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buildSymmetricGB -- Groebner basis of elementary symmetric polynomials algebra

Synopsis

Description

i1 : n=5;
i2 : R=QQ[x_1..x_n];
i3 : buildSymmetricGB R

         5    4      3      2                 4    3      3      2 2    2    
o3 = {- x  + x e  - x e  + x e  - x e  + e , x  + x x  - x e  + x x  - x x e 
         5    5 1    5 2    5 3    5 4    5   4    4 5    4 1    4 5    4 5 1
     ------------------------------------------------------------------------
        2        3      2                      4    3      2                 
     + x e  + x x  - x x e  + x x e  - x e  + x  - x e  + x e  - x e  + e , -
        4 2    4 5    4 5 1    4 5 2    4 3    5    5 1    5 2    5 3    4   
     ------------------------------------------------------------------------
      3    2      2      2        2                        2                
     x  - x x  - x x  + x e  - x x  - x x x  + x x e  - x x  + x x e  - x e 
      3    3 4    3 5    3 1    3 4    3 4 5    3 4 1    3 5    3 5 1    3 2
     ------------------------------------------------------------------------
        3    2      2        2                    3    2                 2  
     - x  - x x  + x e  - x x  + x x e  - x e  - x  + x e  - x e  + e , x  +
        4    4 5    4 1    4 5    4 5 1    4 2    5    5 1    5 2    3   2  
     ------------------------------------------------------------------------
                                  2                         2                
     x x  + x x  + x x  - x e  + x  + x x  + x x  - x e  + x  + x x  - x e  +
      2 3    2 4    2 5    2 1    3    3 4    3 5    3 1    4    4 5    4 1  
     ------------------------------------------------------------------------
      2
     x  - x e  + e , - x  - x  - x  - x  - x  + e }
      5    5 1    2     1    2    3    4    5    1

o3 : List

This function should work up to a size of 15 variables in the base ring

This function is part of the package SymmetricPolynomials.

Ways to use buildSymmetricGB :

For the programmer

The object buildSymmetricGB is a method function.