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SP::x2XX -- from the basis of monomials to XX Schubert basis

Call(s)


SP::x2XX(pol)

Parameters

pol- any expression in the basis of monomials

Introduction

The SP::x2XX function converts any expression from the basis of monomials to XX Schubert basis. It uses a different algorithm than ToXX (taking the leading monomials successively).

The result is not expanded.

One may add NoExpand just after the argument pol to choose not to expand the expression pol before treating it.

One may add Collect just after the argument pol or just after the argument NoExpand to collect the result.

Example 1

>> muEC::SP::x2XX((1+q)^5*x1*x2^2, NoExpand);
             5
      (q + 1)  (y3 XX[2, 3, 1] - XX[3, 2, 1] + XX[2, 4, 1, 3] +
      
         y1 (y1 XX[2, 1] + XX[2, 3, 1]) + y1
      
         (y3 XX[1, 3, 2] - XX[2, 3, 1] - XX[3, 1, 2] - y1 XX[2, 1] +
      
         XX[1, 4, 2, 3] + y2 (y2 XX[1] - XX[2, 1] + XX[1, 3, 2])))
>> muEC::SP::x2XX((1+q)^5*x1*x2, Collect);
                                     2             3
      XX[1] (y1 y2 + 5 q y1 y2 + 10 q  y1 y2 + 10 q  y1 y2 +
      
            4          5
         5 q  y1 y2 + q  y1 y2) + XX[1, 3, 2]
      
                            2          3         4       5
         (y1 + 5 q y1 + 10 q  y1 + 10 q  y1 + 5 q  y1 + q  y1) +
      
                                2       3      4    5
         XX[2, 3, 1] (5 q + 10 q  + 10 q  + 5 q  + q  + 1)

Related Functions

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MuPAD Combinat, an open source algebraic combinatorics package