construct a constructible set from a regular chain - Maple Help

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Home : Support : Online Help : Mathematics : Factorization and Solving Equations : RegularChains : ConstructibleSetTools Subpackage : RegularChains/ConstructibleSetTools/QuasiComponent

RegularChains[ConstructibleSetTools][QuasiComponent] - construct a constructible set from a regular chain

Calling Sequence

QuasiComponent(rc, R)

Parameters

rc

-

regular chain

R

-

polynomial ring

Description

• 

The command QuasiComponent(rc, R) returns a constructible set cs that encodes the quasi-component of the regular chain rc, that is, those points that cancel all equations of rc, but don't cancel any of the initials of the polynomials in rc.

• 

This command is part of the RegularChains[ConstructibleSetTools] package, so it can be used in the form QuasiComponent(..) 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][QuasiComponent](..).

• 

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

withRegularChains:

withConstructibleSetTools:

R:=PolynomialRingx,y,u,v

R:=polynomial_ring

(1)

F:=ux+v,vy+u

F:=ux+v,vy+u

(2)

dec:=TriangularizeF,R,output=lazard

dec:=regular_chain,regular_chain

(3)

mapEquations,dec,R

ux+v,vy+u,u,v

(4)

mapInequations,dec,R

u,v,

(5)

cs1:=QuasiComponentdec1,R;cs2:=QuasiComponentdec2,R

cs1:=constructible_set

cs2:=constructible_set

(6)

Infocs1,R;Infocs2,R

ux+v,vy+u,1

u,v,1

(7)

InfoUnioncs1,cs2,R,R

u,v,1,ux+v,vy+u,1

(8)

See Also

ConstructibleSet, ConstructibleSetTools, Info, RegularChains, RegularSystem, RepresentingChain, RepresentingInequations, RepresentingRegularSystems, Triangularize


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