The function pivotvar(f, List) returns either a variable which has a positive coefficient or FAIL.  The optional List (of variable names) is used to determine the order in which the variables should be examined.  The first success is used. If no List is provided, then pivotvar chooses its own order.

The command with(simplex,pivotvar) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{simplex}\right)\:$

$\mathrm{pivotvar}\left(\mathrm{x1}+3\mathrm{x3}-\mathrm{x4}\right)$

$\mathrm{x1}$

$\mathrm{pivotvar}\left(\mathrm{x1}+3\mathrm{x3}-\mathrm{x4}\,\left[\mathrm{x4}\,\mathrm{x3}\,\mathrm{x1}\right]\right)$

$\mathrm{x3}$