RegularChains[ParametricSystemTools]
PreComprehensiveTriangularize
compute a pre-comprehensive triangular decomposition
Calling Sequence
Parameters
Description
Examples
PreComprehensiveTriangularize(sys, d, R)
sys
-
list of polynomials
d
number of parameters
R
polynomial ring
The command PreComprehensiveTriangularize(sys, d, R) returns a pre-comprehensive triangular decomposition of sys, with respect to the last d variables of R.
A pre-comprehensive triangular decomposition is a refined triangular decomposition (in the Lazard sense) with additional properties, aiming at studying parametric polynomial systems.
Let be the last d variables of R, which we regard as parameters. A finite set of regular chains of R forms a pre-comprehensive triangular decomposition of F with respect to U, if for every parameter value , there exists a subset of such that
(1) the regular chains of specialize well at , and
(2) after specialization at , these chains form a triangular decomposition (in the Lazard sense) of the polynomial system specialized at . See the command DefiningSet for the term specialize well.
A pre-comprehensive triangular decomposition of consists of three regular chains.
Compare it with the output of Triangularize.
See Also
ComprehensiveTriangularize
ConstructibleSet
DefiningSet
DiscriminantSet
Info
RegularChains
Triangularize
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