Algorithm 931: An algorithm and software for computing multiplicity structures at zeros of nonlinear systems

A Matlab implementation, MULTIPLICITY, of a numerical algorithm for computing the multiplicity structure of a nonlinear system at an isolated zero is presented. The software incorporates a newly developed equationby- equation strategy that significantly improves the efficiency of the closedness subspace algorithm and substantially reduces the storage requirement. The equation-by-equation strategy is actually based on a variable-by-variable closedness subspace approach. As a result, the algorithm and software can handle much larger nonlinear systems and higher multiplicities than their predecessors, as shown in computational experiments on the included test suite of benchmark problems.