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RegularChains[ConstructibleSetTools][ConstructibleSet] - construct a constructible set from a list or set of regular systems
Calling Sequence
ConstructibleSet(lrs, R)
Parameters
lrs
-
list or set of regular systems
R
polynomial ring
Description
The command ConstructibleSet(lrs, R) returns a constructible set defined by the list lrs of regular systems.
A point belongs to a constructible set if and only if it is a solution of one of its defining regular systems. That is, a constructible set is the union of the solution sets of its defining regular systems.
Since a regular system always defines a nonempty set, a constructible set is empty if and only if its list of defining regular systems is empty.
This command is part of the RegularChains[ConstructibleSetTools] package, so it can be used in the form ConstructibleSet(..) only after executing the command with(RegularChains[ConstructibleSetTools]). However, it can always be accessed through the long form of the command by using RegularChains[ConstructibleSetTools][ConstructibleSet](..).
See ConstructibleSetTools and RegularChains for the related mathematical concepts, in particular for the ideas of a constructible set, a regular system, and a regular chain.
Examples
This example demonstrates how to build a constructible set structure.
First, define a polynomial ring.
Consider the following linear polynomial system.
The command Triangularize with lazard option decomposes the solution set by means of regular chains. Each regular chain describes a group of solutions with certain mathematical meaning. See RegularChains for more information.
To build constructible sets, you first need to create regular systems. For simplicity, just let be the inequation part of each regular system.
Then is a list of regular systems by which you can create a constructible set cs.
Use Info to see its internal defining polynomials.
See Also
ConstructibleSetTools, Info, QuasiComponent, RegularChains, RegularSystem, RepresentingChain, RepresentingInequations, RepresentingRegularSystems, Triangularize
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