ApCoCoA-1:Weyl.WMul: Difference between revisions

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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.  
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.
<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.
 
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>
   </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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