Re: Lists of all values of a two-variable function

*To*: mathgroup at smc.vnet.net*Subject*: [mg64769] Re: Lists of all values of a two-variable function*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Thu, 2 Mar 2006 06:48:42 -0500 (EST)*Organization*: The Open University, Milton Keynes, UK*References*: <du3vcn$mjd$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

José Carlos Santos wrote: > Hi all, > > I would like to do this: given a function _f_ in two variables and two > lists l1 and l2, to get the list of all values f[a,b] with _a_ in l1 and > _b_ in l2, with all duplicated values removed. How do I do that? > > The closest thing that I am able to do is: > > Table[f[l1[[i]],l2[[j]]],{i,1,Length[l1]},{j,1,Length[l2]}] > > but, of course: > > 1) what I get is a list of lists; > > 2) I eventually get duplicated values. > > Best regards, > > Jose Carlos Santos > Hi Jose Carlos, You could try one of the following approaches among many others. First, starting with your method using *Table* and say that l1, l2 and f are equal to In[1]:= l1 = {1, 2, 3}; l2 = {2, 3, 4, 5}; f[a_, b_] := a^2 + b^2; respectively, you can get the type of result you are looking for by wrapping the list of lists within a *Union* and *Flatten* commands In[4]:= Union[Flatten[Table[f[l1[[i]], l2[[j]]], {i, 1, Length[l1]}, {j, 1, Length[l2]}]]] Out[4]= {5,8,10,13,17,18,20,25,26,29,34} No duplicates and only one level. Hoe does it work? First, *Table* yields a list of lists In[5]:= Table[f[l1[[i]], l2[[j]]], {i, 1, Length[l1]}, {j, 1, Length[l2]}] Out[5]= {{5,10,17,26},{8,13,20,29},{13,18,25,34}} Then, *Flatten* returns a simple list, unsorted and with duplicates In[6]:= Flatten[%] Out[6]= {5,10,17,26,8,13,20,29,13,18,25,34} Finally, *Union* sorts the list and discard any duplicates In[7]:= Union[%] Out[7]= {5,8,10,13,17,18,20,25,26,29,34} Another approach would be to use an outer product as in In[8]:= Outer[f, l1, l2]//Flatten//Union Out[8]= {5,8,10,13,17,18,20,25,26,29,34} since *Outer* yields In[9]:= Outer[f, l1, l2] Out[9]= {{5,10,17,26},{8,13,20,29},{13,18,25,34}} You could try also the *Tuple* function with a slightly modified version of the function f In[10]:= Tuples[{l1,l2}] Out[10]= {{1,2},{1,3},{1,4},{1,5},{2,2},{2,3},{2,4},{2,5},{3,2},{3,3},{3,4},{3,5}} In[11]:= f[{a_,b_}]:=a^2+b^2; In[12]:= f/@Tuples[{l1,l2}]//Union Out[12]= {5,8,10,13,17,18,20,25,26,29,34} Best regards, /J.M.