Dimension - Maple Help
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RegularChains[ChainTools]

  

Dimension

  

dimension of a regular chain

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Dimension(rc, R)

Parameters

rc

-

regular chain of R

R

-

polynomial ring

Description

• 

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](..).

Examples

(1)

(2)

(3)

(4)

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.

(5)

Here is another simple example with a triangular decomposition containing regular chains of different dimensions.

(6)

(7)

(8)

(9)

(10)

These regular chains are a surface, a line, and a point respectively.

See Also

ChainTools

Equations

map

PolynomialRing

RegularChains

Triangularize

 


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