Re: Plus sets in mathematica..?

*To*: mathgroup at smc.vnet.net*Subject*: [mg75959] Re: Plus sets in mathematica..?*From*: dimitris <dimmechan at yahoo.com>*Date*: Mon, 14 May 2007 03:34:46 -0400 (EDT)*References*: <f26ocl$4tn$1@smc.vnet.net>

=CE=9F/=CE=97 changbo =CE=AD=CE=B3=CF=81=CE=B1=CF=88=CE=B5: > I want to make a function "f", its domain is every thinkable two sets, and > the result is {a+b | a=E2=88=88A,b=E2=88=88B} for A,B. > > ex) A={1,2,3}, B={40,50,60,70}, > then I have f[A,B] as > {41,42,43,51,52,53,61,62,63,71,72,73}. > > How can I construct function "f"? Let me know the source.. Thank you very > much I am sure they must be various ways. As regards timing issues I am not the person who will talk about. Anyway, the easiest thing that comes in my mind is: In[36]:= A={1,2,3}; B={40,50,60,70}; Flatten@Outer[Plus,B,A] Out[38]= {41,42,43,51,52,53,61,62,63,71,72,73} where In[39]:= Information["Outer", LongForm -> False] "Outer[f, list1, list2, ... ] gives the generalized outer product of the listi, forming all possible combinations of the \ lowest-level elements in each of them, and feeding them as arguments to f. Outer[f, list1, list2, ... , n] treats as separate \ elements only sublists at level n in the listi. Outer[f, list1, list2, ... , n1, n2, ... ] treats as separate elements only \ sublists at level ni in the corresponding listi."*Button[More=E2=80=A6, ButtonData :> "Outer", Active -> True, ButtonStyle -> "RefGuideLink"] As an one-liner In[4]:= f[o_,e_,he_]:=Flatten@Outer[he,o,e] Example In[5]:= f[A,B,Plus] Out[5]= {41,51,61,71,42,52,62,72,43,53,63,73} In[9]:= f[Table[Random[], {3}], CharacterRange["a", "e"], Times] Out[9]= {0.758958 a,0.758958 b,0.758958 c,0.758958 d,0.758958 e,0.441985 a, 0=2E441985 \ b,0.441985 c,0.441985 d,0.441985 e,0.344708 a,0.344708 b,0.344708 c, 0=2E344708 \ d,0.344708 e} Dimitris