I'm having some difficulties writing sage code to solve linear programming problems using "natural variables", by substituting for them the variables required for MixedIntegerLinearProgram.

The code for "minimize_desired" is what I'd like to do, but it fails during the substitution with the error message "TypeError: no canonical coercion from Linear functions over Real Double Field to Symbolic Ring". What I'd like is for sage to just do the substitution and ignore the lack of coercion.

The code for "minimize_works" works, but I got past the type checking by changing everything to strings and then back into a sage object, which feels like a terrible kludge. However this does illustrate that, despite sage's worries about coercion, everything ends up fine for MixedIntegerLinearProgram.

Is there a way to turn off sage's type checking and just do the substitution?

Thanks,

Mike

Note: I simplified the examples below by eliminating all the code that dealt with constraints.

```
def minimize_desired(objective):
p = MixedIntegerLinearProgram(maximization=false)
pvar = p.new_variable(real=True, nonnegative=True)
variables=set(objective.arguments())
translation={v:pvar[v] for v in variables}
objective=objective.subs(translation) # FAILS HERE
p.set_objective(objective)
print p.solve()
def minimize_works(objective):
p = MixedIntegerLinearProgram(maximization=false)
pvar = p.new_variable(real=True, nonnegative=True)
variables=set(str(v) for v in objective.arguments())
translation={v:pvar[v] for v in variables}
objective=sageobj(str(objective), translation)
p.set_objective(objective)
print p.solve()
var('x y')
minimize_works(x+y)
print
minimize_desired(x+y)
```