Incorrect result for integral of (cos z) / z

asked 2021-06-21 15:09:34 +0100

ripple_carry
91 ●1 ●3 ●11

I am confused by the following result: I'd like to integrate cos(z) / z on a circle around the origin. I tried:

var('z,t')

f = (cos(z))/z

show(f)

gamma = e^(i * t) 

dg = gamma.diff(t)

h = f(z=gamma) * dg
print(h)
show(h.integrate(t, 0, 2 * pi))

and I get:

I*cos(e^(I*t))
0

If I put the same integral into WolframAlpha, I get the result I was expecting (2 pi i).

Is this a bug, or have I specified the problem incorrectly?

answered 2021-06-21 15:39:12 +0100

FrédéricC

5206 ●3 ●43 ●114

Which version of sage do you use ? Mine gives

sage: h.integrate(t,algorithm='maxima')                                         
1/2*Ei(I*e^(I*t)) + 1/2*Ei(-I*e^(I*t))
sage: h.integrate(t,algorithm='giac')                                           
cos_integral(e^(I*t))
sage: h.integrate(t,algorithm='sympy')                                          
cos_integral(e^(I*t))

So one problem is that maxima is not using the correct primitive.

But well, at least one of our integrator gives a correct result in sage 9.4.beta2 :

sage: h.integrate(t,0,2*π,algorithm='maxima')                                   
0
sage: h.integrate(t,0,2*π,algorithm='giac')                                     
2*I*pi
sage: h.integrate(t,0,2*π,algorithm='sympy')                                    
0

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My About tab says:

┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.1, Release Date: 2020-05-20                     │
│ Using Python 3.7.3. Type "help()" for help.                        │
└────────────────────────────────────────────────────────────────────┘

ripple_carry ( 2021-06-21 15:44:23 +0100 )edit

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