The call pivot(C, x, eqn) constructs a new set of equations in a form compatible with the forms used in simplex[setup], by solving the specified equation eqn for x, then substituting the result into C. This is equivalent to the standard simplex pivot on an array of coefficients.

To re-express the objective function f in terms of this new description, one can substitute the result of pivot into f.

If eqn is a list of equations, then ${\mathrm{eqn}}_1$ is used.  This is to facilitate easy user interaction with the function simplex[pivoteqn] used to choose an equation to use for the next pivot.

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

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

$\mathrm{pivot}\left(\left\{\mathrm{\_SL1}=5-4x-3y\,\mathrm{\_SL2}=4-3x-4y\right\}\,x\,\left[\mathrm{\_SL1}=5-4x-3y\right]\right)$

$\left\{\mathrm{\_SL2}=\frac{1}{4}-\frac{7y}{4}+\frac{3\mathrm{\_SL1}}{4}\,x=\frac{5}{4}-\frac{3y}{4}-\frac{\mathrm{\_SL1}}{4}\right\}$