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

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(New page: <command> <title>Weyl.WDim</title> <short_description>Computes the dimension ideal I in Weyl algebra <math>A_n</math>.</short_description> <syntax> Weyl.WDim(I:IDEAL):INT </synta...)
 
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   <command>
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   {{Version|1}}
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<command>
 
     <title>Weyl.WDim</title>
 
     <title>Weyl.WDim</title>
     <short_description>Computes the dimension ideal I in Weyl algebra <math>A_n</math>.</short_description>
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     <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
 
</syntax>
 
</syntax>
 
     <description>
 
     <description>
{{ApCoCoAServer}}
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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.
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<par/>
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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.
  
This function computes the dimension of  an Ideal <math>I = (f_1,f_2, ..., f_r)</math> which represents the module <math>A_n/I</math> where every generator <math>f_i</math> 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
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<itemize>
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<item>@param <em>I</em> An ideal in the Weyl algebra.</item>
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<item>@return The dimension of the given ideal.</item>
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</itemize>
  
 
<example>
 
<example>
 
W3::=ZZ/(7)[x[1..3],d[1..3]];
 
W3::=ZZ/(7)[x[1..3],d[1..3]];
 
Use W3;
 
Use W3;
Cpu time = 0.00, User time = 0
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-- Cpu time = 0.00, User time = 0
 
-------------------------------
 
-------------------------------
 
F1:=-d[1]^3d[2]^5d[3]^5+x[2]^5;
 
F1:=-d[1]^3d[2]^5d[3]^5+x[2]^5;
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   </description>
 
   </description>
 
     <seealso>
 
     <seealso>
       <see>Weyl.WNormalForm</see>
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       <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see>
       <see>Weyl.WGB</see>
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      <see>ApCoCoA-1:Weyl.WNormalForm|Weyl.WNormalForm</see>
       <see>Weyl.IsHolonomic</see>
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       <see>ApCoCoA-1:Weyl.WGB|Weyl.WGB</see>
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       <see>ApCoCoA-1:Weyl.IsHolonomic|Weyl.IsHolonomic</see>
 
     </seealso>
 
     </seealso>
 
     <types>
 
     <types>
       <type>cocoaserver</type>
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       <type>apcocoaserver</type>
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      <type>ideal</type>
 
     </types>
 
     </types>
 
     <key>weyl.wdim</key>
 
     <key>weyl.wdim</key>
     <wiki-category>Package_Weyl</wiki-category>
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    <key>wdim</key>
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     <wiki-category>ApCoCoA-1:Package_weyl</wiki-category>
 
   </command>
 
   </command>

Latest revision as of 10:38, 7 October 2020

This article is about a function from ApCoCoA-1.

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

Introduction to CoCoAServer

Weyl.WNormalForm

Weyl.WGB

Weyl.IsHolonomic