The abundant literature on the subject can be explained by the many equivalent definitions of a regular chain.
12.
Regular chains are special triangular sets which are used in different algorithms for computing unmixed-dimensional decompositions of algebraic varieties.
13.
The "'MatrixTools "'subpackage provides commands for solving linear systems of equations modulo the saturated ideal of a regular chain.
14.
Wu's characteristic set method has exponential complexity; improvements in computing efficiency by weak chains, regular chains, saturated chain were introduced
15.
The "'FastArithmeticTools "'subpackage contains a collection of commands for computing with regular chains in prime characteristic using asymptotically fast algorithms.
16.
When her work in community assistance posted Carol to Guatemala, she didn't question her living accommodations, a regular chain-type hotel.
17.
In Kalkbrener's vision, regular chains are used to represent the generic zeros of the irreducible components of an algebraic variety.
18.
The algorithms which are not based on Gr�bner bases use regular chains but may need Gr�bner bases in some exceptional situations.
19.
I asked because i didn't see anything on just regular chains . talk ) 13 : 08, 26 October 2011 ( UTC)
20.
Indeed, the coefficients of these matrices are polynomials and the computations are performed modulo ( the saturated ideal of ) a regular chain.
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