return the regular chain in a regular system - Maple Help

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RegularChains[ConstructibleSetTools][RepresentingChain] - return the regular chain in a regular system

Calling Sequence

RepresentingChain(rs, R)

Parameters

rs

-

regular system

R

-

polynomial ring

Description

• 

The command RepresentingChain(rs, R) returns the representing regular chain of the regular system rs, where the polynomials of rs belong to R.

• 

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

• 

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:

withChainTools:

withConstructibleSetTools:

Define a polynomial ring.

R:=PolynomialRingx,y,z

R:=polynomial_ring

(1)

Define a set of polynomials of R.

sys:=zx2+y+z,y2+z

sys:=x2z+y+z,y2+z

(2)

The command Triangularize (with lazard option) will decompose the common solutions of polynomial system sys using regular chains.

dec:=Triangularizesys,R,output=lazard

dec:=regular_chain,regular_chain

(3)

Let rc be the first regular chain.

rc:=dec1

rc:=regular_chain

(4)

Consider a polynomial h, and regard it as an inequation.

h:=x+z

h:=x+z

(5)

To obtain a regular system, check if h is regular with respect to rc.

IsRegularh,rc,R

true

(6)

Since h is regular, you can build a regular system.

rs:=RegularSystemrc,h,R

rs:=regular_system

(7)

Retrieve the regular chain by using the command RepresentingChain.

EqualSaturatedIdealsrc,RepresentingChainrs,R,R

true

(8)

See Also

ConstructibleSet, ConstructibleSetTools, QuasiComponent, RegularChains, RegularSystem, RegularSystemDifference, RepresentingInequations, RepresentingRegularSystems


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