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cannot convert log(x)/log(2) to int

asked 2021-06-28 21:17:46 +0200

zplot gravatar image

updated 2021-06-28 23:49:46 +0200

slelievre gravatar image

If I define J(x) function as:

def J(x):
    sum = 0
    for i in range(1, int(log(x)/log(2)) + 1):
        sum = sum + 1 / i * prime_pi(x**(1/i))

when I try to plot it using:

p = plot(J(x), (x, 1, 20))

I get the message:

cannot convert log(x)/log(2) to int

but if try J function acting on any float number I get a perfect value like:

sage: J(123.456789)

I have tried to replace int by floor but with the same result. Any help to solve the plotting problem will be welcome. Thank you.

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answered 2021-06-28 23:50:38 +0200

slelievre gravatar image

updated 2021-06-29 00:00:03 +0200

Many such plotting problems are solved by using a callable function or a lambda function instead of a symbolic expression.

The problem is that J(x) tries to evaluate J with the symbolic variable x as an argument, and it cannot make log(x)/log(2) an integer while x stays symbolic.

To work around that, plot using J rather than J(x):

p = plot(J, (1, 20))

or use a lambda function:

p = plot(lambda x: J(x), (1, 20))

Plot the function J with Sage

The function J could be rewritten as:

def J(x):
    return sum(1/i * prime_pi(x**(1/i))
               for i in range(1, int(log(x)/log(2)) + 1))
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Thank you very much, Samuel. It worked perfectly.

zplot gravatar imagezplot ( 2021-06-29 08:39:54 +0200 )edit

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Asked: 2021-06-28 21:17:46 +0200

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Last updated: Jun 29 '21