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 pivoteqn
 returns a sublist of equations given a pivot

 Calling Sequence pivoteqn(C, var)

Parameters

 C - set of linear equations var - variable chosen to carry out a pivot operation

Description

 • The function pivoteqn(C, var) returns a sublist of equations from C. Each equation eq returned achieves the minimum non-negative ratio of

$-\frac{\mathrm{cterm}\left(\mathrm{eq}\right)}{\mathrm{coeff}\left(\mathrm{eq},\mathrm{var},1\right)}$

 • In the special case where all ratios are negative, the function returns FAIL.
 • The linear equations C are in the special form produced by simplex[setup].
 • The command with(simplex,pivoteqn) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{simplex}\right):$
 > $\mathrm{pivoteqn}\left(\left\{\mathrm{_SL1}=5-4x-3y,\mathrm{_SL2}=4-3x-4y\right\},x\right)$
 $\left[{\mathrm{_SL1}}{=}{5}{-}{4}{}{x}{-}{3}{}{y}\right]$ (1)