A new version of toPol is introduced: it introduces a simplifying shift on the partition (compensated by appropriate pre-factors).
Only the polynomial obtained after this simplification is kept (then toPol uses the old toPol renamed toPolbasic at the internal level, and toPolbasic calls the x-polynomial itself).
All the functions that determine structure constants (like toSchurProductPair, toJackProductPair, etc.) were re-written using the above, and renamed toXXXProductPair rather than toSchurProdPair.
The code for the Jack inner product was also modified to take the new toPol into account.
A new section Essentials : basic commands has been added at the beginning of the SymPol$Example.nb file (this file).