According to the documentation of find_fit, the "model" can be a plain python function:

model Either a symbolic expression, symbolic function, or a Python
function. model has to be a function of the variables (x1;x2;:::;xk) and
free parameters (a1;a2;:::;al).

and nothing stops you from using conditionals inside f:

```
def f(t,a) :
if t<1/2:
return t*a
return (1-t)*a
data = [(i,i*(1-i)) for i in xsrange(0, 1, 0.1)]
var('a, x')
d = find_fit(data,f, parameters=[a], variables=[x], solution_dict=True)
a0 = d[a]
print a0
point(data) + plot(lambda t:f(t,a0), 0,1)
```

Yes. It turns out that piecewise does not have a member function variables. So len(variables) retruns a error. Is there a ticket about this? I could not find any. If the function happens to be piecewise we should call length and not len(variables)

Sounds like you should open a ticket for this :)

A ticket has been created (http://trac.sagemath.org/sage_trac/ticket/12316). I will try to fix it soon.

Ok, thank you.