|
RegularChains[ConstructibleSetTools][RefiningPartition] - compute the coprime factorization of a list of constructible sets
|
|
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
|
|
|
>
|
|
|
>
|
|
|
>
|
![R := PolynomialRing([x, y, u, v])](/support/helpjp/helpview.aspx?si=6410/file06483/math85.png)
|
|
| (1) |
|
>
|
![F := [v*x*y+u*x^2+x, u*y^2+x^2]](/support/helpjp/helpview.aspx?si=6410/file06483/math92.png)
|
|
![F := [v*x*y+u*x^2+x, u*y^2+x^2]](/support/helpjp/helpview.aspx?si=6410/file06483/math95.png)
| (2) |
|
>
|
![cs1 := GeneralConstruct(F, [u], R)](/support/helpjp/helpview.aspx?si=6410/file06483/math99.png)
|
|
| (3) |
|
>
|
![cs2 := GeneralConstruct(F, [v], R)](/support/helpjp/helpview.aspx?si=6410/file06483/math106.png)
|
|
| (4) |
|
>
|
|
|
| (5) |
|
>
|
![RefiningPartition([cs1, cs2], R)](/support/helpjp/helpview.aspx?si=6410/file06483/math120.png)
|
|
![Matrix([[constructible_set, [1]], [constructible_set, [1, 2]], [constructible_set, [2]]])](/support/helpjp/helpview.aspx?si=6410/file06483/math123.png)
| (6) |
|
>
|
![RefiningPartition([cs1, cs2, cs3], R)](/support/helpjp/helpview.aspx?si=6410/file06483/math127.png)
|
|
![Matrix([[constructible_set, [3]], [constructible_set, [3, 1]], [constructible_set, [3, 1, 2]], [constructible_set, [3, 2]]])](/support/helpjp/helpview.aspx?si=6410/file06483/math130.png)
| (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.
|
|
|
Download Help Document
Was this information helpful?
