Cannot assign variable value inside Do Loop

Question

This is more of a conceptual problem.

Suppose I have three lists.

x1 = {1, 2, 9, 10};
x2 = {5, 6, 7};
x3 = {9, 10, 13};

Now, I wish to keep only the first two elements of each list. More precisely, I want

x1= {1, 2};
x2 = {5, 6};
x3 = {9, 10};

One easy way to do is,

x1=x1[[{1,2}; x2=x2[[{1,2}]]; x3=x3[[{1,2}]];

So far, it is okay. But it won't work if I try to do the same using the Do[] loop. For example,

Do[i=i[[{1,2}]],{i,{x1,x2,x3}];

do not assign new values to x1,x2,x3.

I also tried,

(#=#[[{1,2}]])&/@{x1,x2,x3}

But it didn't work.

I don't understand the reason behind this. What will be the correct way to assign variables/lists in a Do[] loop?

Answer 1

Mathematica is a term rewriting system. It will replace x1, x2, x3 by their values as soon as possible. One solution is:

{x1,x2,x3} = #[[{1,2}]]&/@{x1,x2,x3}

We can make it shorter as:

{x1, x2, x3} //= #[[{1, 2}]] & /@ # & 

Here //= is the "apply to" assignment operator. Basically x //= f is shorthand for x=f[x]. Because {x1,x2,x3} appear on the left side of the assignment they won't be replaced by their values (due to the HoldFirst attribute of assignment), and the proper assignment will take place.