Regular chain

Summary

A regular chain is a triangular set of polynomials, with one polynomial for each of some of the variables. In it, the leading coefficient of each polynomial is not a zero divisor modulo the ideal described by the earlier polynomials. Regular chains describe the solution sets of polynomial systems in a triangular form that can be solved one variable at a time. Every polynomial system can be decomposed into finitely many regular chains, and this gives an alternative to Gröbner bases in computer algebra.