Difference between revisions of "ApCoCoA:Weyl.WMul"

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     <short_description>computing a Groebner basis.</short_description>
 
     <short_description>computing a Groebner basis.</short_description>
 
<syntax>
 
<syntax>
Weyl.GBasis(P):LIST
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Weyl.GBasis(I):LIST
 
</syntax>
 
</syntax>
 
     <description>
 
     <description>
 
{{Beta}}
 
{{Beta}}
  
This method computes an both sided ideal's Groebner basis and returns it as a list of WeylPolynoms. Currently, it is not yet implemented, due to some missing link in the server/client communication.  
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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.  
  
 +
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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This implementation is not the final one, but currently due to requests enabled. In a later stage, the packages  data types should be used.
 
{{Stub}}
 
{{Stub}}
 
   </description>
 
   </description>

Revision as of 14:28, 10 March 2008

Weyl.GBasis

computing a Groebner basis.

Syntax

Weyl.GBasis(I):LIST

Description

Beta Warning: This method, package or class is a beta version. It may not work as intended or its interface may change in the next version! So please be careful when you're intending to use it.

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.

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.

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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See also

ApCoCoA:Weyl.WeylIdeal

ApCoCoA:Weyl.WeylPolynom

ApCoCoA:Weyl.NewWeylIdeal