Can't get symbol from callable function x |--> x

[kcrisman]

From  this ask.sagemath question:

I was plotting sin(x)/x and also wanted a seperate plot of sin(x) and x so I could visualize those components as well. However I get an error when plotting x saying "free variable x -> x". If I add a coefficient to h(x) such as h(x) = 1.0001*x then it works fine.

This is the code I am using:

f(x) = sin(x)/x
g(x) = sin(x)
h(x) = x

fig1 = plot(f,-10,10,rgbcolor='green')
fig2 = plot(g,-10,10,rgbcolor='purple')
fig3 = plot(h,-10,10,rgbcolor='red')

figure = fig1 + fig2 + fig3
show(figure,xmin=-10,xmax=10,ymin=-10,ymax=10,figsize=[8,8],fontsize=20)

The underlying problem is

The exception arises in `sage.symbolic.expression_conversions.FastFloatConverter.symbol`:

            try:
                return self.ff.fast_float_constant(float(ex))
            except TypeError:
                raise ValueError, "free variable: %s" % repr(ex)

so that it assumes if a callable expression doesn't have the variable, it must be a constant.  However, it before this asks for `if name in vars` and `if name in svars`, but here the `name` is `'x |--> x'`.

So what we need to do is fix it so that if the operator is `None` in the previous traceback in your error message, we check for this case explicitly, where the name isn't just one of the variables.

---

Apply attachment:trac_10246-callable-x.patch

[kcrisman]

See also  this ask.sagemath.org question where exactly the same thing comes up.

I'm putting this as 'beginner', and moving to 'critical', though that is pretty meaningless... Anyway, it's really dumb that we can't plot x.

[kcrisman]

Based on 4.7.alpha1

[kcrisman]

Ready for review. This should fix the problem, and I tried to do it in a relatively elegant way. Unfortunately, there really is no such elegant way, since symbol shouldn't be relying on strings anyway, right? Oh well.

[mhansen]

Looks good to me.