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RegularChains[ConstructibleSetTools]

  

RefiningPartition

  

compute the coprime factorization of a list of constructible sets

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

RefiningPartition(lcs, R)

Parameters

lcs

-

list of constructible sets

R

-

polynomial ring

Description

• 

The command RefiningPartition(lcs, R) returns a list of pairwise disjoint constructible sets out_lcs such that every constructible set of lcs can be written as a disjoint union of several constructible sets in out_lcs.

• 

This is represented by a matrix showing the constructible set and its associated indices where the constructible set comes from.

• 

This function can also be seen as a set theoretical instance of the co-prime factorization problem.

• 

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

Examples

withRegularChains:

withConstructibleSetTools:

RPolynomialRingx,y,u,v

R:=polynomial_ring

(1)

Fvxy+ux2+x,uy2+x2

F:=ux2+vxy+x,uy2+x2

(2)

cs1GeneralConstructF,u,R

cs1:=constructible_set

(3)

cs2GeneralConstructF,v,R

cs2:=constructible_set

(4)

cs3ProjectionF,2,R

cs3:=constructible_set

(5)

RefiningPartitioncs1,cs2,R

constructible_set1constructible_set1,2constructible_set2

(6)

RefiningPartitioncs1,cs2,cs3,R

constructible_set3constructible_set3,1constructible_set3,1,2constructible_set3,2

(7)

References

  

Chen, C.; Golubitsky, O.; Lemaire, F.; Moreno Maza, M.; and Pan, W. "Comprehensive Triangular Decomposition." Proc. CASC 2007, LNCS, Vol. 4770, pp. 73-101. Springer, 2007.

See Also

ConstructibleSet

ConstructibleSetTools

Difference

MakePairwiseDisjoint

Projection

RegularChains

 


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