The command SeparateSolutions(l_rc, R) returns a list of square-free regular chains such that the ideals they generate are pairwise relatively prime.

The input regular chains must be zero-dimensional.

The algorithm is based on GCD computations.

This command is part of the RegularChains[ChainTools] package, so it can be used in the form SeparateSolutions(..) 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][SeparateSolutions](..).