Regular Chain
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In computer algebra, a regular chain is a particular kind of triangular set in a multivariate polynomial ring over a field. It enhances the notion of characteristic set. Given a linear system, one can convert it to a triangular system via Gaussian elimination. For the non-linear case, given a polynomial system F over a field, one can convert (decompose or triangularize) it to a finite set of triangular sets, in the sense that the algebraic variety V(F) is described by...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In computer algebra, a regular chain is a particular kind of triangular set in a multivariate polynomial ring over a field. It enhances the notion of characteristic set. Given a linear system, one can convert it to a triangular system via Gaussian elimination. For the non-linear case, given a polynomial system F over a field, one can convert (decompose or triangularize) it to a finite set of triangular sets, in the sense that the algebraic variety V(F) is described by these triangular sets. A triangular set may merely describe the empty set. To fix this degenerated case, the notion of regular chain was introduced, independently by Kalkbrener (1993), Yang and Zhang (1994). Regular chains also appear in Chou and Gao (1992).
