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With the kind permission of the authors of Singular, G.-M. Greuel, R. Stobbe, G. Pfister, H. Schoenemann, and J. Schmidt, University of Kaiserslautern, Macaulay2 incorporates Singular-Factory, version 4.3.2, a free library of polynomial routines that provides for factorization of polynomials. It is available at and at It is part of Singular, whose home page is

The following important routines call upon it: