Regular chain
Type of triangular sets of polynomial / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Regular chain?
Summarize this article for a 10 year old
In mathematics, and more specifically in computer algebra and elimination theory, a regular chain is a particular kind of triangular set of multivariate polynomials over a field, where a triangular set is a finite sequence of polynomials such that each one contains at least one more indeterminate than the preceding one. The condition that a triangular set must satisfy to be a regular chain is that, for every k, every common zero (in an algebraically closed field) of the k first polynomials may be prolongated to a common zero of the (k + 1)th polynomial. In other words, regular chains allow solving systems of polynomial equations by solving successive univariate equations without considering different cases.
Regular chains enhance the notion of Wu's characteristic sets in the sense that they provide a better result with a similar method of computation.