On Tue, Jun 7, 2016 at 4:12 AM, Ralf Stephan wrote:
> In an SMC terminal session:
>
> ~$ sage
> ┌┐
> │ SageMath Version 6.10, Release Date: 2015-12-18│
> │ Enhanced for SageMathCloud.
>
> > on SMC terminal
> > $ sage-develop
> >
> > gives you 7.3.beta2
>
> Now how can I use this kernel in my yupyter notebook?
> Ahh, it's there also! Is this new? Anyway thanks for this hint!
>
This was perhaps not a good idea. It's been long since I got so many ugly
error messages.
/pro
> on SMC terminal
> $ sage-develop
>
> gives you 7.3.beta2
Now how can I use this kernel in my yupyter notebook?
Ahh, it's there also! Is this new? Anyway thanks for this hint!
Peter
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on SMC terminal
$ sage-develop
gives you 7.3.beta2
On Tuesday, June 7, 2016 at 9:12:19 AM UTC+1, Ralf Stephan wrote:
>
> In an SMC terminal session:
>
> ~$ sage
> ┌┐
> │ SageMath Version 6.10, Release Date: 2015-12-18
In an SMC terminal session:
~$ sage
┌┐
│ SageMath Version 6.10, Release Date: 2015-12-18│
│ Enhanced for SageMathCloud.│
└
> Your Sage is too old, this Pynac bug (existing for years) was fixed
> months ago and should be in 7.2.
Thanks Ralf!
As I said I work on SMC. So I have to wait until William updates the cloud.
Peter
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On Friday, June 3, 2016 at 9:45:02 AM UTC+2, Peter Luschny wrote:
>
> plot([tanh(exp(i*t)).real(),
> (exp(exp(i*t))/cosh(exp(i*t))-1).real()],t,0,2*pi)
> The two functions are identical, the plot shows different functions.
>
Your Sage is too old, this Pynac bug (existing for years) was fixed
mo
>
>
>
> Thanks Robert, yes, I suspected the numerical integration
> prematurely. A plot clearly shows that the culprit are the
> real parts of the hyperbolic functions.
>
> plot([tanh(exp(i*t)).real(),
> (exp(exp(i*t))/cosh(exp(i*t))-1).real()],t,0,2*pi)
> The two functions are identical, the
> With Maxima built from recent source (approximately Maxima 5.38),
> I get results that agree with what you expected
Thanks Robert, yes, I suspected the numerical integration
prematurely. A plot clearly shows that the culprit are the
real parts of the hyperbolic functions.
plot([tanh(exp(i*t)).r
On 2016-05-31, Peter Luschny wrote:
> def T(v):
> def f(t): return (tanh(exp(i*t))/exp(i*t*v)).real()
> c = integral_numerical(f(t), 0, 2*pi)[0]
> return (c*gamma(v+1)/(2*pi)).n()
>
> print [round(T(n)) for n in range(10)]
>
> Sage returned: [0, 1, 0, -1, 0, 8, 0, -136, 0, 3968]
> I
Further investigation shows that things work with the
integrand defined as:
def f(t): return exp(x*exp(i*t)-v*i*t)*(exp(exp(i*t))/cosh(exp(i*t))-1)
So the source of the trouble seems to be related to the identity
(exp(exp(I*t))/cosh(exp(I*t))-1) = tanh(exp(I*t))
Peter
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