RegularChains[ChainTools]
Dimension
dimension of a regular chain
Calling Sequence
Parameters
Description
Examples
Dimension(rc, R)
rc
-
regular chain of R
R
polynomial ring
The command Dimension(rc, R) returns the dimension of the saturated ideal of rc. This is also the number of variables of R minus the number of elements in rc.
This command is part of the RegularChains[ChainTools] package, so it can be used in the form Dimension(..) 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][Dimension](..).
We see that RegularChains[Triangularize] produces the regular chains in decreasing order of dimension. This is, in fact, part of the specifications of this function.
Here is another simple example with a triangular decomposition containing regular chains of different dimensions.
These regular chains are a surface, a line, and a point respectively.
See Also
ChainTools
Equations
map
PolynomialRing
RegularChains
Triangularize
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