> sage: n(a) # Why doesn't this return the result of numerical_integral?
> ---------------------------------------------------------------------------
> TypeError                                 Traceback (most recent call last)
>
> /home/jason/.sage/temp/littleone/29880/_home_jason__sage_init_sage_0.py
> in <module>()
>
> /home/jason/sage/local/lib/python2.5/site-packages/sage/misc/functional.pyc
> in numerical_approx(x, prec, digits)
>      765             prec = int((digits+1) * 3.32192) + 1
>      766     try:
> --> 767         return x.numerical_approx(prec)
>      768     except AttributeError:
>      769         from sage.rings.complex_double import
> is_ComplexDoubleElement
>
> /home/jason/sage/local/lib/python2.5/site-packages/sage/calculus/calculus.p yc
> in numerical_approx(self, prec, digits)
>     1514         except TypeError:
>     1515             # try to return a complex result
> -> 1516             approx = self._complex_mpfr_field_(ComplexField(prec))

Here's the problem: the only TypeError it recognizes is to try to
evaluate a complex integral, but since sin(cos(x)) doesn't have an
antiderivative Maxima knows about, it tries this.  Maybe one
(you? :) ) can implement a catch for the event that the integral does
not completely resolve symbolically (e.g. try sage: integrate(1/
(1+x^8)) versus sage: integrate(1/(1+x^7)), where the first just
returns the question but the second did the only piece of the partial
fraction it could, yet both should probably have numerical_integral
applied somehow when n() is called.)

- kcrisman
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