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

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   <command>
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   {{Version|1}}
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<command>
 
     <title>Weyl.IsHolonomic</title>
 
     <title>Weyl.IsHolonomic</title>
     <short_description>Checks whether an ideal in Weyl algebra An is Holonomic or not.</short_description>
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     <short_description>Checks whether an ideal in Weyl algebra <tt>A_n</tt> is holonomic or not.</short_description>
 
<syntax>
 
<syntax>
 
Weyl.IsHolonomic(I:IDEAL):BOOL
 
Weyl.IsHolonomic(I:IDEAL):BOOL
 
</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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An ideal <tt>I</tt> is holonomic if it has dimension n, the number of variables in the Weyl algebra <tt>A_n = C[x_1,...,x_n,y_1,...,y_n]</tt>.
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This function determines whether an ideal I is holonomic by checking its dimension.
  
An ideal I is holonomic if it has dimension n, the number of variables in the Weyl algebra <math>A_n = C[x_1,...,x_n,y_1,...,y_n]</math>
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<itemize>
This function determines whether an ideal I is holonomic by checking its dimension.
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<item>@param <em>I</em> An ideal in the Weyl algebra <tt>A_n</tt>.</item>
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<item>@return <tt>TRUE</tt> if the given ideal is holonomic.</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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</example>
 
</example>
 
   </description>
 
   </description>
     <seealso>
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     <seealso>  
       <see>Weyl.WDim</see>
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       <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see>
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      <see>ApCoCoA-1:Weyl.WDim|Weyl.WDim</see>
 
     </seealso>
 
     </seealso>
 
     <types>
 
     <types>
       <type>cocoaserver</type>
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       <type>apcocoaserver</type>
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      <type>ideal</type>
 
     </types>
 
     </types>
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     <key>weyl.isholonomic</key>
 
     <key>weyl.isholonomic</key>
     <wiki-category>Package_weyl</wiki-category>
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    <key>isholonomic</key>
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     <wiki-category>ApCoCoA-1:Package_weyl</wiki-category>
 
   </command>
 
   </command>

Latest revision as of 10:35, 7 October 2020

This article is about a function from ApCoCoA-1.

Weyl.IsHolonomic

Checks whether an ideal in Weyl algebra A_n is holonomic or not.

Syntax

Weyl.IsHolonomic(I:IDEAL):BOOL

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.

An ideal I is holonomic if it has dimension n, the number of variables in the Weyl algebra A_n = C[x_1,...,x_n,y_1,...,y_n].

This function determines whether an ideal I is holonomic by checking its dimension.

  • @param I An ideal in the Weyl algebra A_n.

  • @return TRUE if the given ideal is holonomic.

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.IsHolonomic(I);
-- CoCoAServer: computing Cpu Time = 2.36
-------------------------------
FALSE
-------------------------------

Example

A2::=QQ[x[1..2],d[1..2]];
Use A2;
-------------------------------
I:=Ideal(x[1]d[1] + 2x[2]d[2] - 5, d[1]^2 - d[2]);
-------------------------------
Weyl.IsHolonomic(I);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
TRUE
-------------------------------

See also

Introduction to CoCoAServer

Weyl.WDim