Difference between revisions of "ApCoCoA:Weyl.WMul"

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(fixed formula tag)
(update w.r.t. http://www.apcocoa.org/forum/viewtopic.php?f=20&t=918)
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     <description>
 
     <description>
  
This function computes a Groebner Basis for an ideal in a Weyl Algebra. It is currently completely independent from the other methods of package Weyl and does NOT use its data types.  
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This function computes a Groebner Basis for a left Ideal in a Weyl Algebra. It uses the ApCoCoAServer and needs currently a patched cocoa5.cpkg. Please
 +
considerthe corresponding thread in the forum  for details.
  
The input is an ideal in a ring, having 2n indeterminates. The last n indeterminates are assumed to be the derivatives. All polynomails are assumed to be in their normal form with respect to the indeterminates' commutators, e.g. all <formula>x_i </formula> are in front of all <formula>\partial_i</formula>, so the  'normal' CoCoA polynomials can be (and are) used to store the weyl polynomials. The output is again a list of polynomials in a normal ring, containing the Weyl-GBasis polynomials in their normal forms.
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<example>
 +
A := $weyl.NewRationalWeylAlgebra(3);
  
This implementation is not the final one, but currently due to requests enabled. In a later stage, the packages  data types should be used.
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 +
Use Var(A.Identifier);
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P := $weyl.NewWeylPolynom( x[1]^2 + 3);
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Q := $weyl.NewWeylPolynom( x[2]d[1]^2 + 3);
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 +
--I;
 +
 
 +
--CurrentRing();
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I := $weyl.NewWeylLeftIdeal([P,Q]);
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$weyl.GBasis(I);
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</example>
 
   </description>
 
   </description>
 
     <seealso>
 
     <seealso>

Revision as of 11:24, 17 April 2008

 <command>
   <title>Weyl.GBasis</title>
   <short_description>computing a Groebner basis in a weyl algebra.</short_description>

<syntax> Weyl.GBasis(I):LIST </syntax>

   <description>

This function computes a Groebner Basis for a left Ideal in a Weyl Algebra. It uses the ApCoCoAServer and needs currently a patched cocoa5.cpkg. Please considerthe corresponding thread in the forum for details.

<example> A := $weyl.NewRationalWeylAlgebra(3);


Use Var(A.Identifier);

P := $weyl.NewWeylPolynom( x[1]^2 + 3); Q := $weyl.NewWeylPolynom( x[2]d[1]^2 + 3);

--I;

--CurrentRing();

I := $weyl.NewWeylLeftIdeal([P,Q]);

$weyl.GBasis(I); </example>

  </description>
   <seealso>
     <see>Weyl.WeylIdeal</see>
     <see>Weyl.WeylPolynom</see>
     <see>Weyl.NewWeylIdeal</see>
   </seealso>
   <types>
     <type>cocoaserver</type>
   </types>
   <key>heldt</key>
   <key>weyl.gbasis</key>
   <wiki-category>Package_Weyl</wiki-category>
 </command>