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
RemoveRedundantComponents(lrc, R)
RemoveRedundantComponents(lrsas, R)
lrc
-
list of regular chains
lrsas
list of regular semi-algebraic systems
R
polynomial ring
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.
Consider a polynomial ring with two variables
Consider two regular chains in R
The solutions of one are contained in those of the other. The redundant one will be removed as follows
The case of semi-algebraic system.
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.
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
Download Help Document