Oberwolfach References on Mathematical Software

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LiE is the name of a software package that enables mathematicians and physicists to perform computations of a Lie group theoretic nature. It focuses on the representation theory of complex semisimple (reductive) Lie groups and algebras, and on the structure of their Weyl groups and root systems. LiE does not compute directly with elements of the Lie groups and algebras themselves; it rather computes with weights, roots, characters and similar objects.

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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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PSPP is a program for statistical analysis of sampled data. It is a Free replacement for the proprietary program SPSS.

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Sums over integral points of a polygon

Maple program for computing the sum of values of a polynomial function over the set of integral points of a polygon and the corresponding weighted Ehrhart quasi-polynomial.

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