I dunno if ignoring the discontinuity is the only problem here. integrate(..., x, 0, 1/2) returns 23/24 which seems to be incorrect (should be 1/8 I guess).
integrate(..., x) returns an antiderivative and then ev(%, x = 1/2 - foo) - ev(%, x = 0) followed by limit(%, foo, 0, plus) yields 1/8. I don't know where it goes wrong.
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Numerical solution seems to be right (it is calculated at r=0.99; at r=1.00 it should be cos(2 * phi) - 1), but symbolic one is radically different. Note that it is calculated using ldefint; integrate yields similarly looking non-smooth function (full of atan(tan(phi)))
ooops.. posted the wrong link! See also: https://trac.sagemath.org/ticket/21440
Maxima's antiderivative has a discontinuity at
x=1/2
, which it doesn't detect, so it just doesF(1)-F(0)
. I believe that's where the error comes from.I dunno if ignoring the discontinuity is the only problem here.
integrate(..., x, 0, 1/2)
returns 23/24 which seems to be incorrect (should be 1/8 I guess).integrate(..., x)
returns an antiderivative and thenev(%, x = 1/2 - foo) - ev(%, x = 0)
followed bylimit(%, foo, 0, plus)
yields 1/8. I don't know where it goes wrong.The same problem here:
Numerical solution seems to be right (it is calculated at
r=0.99
; atr=1.00
it should becos(2 * phi) - 1
), but symbolic one is radically different. Note that it is calculated usingldefint
;integrate
yields similarly looking non-smooth function (full ofatan(tan(phi))
)