RegularChains[ConstructibleSetTools] - Maple Programming Help

Online Help

All Products    Maple    MapleSim


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

RegularChains[ConstructibleSetTools]

  

MakePairwiseDisjoint

  

make the defining regular systems in a constructible set pairwise disjoint

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

MakePairwiseDisjoint(cs, R)

Parameters

cs

-

constructible set

R

-

polynomial ring

Description

• 

The command MakePairwiseDisjoint(cs, R) returns a constructible set cs1 such that cs1 and cs are equal and the regular systems representing cs1 are pairwise disjoint.

• 

Generally, in a constructible set, there is some redundancy among its components defined by regular systems. By default, functions on constructible sets do not remove redundancy because such a computation is expensive.

• 

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

Examples

withRegularChains:

withConstructibleSetTools:

First, define the polynomial ring.

RPolynomialRingx,y,a,b,c,d,e

Rpolynomial_ring

(1)

Consider the following almost general linear equations. They are not completely general, since their constant term, namely e, is the same.

Fax+bye

Fax+bye

(2)

Gcx+dye

Gcx+dye

(3)

After projecting the variety defined by F and G into the parameter space given by the last 5 variables, you can see when such general linear equations have solutions after specializing the last 5 variables.

csProjectionF,G,5,R

csconstructible_set

(4)

lrsRepresentingRegularSystemscs,R

lrsregular_system,regular_system,regular_system,regular_system,regular_system,regular_system,regular_system,regular_system,regular_system

(5)

Infocs,R

,c,dabc,ac,bd,c,c,d,a,dabc,e,d,c,a,bd,c,d,a,c,e,1,b,d,e,1,c,d,e,a,a,b,c,d,e,1

,c,dabc,c,d,a,ac,bd,c,dabc,e,d,c,a,c,e,1,a,bd,c,d,b,d,e,1,c,d,e,a,a,b,c,d,e,1

(6)

nopslrs

9

(7)

There are 9 regular systems defining the image cs of the projection. To remove common parts of these regular systems, use MakePairwiseDisjoint.

cs_mpdMakePairwiseDisjointcs,R

cs_mpdconstructible_set

(8)

lcs_mpdRepresentingRegularSystemscs_mpd,R

lcs_mpdregular_system,regular_system,regular_system,regular_system,regular_system,regular_system,regular_system,regular_system,regular_system

(9)

nopslcs_mpd

9

(10)

Now, there are 10 components.

Infocs_mpd,R

a,b,c,d,e,1,c,d,e,a,b,b,d,e,ac,a,c,e,bd,dabc,e,d,c,bd,a,bd,c,d,c,d,a,ac,bd,c,,c,dabc

(11)

Notice that some components have split during the redundancy removal.

See Also

ConstructibleSet

ConstructibleSetTools

GeneralConstruct

Projection

RefiningPartition

RegularChains