Comprehensive standard system for generalized mixed module and its application to singularity theory.

The concept of standard basis for a module is generalized to that for a mixed module that can be written as sums of more than one modules over different rings. An algorithm to compute a standard basis for a mixed module is presented, along with a proof of its correctness and termination in finite steps. The algorithm is demonstrated in several examples appearing in computations of codimensions of divergent diagrams. A parametric extension of the standard basis (comprehensive standard system, CSS) for a mixed-module is also presented, along with a proof of its correctness and termination in finite steps and its computational algorithms. The algorithm is demonstrated in several examples in the classification of divergent diagrams including applications of Mather's lemma and the complete transversal theorem. [ABSTRACT FROM AUTHOR]