarville University, Ohio, USA), Biljana Radovanovic (University of Belgrade), Nedeljko Stefanovic (University of Belgrade), Milan Mitrovic (Slovenia), Thomas Speziale (USA), Ania Piktas (Poland), Bojan Radusinovic (Serbia), Pierre Larochelle (Florida Institute of Technology, USA), Robert Hartmann (TU Clausthal, Clausthal-Zellerfeld, Germany), and Xavier Allamigeon for useful feedback and suggestions on different versions of GCLC/WinGCLC.

• All GCLC/WinGCLC users for their support, feedback and suggestions.

Predrag Janicic