Oberwolfach References on Mathematical Software

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KnotPlot is a program to visualize and manipulate knots in three and four dimensions. Knots can be loaded from a database of almost 1000 knots and links or sketched by hand in three dimensions. Also, knots may be constructed via the Conway notation or using a tangle calculator. A number of special knot types (torus knots, knot chains, Lissajous knots) may be created on the fly. Finally, new knots can be created from old knots using a number of transformations.

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polymake is an object-oriented system for experimental discrete mathematics. The typical working cycle of a polymake user starts with the construction of an object of interest, auch as a convex polytope, a finite simplicial complex, a graph, etc. It is then possible to ask the system for some of the object's properties or for some form of visualization. Further steps might include more elaborate constructions based on previously defined objects. Each class of polymake objects comes with a set of rules which describe how a new property of an object can be derived from previously known ones. It is a key feature that the user can extend or modify the set of rules, add further properties or even new classes of objects (with entirely new rule bases). The functions provided include: several convex hull algorithms, face lattices of convex polytopes, Voronoi diagrams and Delaunay decompositions (in arbitrary dimensions), simplicial homology (with integer coefficients), simplicial cup and cap products, intersection forms of triangulated 4-manifolds. Several forms of (interactive) visualization via interfaces to Geomview, JavaView and other programs.

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