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RegularChains[ConstructibleSetTools]

  

GeneralConstruct

  

construct a constructible set from a regular chain, equalities, and inequalities

 

Calling Sequence

Parameters

Description

Examples

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.

RPolynomialRingx,y,t

R:=polynomial_ring

(1)

p5t+5xy10t+7;q5t5xt+2y7t+11;hx+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.

rcEmptyR:rcChainq,rc,R

rc:=regular_chain

(3)

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

csGeneralConstructp,rc,h,R

cs:=constructible_set

(4)

cs is a constructible set consisting of one regular system.

lrsRepresentingRegularSystemscs,R

lrs:=regular_system

(5)

The inequalities form the following list.

ineqsmapRepresentingInequations,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

 


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