Editing Reduce (computer algebra system) (section)

==== Repetition statements: for ... ====
The <code>for</code> statement is a flexible loop construct that executes ''statement'' repeatedly a number of times that must be known in advance. One version has the form
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<code>for</code> ''variable'' := ''initial'' <code>step</code> ''increment'' <code>until</code> ''final'' <code>do</code> ''statement''
</div>
where ''variable'' names a variable whose value can be used within ''statement'', and ''initial, increment'' and ''final'' are numbers (preferably integers). The value of ''variable'' is initialized to ''initial'' and ''statement'' is executed, then the value of ''variable'' is repeatedly increased by ''increment'' and the ''statement'' executed again, provided the value of ''variable'' is not greater than ''final''. The common special case "''initial'' <code>step 1 until</code> ''final''" can be abbreviated as "''initial'' : ''final''".

The following <code>for</code> statement computes the value of <math>n!</math> as the value of the variable <code>fac</code>.
<syntaxhighlight lang="octave" copy="">
n := 5;
fac := 1$ for r := 2 : n do fac := fac*r; fac;
</syntaxhighlight>

Another version of the <code>for</code> statement iterates over a list, and the keyword <code>do</code> can be replaced by <code>product</code>, <code>sum</code>, <code>collect</code> or <code>join</code>, in which case the <code>for</code> statement becomes an expression and the controlled ''statement'' is treated as an expression. With <code>product</code>, the value is the product of the values of the controlled ''statement''; with <code>sum</code>, the value is the sum of the values of the controlled ''statement''; with <code>collect</code>, the value is the values of the controlled ''statement'' collected into a list; with <code>join</code>, the value is the values of the controlled ''statement'', which must be lists, joined into one list.

The following <code>for</code> statement computes the value of <math>n!</math> much more succinctly and elegantly than the previous example.
<syntaxhighlight lang="octave" copy="">
n := 5;
for r := 2 : n product r;
</syntaxhighlight>