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Computes extremal rays with filtering

Project description

This package is a small, fast implementation of an algorithm for finding extremal rays of a polyhedral cone, with filtering. It is intended for finding normal surfaces in triangulated 3-manifolds, and therefore does not implement various features that might be useful for general extremal ray problems.

The setup is this. Define the support of a vector v in R^n to be the set of indices i such that v_i is non-zero. We are given an integer matrix M, typically with many more columns than rows, and a list of “illegal supports”. The support of a vector is illegal if its support contains one of the illegal supports on the list.

We want to find all the extremal rays of the cone (Null space of M) intersect (positive orthant), which are generated by vectors with legal support. (The restriction to vector with legal support is what is meant by “filtering”.)

The algorithm is due to Dave Letscher, and incorporates ideas of Komei Fukuda’s.

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