def pivot(constraints: List[LinearFunction], objective_fn: LinearFunction,
callback: Callable[[int, int], None]) -> None:
"""
>>> from linear_function import LinearFunction
>>> constraints = [ \
LinearFunction(18, [-2, -1, -1]), \
LinearFunction(30, [-1, -2, -2]), \
LinearFunction(24, [-2, -2, -2]), \
]
>>> objective_fn = LinearFunction(0, [6, 5, 4])
>>> _pivot(constraints, objective_fn)
>>> print(objective_fn)
54 + -3*x₀ + 2*x₁ + 1*x₂
>>> for i in constraints: print(i)
9 + -1/2*x₀ + -1/2*x₁ + -1/2*x₂
21 + 1/2*x₀ + -3/2*x₁ + -3/2*x₂
6 + 1*x₀ + -1*x₁ + -1*x₂
"""
arg_number = first_index(objective_fn.coefs, lambda x: x > 0)
index = tightest_constraint(constraints, arg_number)
assert -constraints[index].free / constraints[index].coefs[arg_number] > 0
constraints[index].rearrange(arg_number)
for c in skip_at(constraints, index):
c.substitute(arg_number, constraints[index])
objective_fn.substitute(arg_number, constraints[index])
callback(arg_number, index)
