construct a constructible set from a regular chain, equalities, and inequalities
GeneralConstruct(F, T, H, R)
GeneralConstruct(F, T, R)
GeneralConstruct(T, H, R)
GeneralConstruct(F, H, R)
lists of polynomials
The command GeneralConstruct(F, T, H, R) returns a constructible set C.
Assume that the quasi-component of T is W⁡T (see RegularChains for the definition). Then C consists of points in W⁡T 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 1.
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.
R ≔ PolynomialRing⁡x,y,t
p ≔ 5⁢t+5⁢x−y−10⁢t+7;q ≔ 5⁢t−5⁢x−t+2⁢y−7⁢t+11;h ≔ x+t
Build a regular chain using q, which means q vanishes but the initial 5⁢t−5 of q does not vanish.
rc ≔ Empty⁡R:rc ≔ Chain⁡q,rc,R
Use GeneralConstruct to figure out the points in W⁡rc which cancel p but do not cancel h.
cs ≔ GeneralConstruct⁡p,rc,h,R
cs is a constructible set consisting of one regular system.
lrs ≔ RepresentingRegularSystems⁡cs,R
The inequalities form the following list.
ineqs ≔ map⁡RepresentingInequations,lrs,R
To see complete information, use the Info command.
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