Multiple assignment between lists in Mathematica 7 - wolfram-mathematica

Question

Suppose there are two lists a = {a1, a2, a3} and b = {b1, b2, b3}, and I want to write an assignment statement to make a1=b1,a2=b2,a3=b3 which only refers to a and b:
Thread[a = b]
But it only makes a={b1,b2,b3}. Using := (SetDelayed) instead of = doesn't work either.
Any solution? Thanks.

Answer 1

I think the Thread only works on "explicit" lists; the variables need to be expanded before being operated on.
After some experimentation, this works for me:
a = {a1, a2, a3};
b = {b1, b2, b3};
Thread[Set[Evaluate#a, Evaluate#b]];
{a1, a2, a3}
You could also write Thread[Evaluate#a = Evaluate#b]; just depends whichever you find more readable.

Answer 2

What's wrong with
MapThread[Set,{{a1,a2,a3},{b1,b2,b3}}]
?

Answer 3

Here's another solution:
a = {a1, a2, a3};
b = {b1, b2, b3};
each[{x_, y_}, Transpose[{a, b}],
x = y]
Which uses my handy each function:
SetAttributes[each, HoldAll]; (* each[pattern, list, body] *)
each[pat_, lst_, bod_] := (* converts pattern to body for *)
Scan[Replace[#, pat:>bod]&, Evaluate#lst] (* each element of list. *)
Similarly, you can do this:
MapThread[(#1 = #2)&, {a, b}]

Answer 4

Well, if they are really called a1, a2, etc, you could do this:
Assign[x_, y_] := Module[{s1, s2, n, sn},
s1 = SymbolName[Unevaluated[x]];
s2 = SymbolName[Unevaluated[y]];
For[n = 1, n <= Length[x] && n <= Length[y], n++,
sn = ToString[n];
Evaluate[Symbol[s1 <> sn]] = Evaluate[Symbol[s2 <> sn]]
]
]
SetAttributes[Assign, HoldAll]
And then
Clear[b1, b2, b3];
Clear[a1, a2, a3];
a = {a1, a2, a3}
b = {b1, b2, b3}
Assign[a, b]
a
Gives the results for a, b and a again as:
{a1, a2, a3}
{b1, b2, b3}
{b1, b2, b3}
As expected.
In general you can create expressions like these from proper use of SymbolName and Symbol, but be careful with your evaluation. If I had written SymbolName[x] (without the Unevaluated) then it would've interpreted that as SymbolName[{a1, a2, a3}], which is clearly not desirable. Not using Evaluate on Symbol[s1 <> sn] will have Mathematica complain that you're trying to reassign the Symbol function.