RegularChains[ConstructibleSetTools]
GeneralConstruct
construct a constructible set from a regular chain, equalities, and inequalities
Calling Sequence
Parameters
Description
Examples
GeneralConstruct(F, T, H, R)
GeneralConstruct(F, T, R)
GeneralConstruct(T, H, R)
GeneralConstruct(F, H, R)
F, H
-
lists of polynomials
T
regular chain
R
polynomial ring
The command GeneralConstruct(F, T, H, R) returns a constructible set .
Assume that the quasi-component of T is (see RegularChains for the definition). Then consists of points in which cancel all polynomials in F, but do not cancel any polynomials in H.
If F is not specified, it is set to be the empty list.
If T is not specified, it is set to be the empty regular chain.
If H is not specified, it is set to .
The quasi-component of the empty regular chain is the whole space.
Any other inputs will be rejected and an error message will be reported.
This command is part of the RegularChains[ConstructibleSetTools] package, so it can be used in the form GeneralConstruct(..) 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][GeneralConstruct](..).
First, define a polynomial ring and three polynomials in the ring.
Build a regular chain using , which means vanishes but the initial of does not vanish.
Use GeneralConstruct to figure out the points in which cancel but do not cancel .
cs is a constructible set consisting of one regular system.
The inequalities form the following list.
To see complete information, use the Info command.
See Also
ConstructibleSet
ConstructibleSetTools
Info
Intersect
RegularChains
RepresentingInequations
Triangularize
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