construct a constructible set from a regular chain, equalities, and inequalities - Maple Help

Online Help

All Products    Maple    MapleSim


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

RegularChains[ConstructibleSetTools][GeneralConstruct] - construct a constructible set from a regular chain, equalities, and inequalities

Calling Sequence

GeneralConstruct(F, T, H, R)

GeneralConstruct(F, T, R)

GeneralConstruct(T, H, R)

GeneralConstruct(F, H, R)

Parameters

F, H

-

lists of polynomials

T

-

regular chain

R

-

polynomial ring

Description

• 

The command GeneralConstruct(F, T, H, R) returns a constructible set C.

  

Assume that the quasi-component of T is WT (see RegularChains for the definition). Then C consists of points in WT 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](..).

Examples

withRegularChains:

withChainTools:

withConstructibleSetTools:

First, define a polynomial ring and three polynomials in the ring.

R:=PolynomialRingx,y,t

R:=polynomial_ring

(1)

p:=5t+5xy10t+7;q:=5t5xt+2y7t+11;h:=x+t

p:=5t+5xy10t7

q:=5t5xt+2y7t+11

h:=x+t

(2)

Build a regular chain using q, which means q vanishes but the initial 5t5 of q does not vanish.

rc:=EmptyR:rc:=Chainq,rc,R

rc:=regular_chain

(3)

Use GeneralConstruct to figure out the points in Wrc which cancel p but do not cancel h.

cs:=GeneralConstructp,rc,h,R

cs:=constructible_set

(4)

cs is a constructible set consisting of one regular system.

lrs:=RepresentingRegularSystemscs,R

lrs:=regular_system

(5)

The inequalities form the following list.

ineqs:=mapRepresentingInequations,lrs,R

ineqs:=t1,t3+4t2+7t+5

(6)

To see complete information, use the Info command.

Infocs,R

5t5x+t2y7t+11,t2+2t+3y3t2t4,t1,t3+4t2+7t+5

(7)

See Also

ConstructibleSet, ConstructibleSetTools, Info, Intersect, RegularChains, RepresentingInequations, Triangularize


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