The command Upper(v, rc, R) returns the list of the polynomials of rc with main variable strictly greater than v.

This command is part of the RegularChains[ChainTools] package, so it can be used in the form Upper(..) only after executing the command with(RegularChains[ChainTools]).  However, it can always be accessed through the long form of the command by using RegularChains[ChainTools][Upper](..).