Status: Valid
Owner: ----
Labels: Type-Defect Priority-Medium
New issue 3853 by [email protected]: recognize elliptical integrals
http://code.google.com/p/sympy/issues/detail?id=3853
This requires about 2 minutes
Ellipse((0,0),3,1).circumference.n()
13.3648932205553
This is nearly instantaneous
def EllipseCircumference(a, b):
... """
... Compute the circumference of an ellipse with semi-axes a and b.
... Require a >= 0 and b >= 0. Relative accuracy is about 0.5^53.
... """
... import math
... x, y = max(a, b), min(a, b)
... digits = 53; tol = math.sqrt(math.pow(0.5, digits))
... if digits * y < tol * x: return 4 * x
... s = 0; m = 1
... while x - y > tol * y:
... x, y = 0.5 * (x + y), math.sqrt(x * y)
... m *= 2; s += m * math.pow(x - y, 2)
... return math.pi * (math.pow(a + b, 2) - s) / (x + y)
...
EllipseCircumference(3,1)
13.364893220555258
Perhaps recognition of such integrals by integrate/Integral.evalf would be
a good idea.
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