ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 31 May 2016 23:12:21 -0500Solving zeta function equation numericallyhttp://ask.sagemath.org/question/33605/solving-zeta-function-equation-numerically/ I'm trying to solve the equation
$$ \zeta'(x)/\zeta(x) = - 3/4 $$
numerically. I'm expecting/hoping for an answer between 1 and 10.
I tried
$\texttt{ find_root(diff(zeta(x))/zeta(x) + 0.75, 2, 40)}$,
but this returns 0.0. I don't know what that ratio of zeta functions looks like, so it's possible there isn't a root, but I don't see why I'm getting an answer outside the specified interval.
Can anyone help find the true root? Thanks.
Tue, 31 May 2016 18:07:50 -0500http://ask.sagemath.org/question/33605/solving-zeta-function-equation-numerically/Comment by slelievre for <p>I'm trying to solve the equation
$$ \zeta'(x)/\zeta(x) = - 3/4 $$
numerically. I'm expecting/hoping for an answer between 1 and 10. </p>
<p>I tried </p>
<p>$\texttt{ find_root(diff(zeta(x))/zeta(x) + 0.75, 2, 40)}$,</p>
<p>but this returns 0.0. I don't know what that ratio of zeta functions looks like, so it's possible there isn't a root, but I don't see why I'm getting an answer outside the specified interval.</p>
<p>Can anyone help find the true root? Thanks. </p>
http://ask.sagemath.org/question/33605/solving-zeta-function-equation-numerically/?comment=33607#post-id-33607What version of Sage are you using? I get the following in Sage 7.2:
sage: find_root(diff(zeta(x))/zeta(x)+.75, 2, 40)
Traceback (most recent call last):
...
RuntimeError: f appears to have no zero on the intervalTue, 31 May 2016 23:12:21 -0500http://ask.sagemath.org/question/33605/solving-zeta-function-equation-numerically/?comment=33607#post-id-33607Answer by paulmasson for <p>I'm trying to solve the equation
$$ \zeta'(x)/\zeta(x) = - 3/4 $$
numerically. I'm expecting/hoping for an answer between 1 and 10. </p>
<p>I tried </p>
<p>$\texttt{ find_root(diff(zeta(x))/zeta(x) + 0.75, 2, 40)}$,</p>
<p>but this returns 0.0. I don't know what that ratio of zeta functions looks like, so it's possible there isn't a root, but I don't see why I'm getting an answer outside the specified interval.</p>
<p>Can anyone help find the true root? Thanks. </p>
http://ask.sagemath.org/question/33605/solving-zeta-function-equation-numerically/?answer=33606#post-id-33606 If you plot your function first, for example with
f = diff(zeta(x))/zeta(x)+.75
plot(f,0,10,ymin=-5,ymax=5,detect_poles=True,figsize=[4,3])
you can see approximately where the zero is:
![image description](/upfiles/14647427691047531.png)
You just need to change the range over which you're searching:
find_root(f,0,10)
1.8333259941894324
Here's a [link](http://sagecell.sagemath.org/?z=eJxLU7BVSMlMS9OoSi1J1KjQ1NSHMrT1zE15uXi5ijPyyzUKcvJLNNJ0DHQMDXQqczPzbHVNgXRiha2pTkpqSWpySXxBfk5qsW1IUWmqTlpmenFmVapttImOcaymJsiQtMy8lPiifLghYEEAIkYkqQ==&lang=sage) to live example.Tue, 31 May 2016 20:04:24 -0500http://ask.sagemath.org/question/33605/solving-zeta-function-equation-numerically/?answer=33606#post-id-33606