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SYMF::Tom -- converts any symmetric function into a m-polynomial

Call(s)


SYMF::Tom(sf <,b> <,Collect> <,NoExpand>)

Parameters

sf- any symmetric function
b- converts only b-polynomials appearing in sf

Options

NoExpand- keeps the recursive structure of sf
Collect- expresses the result on the m-basis

Introduction

The SYMF::Tom function converts any symmetric function into a m-polynomial.

The symmetric function sf is expanded and the result is not collected.

One may convert only b-polynomials of sf by adding the base b in the arguments.

One may preserve the recursive structure of sf by adding the argument NoExpand.

One may collect the result by adding the argument Collect. The result will be collected in all m-polynomials appearing in sf.

Example 1

>> muEC::SYMF::Tom( (s[2] - k*e[2])^2 * q - p[1]^3 );
      q m[4] + 3 q m[2, 2] + 2 q m[3, 1] + 4 q m[2, 1, 1] +
      
         6 q m[1, 1, 1, 1] - m[3] - 2 k q (m[3, 1] + m[2, 1, 1]) -
      
         2 k q (m[2, 2] + 2 m[2, 1, 1] + 6 m[1, 1, 1, 1]) +
      
          2                2                   2
         k  q m[2, 2] + 2 k  q m[2, 1, 1] + 6 k  q m[1, 1, 1, 1] -
      
         3 m[2, 1] - 6 m[1, 1, 1]
>> muEC::SYMF::Tom( (s[2] - k*e[2])^2 * q - p[1]^3, Collect );
                       2
      q m[4] + (3 q + k  q - 2 k q) m[2, 2] +
      
                   2
         (4 q + 2 k  q - 6 k q) m[2, 1, 1] +
      
                   2
         (6 q + 6 k  q - 12 k q) m[1, 1, 1, 1] +
      
         (2 q - 2 k q) m[3, 1] - m[3] - 3 m[2, 1] - 6 m[1, 1, 1]
>> muEC::SYMF::Tom( (s[2] - k*e[2])^2 * q - p[1]^3, Collect, NoExpand );
                                              2       3
                    q ((k - 1) m[1, 1] - m[2])  - m[1]
>> muEC::SYMF::Tom( (s[2] - k*e[2])^2 * q - p[1]^3, NoExpand, s );
                                              2       3
                   q (m[2] - k e[2] + m[1, 1])  - p[1]

Related Functions

Toe, Toh, Top, Tos, SfAddBasis, Sf

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MuPAD Combinat, an open source algebraic combinatorics package