return the list of inequations in a regular system - Maple Help

Online Help

All Products    Maple    MapleSim


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

RegularChains[ConstructibleSetTools][RepresentingInequations] - return the list of inequations in a regular system

Calling Sequence

RepresentingInequations(rs, R)

Parameters

rs

-

regular system

R

-

polynomial ring

Description

• 

The command RepresentingInequations(rs, R) returns the inequations of the regular system rs, assuming that the polynomials of rs belong to R

• 

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

• 

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 the polynomials system sys by means of regular chains.

dec:=Triangularizesys,R,output=lazard

dec:=regular_chain,regular_chain

(3)

Let rc be the first regular chain and h be a polynomial regarded as an inequation.

rc:=dec1;h:=x+z

rc:=regular_chain

h:=x+z

(4)

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

IsRegularh,rc,R

true

(5)

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

rs:=RegularSystemrc,h,R

rs:=regular_system

(6)

Notice that the inequation h is returned by the command RepresentingInequations.

ineqs:=RepresentingInequationsrs,R

ineqs:=x+z

(7)

See Also

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


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam