RemoveRedundantComponents - Maple Help
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RegularChains

  

ChainTools[RemoveRedundantComponents]

  

remove redundant quasi-components from a list of regular chains

  

SemiAlgebraicSetTools[RemoveRedundantComponents]

  

remove redundant quasi-components from a list of regular semi-algebraic systems

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

RemoveRedundantComponents(lrc, R)

RemoveRedundantComponents(lrsas, R)

Parameters

lrc

-

list of regular chains

lrsas

-

list of regular semi-algebraic systems

R

-

polynomial ring

Description

• 

The command RemoveRedundantComponents(lrc, R) returns a list  of regular chains whose quasi-components are pairwise noninclusive and such that lrc and  are Lazard decompositions of the same algebraic variety. Consequently, this command removes from  those quasi-components that are redundant for inclusion.

• 

The command RemoveRedundantComponents(lrsas, R) returns a list  of regular semi-algebraic system whose zero sets are pairwise noninclusive, and such that lrsas and  have the same zero set.

• 

For more details, see Algorithm 35 in the Ph.D. thesis of Yuzhen Xie.

Examples

Consider a polynomial ring with two variables

(1)

Consider two regular chains in R

(2)

(3)

The solutions of one are contained in those of the other. The redundant one will be removed as follows

(4)

(5)

The case of semi-algebraic system.

(6)

(7)

(8)

(9)

(10)

(11)

References

  

Xie, Y. "Fast Algorithms, Modular Methods, Parallel Approaches and Software Engineering for Solving Polynomial Systems Symbolically" Ph.D. Thesis, University of Western Ontario, Canada, 2007.

Compatibility

• 

The RegularChains[SemiAlgebraicSetTools][RemoveRedundantComponents] command was introduced in Maple 16.

• 

The lrsas parameter was introduced in Maple 16.

• 

For more information on Maple 16 changes, see Updates in Maple 16.

See Also

ChainTools

EqualSaturatedIdeals

IsContained

IsIncluded

IsInSaturate

PolynomialRing

RegularChains

 


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