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# Re: st: A question for those using Mathematica

 From Quang Nguyen <[email protected]> To [email protected] Subject Re: st: A question for those using Mathematica Date Thu, 6 Jan 2011 17:15:41 -1000

```Many thanks Greg for your very thoughtful answer. I would like to

Here is my question:

Do you know an equavalent way of using the loop index in a variable
name in Mathematica. In particular, in Stata can we define variable
such as: var`i' ; where i is an index of a loop (e.g., "for" loop

I don’t know if it’s still relevant or if you solved your problem, but
here’s the answer to your question. I do not have the rights post on
the Stata Listserv, so I’d really appreciate it if you’d respond to

In Mathematica, all code representation is symbolic. All notation is
either a string, a symbol, or a special character. Symbols and special
characters combine into expressions, and everything then further
combines to form “boxes”. In this way you can represent EVERYTHING in
any formatting/style/color, etc etc. Aside from these core
definitions, such as symbol, string, integer, real, etc, everything
else is an expression combining these things. For example input x+5
will be re-sorted internally to 5+x and will be stored as Plus[5,x],
where 5 will be an exact integer (important when you want rational
results), x will be a symbol, and “Plus” will also be a symbol which
will actually be a “Head” of the “Sequence” 5,x. So First[x+5] will
return 5, (x+5)[[-1]] will return x, and Head[x+5] will return Plus.
To go from expression to a string you use ToString, and ToExpression
to travel in the other direction. Several functions exist to travel
into the world of numbers, but you have to be careful with precision
and other aspects of numerical representation in Mathematica.

For your specific case, you should just generate a symbol (more
closely an entire expression consisting of just one symbol) from a
string which contains your iterator variable’s value:

For[i=0,i<10,i++,Print[Row[{“x”<>i,” = “,ToExpression[“x”<>i]}]];

If you need to assign to such a variable, the Head for = is Set, but
it has a HoldFirst attribute, which means that you will try to assign
a value to the ToExpression[…] expression, not to the variable, which
will be protected from assignment. The solution is to use the Evaluate
head, which causes evaluation of the held parameter:

For[i=0,i<10,i++, Set[Evaluate@ToExpression[“x”<>i] , i] ];
or simply
For[i=0,i<10,i++, Evaluate@ToExpression[“x”<>i] = i];

Of course this goes well beyond simple iterators. You can create
variables out of column names returned from SQLColumns or entire
using player0 and player1 to represent human and computer player, you
can actually use the word in your variable name and then create a
variable based on playr type, game/move number, so on and so forth.

Having said all that, I question practicality and readability of this
approach, and auto-optimization of ad-hoc expressions. In your
specific example, I think you’d be much better off just using arrays:
x[i], or indexes: xi
You can also create x[n_] where x is a function of n, but instead of
assigning it a latent value, computed at the time of evaluation (:=),
just assign the value you need.
Similarly, you can use a SparseArray, which allows you to have x[5]
and x[10] with nothing between (not just 0), but I prefer regular
Lists with Null elements x={1,,,,5}; Print@x[5] prints 5.

Good luck! Hope the description helps better understand and use Mathematica.

-Greg Klopper

On Tue, Sep 28, 2010 at 2:37 AM, Quang Nguyen <[email protected]> wrote:
>
> Do you know an equavalent way of using the loop index in a variable
> name in Mathematica. In particular, in Stata can we define variable
> such as: var`i' ; where i is an index of a loop (e.g., "for" loop
>
> Many thanks!
>
> --
> "My father gave me the greatest gift anyone could give another person,
> he believed in me." - Jim Valvano
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
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> *   http://www.ats.ucla.edu/stat/stata/

--
"My father gave me the greatest gift anyone could give another person,
he believed in me." - Jim Valvano

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```