# Difference between revisions of "ApCoCoA-1:Weyl.WDim"

From ApCoCoAWiki

(Updated example.) |
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<command> | <command> | ||

<title>Weyl.WDim</title> | <title>Weyl.WDim</title> | ||

− | <short_description>Computes the dimension of an ideal I in Weyl algebra < | + | <short_description>Computes the dimension of an ideal <tt>I</tt> in Weyl algebra <tt>A_n</tt>.</short_description> |

<syntax> | <syntax> | ||

Weyl.WDim(I:IDEAL):INT | Weyl.WDim(I:IDEAL):INT | ||

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<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | <em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | ||

<par/> | <par/> | ||

− | This function computes the dimension of an Ideal <tt>I = (f_1,f_2, ..., f_r)</tt> which represents the module <tt>A_n/I</tt> where every generator <tt>f_i</tt> should be a Weyl polynomial in Normal form. This dimension of I is equal to the dimension of the associated graded module with respect to the Bernstein filtration. | + | This function computes the dimension of an Ideal <tt>I = (f_1,f_2, ..., f_r)</tt> which represents the module <tt>A_n/I</tt> where every generator <tt>f_i</tt> should be a Weyl polynomial in Normal form. This dimension of <tt>I</tt> is equal to the dimension of the associated graded module with respect to the Bernstein filtration. |

<itemize> | <itemize> |

## Revision as of 13:26, 10 July 2009

## Weyl.WDim

Computes the dimension of an ideal `I` in Weyl algebra `A_n`.

### Syntax

Weyl.WDim(I:IDEAL):INT

### Description

*Please note:* The function(s) explained on this page is/are using the *ApCoCoAServer*. You will have to start the ApCoCoAServer in order to use it/them.

This function computes the dimension of an Ideal `I = (f_1,f_2, ..., f_r)` which represents the module `A_n/I` where every generator `f_i` should be a Weyl polynomial in Normal form. This dimension of `I` is equal to the dimension of the associated graded module with respect to the Bernstein filtration.

@param

*I*An ideal in the Weyl algebra.@return The dimension of the given ideal.

#### Example

W3::=ZZ/(7)[x[1..3],d[1..3]]; Use W3; -- Cpu time = 0.00, User time = 0 ------------------------------- F1:=-d[1]^3d[2]^5d[3]^5+x[2]^5; F2:=-3x[2]d[2]^5d[3]^5+x[2]d[1]^3; F3:=-2d[1]^4d[2]^5-x[1]d[2]^7+x[3]^3d[3]^5; I:=Ideal(F1,F2,F3); Weyl.WDim(I); -- CoCoAServer: computing Cpu Time = 2.36 ------------------------------- 2 -------------------------------

#### Example

A3::=QQ[x[1..2],d[1..2]]; Use A3; ------------------------------- I:=Ideal(x[1]d[1] + 2x[2]d[2] - 5, d[1]^2 - d[2]); ------------------------------- Weyl.WDim(I); -- CoCoAServer: computing Cpu Time = 0 ------------------------------- 2 ------------------------------- -- If the dimension is ZERO, -1 will be returned Weyl.WDim(Ideal(x[1],d[1])); -- CoCoAServer: computing Cpu Time = 0 ------------------------------- -1 -------------------------------

### See also