RegularChains[ConstructibleSetTools] - Maple 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

R:=polynomial_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

F:=ax+bye

(2)

Gcx+dye

G:=cx+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

cs:=constructible_set

(4)

lrsRepresentingRegularSystemscs,R

lrs:=regular_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_mpd:=constructible_set

(8)

lcs_mpdRepresentingRegularSystemscs_mpd,R

lcs_mpd:=regular_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

 


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