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Knot theory program LinKnot
by
Radmila Sazdanovic
The Faculty of Mathematics, University of Belgrade, Serbia and Montenegro
Coauthors: Slavik Jablan (The Mathematical Institute, Knez Mihailova 35, P.O.Box 367 11001 Belgrade, Serbia and Montenegro)
The Mathematica-based Windows knot theory program LinKnot is the extension of the program Knot2000 (K2K) written by M.Ochiai and N.Imafuji. LinKnot provides solutions and tools for problems in knot theory and supports working with links (not only with knots). For the first time, input for a computer program is not Dowker code or graphics, but human-comprehensive Conway notation of KLs represented as a Mathematica string. For all KLs there is no restriction on the number of crossings. The program also provides the complete data base of alternating KLs with at most 12 crossings, non-alternating KLs with at most 11 crossings and the data base of basic polyhedra with at most 20 crossings.
LinKnot provides tools for drawing KLs, calculating all polynomial invariants of KLs, working with braids, KLs reduction, etc. The most significant result is computing unknotting and unlinking numbers, calculated according to Bernhard-Jablan Conjecture. Moreover, for all alternating KLs one can compute minimum Dowker codes, find all non-isomorphic projections, work with the graphs of KLs, compute linking numbers, breaking and spliting numbers, signatures, and many other KL invariants. All this makes creating of ones own experiments in knot theory possible, while at the same time profiting from the visualization capabilities and fast and easy obtained results.
Date received: November 10, 2003
Copyright © 2003 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # camw-02.