# 5. Variables¶

reFORM has variables (not to be confused with the algebraic variables of the input), which are expressions that must fit in memory. They are shared between terms and between the global and the local scope.

They start with a $ sign. For example: $a = 5;
print $a;  yields 5. Variables can be used for many things as this chapter will show. Below we give an example where the variable gives each term a unique id (if not run in parallel): expr F = x + y + z;$counter = 0;
apply {
Multiply f($counter);$counter = $counter + 1; print; }  yields x*f(1) + y*f(2) + z*f(3)  ## 5.1. Pattern matching¶ Parts of a pattern can be stored in a dollar variable using matchassign: expr F = f(x,1,2,3);$a = 0;
apply {
matchassign f(y?,?b) {
$a = 2*y?*f(?b); } } print$a;


yields

2*f(1,2,3)*x


## 5.2. Control flow¶

Variables are also used as loop parameters in for:

$a = 0; for$i in 1..3 {
$a =$a + $i; } print$a;


yields 2.

## 5.3. Indexing¶

Variables can be indexed as if they were functions. Combined with loops this is very flexible:

for $i in 1..3 {$a[$i+x,2] =$i;
}

$b =$a[2+x,4] + f(x);

inside $b { id f(x?) =$a[1+x?,2];
id $a[x?,?a,y?] =$a[x?,?a,y?-2];
}

print $b;  yields 3. As this example shows, variables will be automatically substituted. ## 5.4. Between modules¶ Variables can be used to collect global information about an expression, like the maximum value of a certain functions argument over all the terms. This information can be used in a later module. For example: expr F = f(10) + f(20) + f(30);$a = 0;

apply {
matchassign f(x?) {
$a = x?; } maximum$a;
}

apply {
id f(x?) = f($a); }  yields 3*f(30). This piece of code stores the maximum value of $a over all terms (see maximum). In the next module, $a will be set to 30. ## 5.5. Command line arguments¶ Dollar variables can be specified on the command line using the -d flag. Using the $ is optional and will be added automatically.

For example:

reform -d \$a=5,b=6,c=1+x,d="1 + t^2" test.frm