On 11/12/2011 03:39 PM, William Stein wrote:
>
> I wonder if Sage should not call Maxima for definite integrals -- only
> call Maxima for finding a primitive, then do the rest itself?
>
> Here's a version of the integrate function that does what I'm speculating
> about:
>
> def integrate2(f, x, a, b):
> g = integrate(f, x)
> return g(x=b) - g(x=a)
>
> Here is some sample usage:
>
> sage: integrate2(1/(sqrt(x)*((1+sqrt(x))^2)), x, 1, 9)
> 1/2
>
> sage: integrate2(x^3, x, 2, pi)
> 1/4*pi^4 - 4
>
This was my fix for a different issue,
sage: u = SR.symbol('u', domain='real')
sage: f = function('f', x, u)
sage: g(x) = integrate(f, u, 0, sqrt(x))
...
RuntimeError: ECL says: Error executing code in Maxima: defint: upper
limit of integration must be real; found sqrt(x)
This is a simple case where assume(x>0) saves you, but I deduce that
Maxima will bail whenever it can't prove to itself that the bounds are real.
With a real-life expression, I get the mysterious,
RuntimeError: ECL says: Error executing code in Maxima: defint: upper
limit of integration must be real; found errexp1
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