In `mip.pyx`, there is:
{{{
A mixed integer linear program can give you an answer:
...
#. By default, all variables are non-negative. We remove that constraint
via ``p.set_min(variable, None)``, see :meth:`set_min
<sage.numerical.mip.MixedIntegerLinearProgram.set_min>`.
}}}
There's also this text in `class MixedIntegerLinearProgram`:
{{{
.. WARNING::
All LP variables are non-negative by default (see
:meth:`new_variable`
and :meth:`set_min`).
}}}
However, it doesn't seem to be the case. For example, the code:
{{{
sage: p = MixedIntegerLinearProgram()
sage: x, y, z = p['x'], p['y'], p['z']
sage: p.set_objective(x+y+3*z)
sage: p.add_constraint(x+2*y <= 4)
sage: p.add_constraint(5*z-y <= 8)
}}}
produces:
{{{
sage: p.show()
Maximization:
x_0 + x_1 + 3.0 x_2
Constraints:
x_0 + 2.0 x_1 <= 4.0
- x_1 + 5.0 x_2 <= 8.0
Variables:
x_0 is a continuous variable (min=-oo, max=+oo)
x_1 is a continuous variable (min=-oo, max=+oo)
x_2 is a continuous variable (min=-oo, max=+oo)
}}}
Of course one can set `p.set_min(x, 0)` etc. in the problem of above, but
it doesn't seem to be the default. Ticket?
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