|
RegularChains[ChainTools][EquiprojectableDecomposition] - equiprojectable decomposition of a variety
|
|
Calling Sequence
|
|
EquiprojectableDecomposition(lrc, R)
|
|
|
Parameters
|
|
|
lrc
|
-
|
list of regular chains of R
|
|
R
|
-
|
polynomial ring
|
|
|
|
|
|
Description
|
|
|
•
|
The command EquiprojectableDecomposition(lrc, R) returns the equiprojectable decomposition of the variety given by lrc.
|
|
•
|
The variety encoded by lrc is the union of the regular zero sets of the regular chains of lrc.
|
|
•
|
It is assumed that every regular chain in lrc is zero-dimensional and strongly normalized.
|
|
•
|
This command is part of the RegularChains[ChainTools] package, so it can be used in the form EquiprojectableDecomposition(..) only after executing the command with(RegularChains[ChainTools]). However, it can always be accessed through the long form of the command by using RegularChains[ChainTools][EquiprojectableDecomposition](..).
|
|
|
|
Examples
|
|
|
>
|
|
|
>
|
|
|
>
|
![R := PolynomialRing([z, y, x])](/support/helpjp/helpview.aspx?si=5680/file06442/math89.png)
|
|
| (1) |
|
>
|
![sys := [x^2+y+z-1, x+y^2+z-1, x+y+z^2-1]](/support/helpjp/helpview.aspx?si=5680/file06442/math96.png)
|
|
![sys := [x^2+y+z-1, x+y^2+z-1, x+y+z^2-1]](/support/helpjp/helpview.aspx?si=5680/file06442/math99.png)
| (2) |
|
>
|
|
|
![lrc := [regular_chain, regular_chain, regular_chain, regular_chain]](/support/helpjp/helpview.aspx?si=5680/file06442/math106.png)
| (3) |
|
>
|
|
|
![[[z-x, y-x, x^2+2*x-1], [z, y, x-1], [z, y-1, x], [z-1, y, x]]](/support/helpjp/helpview.aspx?si=5680/file06442/math113.png)
| (4) |
|
>
|
|
|
| (5) |
|
>
|
|
|
![{[z+y-1, y^2-y, x], [2*z+x^2-1, 2*y+x^2-1, x^3+x^2-3*x+1]}](/support/helpjp/helpview.aspx?si=5680/file06442/math127.png)
| (6) |
|
|
|
References
|
|
|
|
Dahan, X.; Moreno Maza, M.; Schost, E.; Wu, W. and Xie, Y. "Equiprojectable decompositions of zero-dimensional varieties" In proc. of International Conference on Polynomial System Solving, University of Paris 6, France, 2004.
|
|
|
Download Help Document
Was this information helpful?
