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

From ApCoCoAWiki
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     <description>
 
     <description>
  
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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
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considerthe corresponding thread in the forum  for details.
  
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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>
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A := $weyl.NewRationalWeylAlgebra(3);
  
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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;
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--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 10:24, 17 April 2008

Weyl.GBasis

computing a Groebner basis in a weyl algebra.

Syntax

Weyl.GBasis(I):LIST

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);

See also

Weyl.WeylIdeal

Weyl.WeylPolynom

Weyl.NewWeylIdeal




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