The reciprocal of tangent is not a constant function, but Sage says
otherwise.  This is now http://trac.sagemath.org/sage_trac/ticket/3980
.

(Incidentally, using z(x)=tan(x) also doesn't work, as it yields a
NotImplementedError (whose message could be better) for 1/z;
presumably the bug below would occur even if it were implemented,
though.)

- kcrisman

sage: z=tan
sage: z
tan
sage: 1/z
1/tan
sage: find_root(1/z,1,2)
---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call
last)

<snip>

/Applications/sage/local/lib/python2.5/site-packages/sage/numerical/
optimize.py in find_root(f, a, b, xtol, rtol, maxiter, full_output)
     52     """
     53     try:
---> 54         return
f.find_root(a=a,b=b,xtol=xtol,rtol=rtol,maxiter=maxiter,full_output=full_output)
     55     except AttributeError:
     56         pass

/Applications/sage/local/lib/python2.5/site-packages/sage/calculus/
calculus.py in find_root(self, a, b, var, xtol, rtol, maxiter,
full_output)
   3088                     return a
   3089                 else:
-> 3090                     raise RuntimeError, "no zero in the
interval, since constant expression is not 0."
   3091             var = repr(w[0])
   3092

RuntimeError: no zero in the interval, since constant expression is
not 0.

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