PreComprehensiveTriangularize - Maple Help
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RegularChains[ParametricSystemTools]

  

PreComprehensiveTriangularize

  

compute a pre-comprehensive triangular decomposition

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

PreComprehensiveTriangularize(sys, d, R)

Parameters

sys

-

list of polynomials

d

-

number of parameters

R

-

polynomial ring

Description

• 

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.

Examples

(1)

(2)

A pre-comprehensive triangular decomposition of  consists of three regular chains.

(3)

(4)

Compare it with the output of Triangularize.

(5)

(6)

See Also

ComprehensiveTriangularize

ConstructibleSet

DefiningSet

DiscriminantSet

Info

RegularChains

Triangularize

 


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