|
RegularChains[ConstructibleSetTools][RepresentingChain] - return the regular chain in a regular system
|
|
Calling Sequence
|
|
RepresentingChain(rs, R)
|
|
|
Parameters
|
|
|
rs
|
-
|
regular system
|
|
R
|
-
|
polynomial ring
|
|
|
|
|
|
Description
|
|
|
•
|
The command RepresentingChain(rs, R) returns the representing regular chain of the regular system rs, where the polynomials of rs belong to R.
|
|
•
|
This command is part of the RegularChains[ConstructibleSetTools] package, so it can be used in the form RepresentingChain(..) 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][RepresentingChain](..).
|
|
•
|
See ConstructibleSetTools and RegularChains for the related mathematical concepts, in particular for the ideas of a constructible set, a regular system, and a regular chain.
|
|
|
|
Examples
|
|
|
>
|
|
|
>
|
|
|
>
|
|
Define a polynomial ring.
|
>
|
![R := PolynomialRing([x, y, z])](/support/helpjp/helpview.aspx?si=6415/file06486/math95.png)
|
|
| (1) |
Define a set of polynomials of R.
|
>
|
![sys := [z*x^2+y+z, y^2+z]](/support/helpjp/helpview.aspx?si=6415/file06486/math106.png)
|
|
![sys := [z*x^2+y+z, y^2+z]](/support/helpjp/helpview.aspx?si=6415/file06486/math109.png)
| (2) |
The command Triangularize (with lazard option) will decompose the common solutions of polynomial system  using regular chains.
|
>
|
|
|
![dec := [regular_chain, regular_chain]](/support/helpjp/helpview.aspx?si=6415/file06486/math125.png)
| (3) |
Let  be the first regular chain.
|
>
|
![rc := dec[1]](/support/helpjp/helpview.aspx?si=6415/file06486/math133.png)
|
|
| (4) |
Consider a polynomial  , and regard it as an inequation.
|
>
|
|
|
| (5) |
To obtain a regular system, check if  is regular with respect to  .
|
>
|
|
|
| (6) |
Since  is regular, you can build a regular system.
|
>
|
![rs := RegularSystem(rc, [h], R)](/support/helpjp/helpview.aspx?si=6415/file06486/math168.png)
|
|
| (7) |
Retrieve the regular chain by using the command RepresentingChain.
|
>
|
|
|
| (8) |
|
|
Download Help Document
Was this information helpful?
