gathers into sublists each set of elements in list that gives the same value when f is applied.

gathers list into nested sublists using fi at level i.


  • GatherBy[{e1,e2,e3,},f] evaluates f[ei] for each i to determine how to gather the ei.
  • GatherBy[list,] gives results that follow the ordering of elements in list.
  • Within each sublist generated by GatherBy[list,], elements appear in the same order as in list; the complete sublists are ordered so that their first elements appear in the same order as in list.
  • GatherBy[list] is equivalent to GatherBy[list,Identity], which is also equivalent to Gather[list]. »
  • GatherBy effectively produces an equivalence partition.
  • GatherBy[list,{f1,f2}] is equivalent to Map[GatherBy[#,f2]&,GatherBy[list,f1]].
Introduced in 2008