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# `SYMF` - library for symmetric functions

## Table of contents

1. The library `muEC::SYMF`

1. `Char2Sf` - converts a virtual character into a symmetric function
2. `Sf2Char` - converts a symmetric function into a virtual character
3. `Sf2Table` - converts a symmetric function into a table
4. `Sf2TableVar` - variable set of a symmetric function
5. `SfCCProd` - computes the conjugacy class product of symmetric functions
6. `SfCollect` - collects products that are on algebraic bases (`e, h, p`) and expands products on linear bases (`m, s`)
7. `SfDiff` - differential operator
8. `SfInternal` - computes the inner tensor product of symmetric functions
9. `SfEval` - realizes the action of symmetric functions on polynomials
10. `SfJtMat` - computes the Jacobi-Trudi matrix
11. `SfMat` - transition matrix between symmetric functions bases
12. `SfOmega` - applies the Omega-automorphism
13. `SfPlethysm` - plethysm of symmetric functions
14. `SfScalar` - scalar product of symmetric functions
15. `SfTheta` - applies the Theta-automorphism
16. `SfZee` - computes the scalar product of a `p`-function with itself
17. `Table2Sf` - converts a table into a symmetric function
18. `Toe` - converts any symmetric function into a `e`-polynomial
19. `Toh` - converts any symmetric function into a `h`-polynomial
20. `Tom` - converts any symmetric function into a `m`-polynomial
21. `Top` - converts any symmetric function into a `p`-polynomial
22. `Tos` - converts any symmetric function into a `s`-polynomial

[Contents]

MuPAD Combinat, an open source algebraic combinatorics package