Robert Dodier wrote:
> On Dec 4, 2:04 pm, "William Stein" <[EMAIL PROTECTED]> wrote:
> 
>> sage: f.n()
>>
>> and get back a floating point number.  This is surprisingly not
>> implemented in Sage, but it isn't.
>> (That's basically because Maxima itself doesn't seem to have such
>> functionality.)
> 
> I'm guessing that f.n() just turns on the numer flag for Maxima.
> numer causes any literal numbers or symbolic constants
> to be replaced by floating point values. However the integrate
> function is called as without numer. If you want a numerical
> integration, call quad_qags or some other Quadpack function.


FYI, scipy has numerical integration, based on quadpack:

http://docs.scipy.org/doc/scipy/reference/integrate.html

sage: from scipy.integrate import quad
sage: f(x) = 250*cos(pi*x/180)^1.8 + 170.35
sage: from sage.ext.fast_eval import fast_float
sage: ff = fast_float(f, 'x')
sage: quad(ff,0,18)
(7435.2795815640284, 8.2548185859776835e-11)
sage: timeit('quad(ff,0,18)')
625 loops, best of 3: 118 µs per loop

There are lots of options you can pass.  If you want an infinite limit, 
then, use scipy.integrate.Inf.

It sounds like it would be good to use this if we wanted a numerical 
approximation of an integral.

Jason


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