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I'm using Sage 9.3

I plot an integral with quad() function in a Python file.

I wanted to plot the same result with SageMath but the values returned are different and I really don't understand why the two graphics are not the same ...

Here is my Sage code :

import scipy.integrate as sp_int

int1(a, j, k, L) =  piecewise([[[0, 1/4], 1 * cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)], [(1/4, 3/4), 2 * cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)], [[3/4, 1], 1 * cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)]])

def int2(a, j, k, L):
    if a < 1 / 4 or a > 3 / 4:
        return cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)
    else:
        return 2* cos(pi * (j + 1) * a/L) * cos(pi * (k + 1) * a/L)

def integral1(j):
    k = 2
    L = 0.5
    return numerical_integral(int1, 0, 1, max_points=10, params=[j, k, L])[0]

def integral2(j):
    k = 2
    L = 0.5
    return sp_int.quad(int2, 0, 1, args=(j, k, L))[0]

i1 = plot(integral1, 0, 10, rgbcolor=(0.8,0, 0),
          legend_label='SageMath/numerical_integral')
i2 = plot(integral2, 0, 10, rgbcolor=(0, 0.8, 0),
          legend_label='Python/Quad')
show(i2 + i1)

What a great answer ! Deep but clear explanation. I learned a lot from reading you. Thanks.

Thanks for your comments. Frédéric, certes ... : How to piecewise on 'a' ? Tolga : I will try

Thanks for your comments. - Frédéric, certes ... : How to piecewise on 'a' ? - Tolga : I will try

Thanks for your comments - Frédéric, certes ... : How to piecewise on 'a' ? - Tolga : I will try

Frédéric : How to piecewise on 'a' ? Tolga : I will try

Frédéric : How to piecewise on 'a' ? Tolga : I will try

Difference between numerical_integral and spicy.integrate.quad I plot an integral with quad() function in a Python file.

Difference between numerical_integral and spicy.integrate.quad I plot an integral with quad() function in a Python file.

Difference between numerical_integral and spicy.integrate.quad I plot an integral with quad() function in a Python file.

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It works perfectly ! Thanks a lot

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