Vickram,
Thanks for the additional information. I am forwarding your reply to the
whole mailing list, as I am not a specialist in numerical quadrature, but
others on the list are.
-s
On Sat, Dec 8, 2012 at 6:34 AM, Vickram <vick1975 at intnet.mu> wrote:
> I am trying to do so for two main reasons:****
>
> 1) This definite integral is a computation for the Hubble parameter. I use
> the Hubble parameter in a python code to calculate cosmological distances
> from a given redshift. In order to calculate the conditions when the
> universe was several seconds old, the redshift must be in the order of
> 1e+13 and above, up to 1e+43! However, even using such large redshift the
> conditions become negative or meaningless, if higher precision is not
> ordered. For me to get a meaningful or positive figure for such large
> redshifts, I need a minimum of 200 digits accuracy.****
>
> 2) My main program to perform these calculations is python with mpmath.
> Python mpmath has always been very accurate and allow for the computation
> of larger digits accuracy. However, I?m not so sure with regard to its
> quadrature module. And so I checked the answer against mathematica (trial
> version), and the result diverged at about the 186th digit. So I needed a
> third source to know which one is correct!!!****
>
> ** **
>
> ** **
>
> Yeah I checked maxima computation of pi, it worked very well for a 1000
> digits. But I just don?t know how to use the same precision with regard to
> any in-built maxima quadrature module.****
>
> ** **
>
> I?ve attached the result from mathematica in the file resultmath.docx****
>
> ** **
>
> And here is a reproduction of sage or python mpmath result:****
>
> ** **
>
> mpf('3.37384610380011411639276017299071962336315208512187429308244524692\****
>
> 045408383159261986058700164785239715760980882005113744409027491454736698\****
>
> 265677706897849410300120235641862634820787971501677360673722092085500729\****
>
> 400684840196362348221869360897821068576910702514214008864442443503717684\****
>
> 502197331334033546973')****
>
> ** **
>
> The results diverge after the red digits in the above result!****
>
> ** **
>
> I?d really appreciate if you could just show me how to compute the
> tanh-sinh quadrature definite integral of my function with a precision of
> above 200 digits please!****
>
> ** **
>
> Thanks****
>
> Vick****
>
> ** **
>
> ** **
> ------------------------------
>
> *From:* macrakis at gmail.com [mailto:macrakis at gmail.com] *On Behalf Of *Stavros
> Macrakis
> *Sent:* Saturday, December 08, 2012 3:52 AM
> *To:* Vickram Ratnam
> *Cc:* maxima at math.utexas.edu
> *Subject:* Re: [Maxima] Hello****
>
> ** **
>
> Vickram,****
>
> ** **
>
> Thanks for your interest in Maxima.****
>
> ** **
>
> What problem are you trying to solve? i.e. why do you want to calculate a
> numeric integral to 200 digits of precision in the first place?****
>
> ** **
>
> Also, what do you mean by "Maxima cannot compute up to 1e+13!"? Maxima
> floating-point numbers have standard IEEE float ranges (up to roughly
> 1e+308). Maxima bfloat's have essentially unlimited range (10^10^100b0 is
> unproblematic).****
>
> ** **
>
> Perhaps if you could show us a self-contained minimal example of how to
> generate the error you're seeing, we could help find the problem.****
>
> ** **
>
> -s****
>
>
> -- ****
>
> On Fri, Dec 7, 2012 at 12:07 AM, Vickram Ratnam <accts at goldox.mu> wrote:**
> **
>
> Hi,****
>
> ****
>
> I?m new to Maxima. I am using Maxima for windows!****
>
> ****
>
> I?m trying to compute a definite integral using Woollett?s tanh-sinh
> maxima code and the maxima built-in integration methods but with no success!
> ****
>
> ****
>
> My function is the following:****
>
> ****
>
> 1/sqrt((.0000812*(1+x)^4)+(.2719188*(1+x)^3)+(0*(1+x)^2)+.728)****
>
> ****
>
> From 0 to 1e+13****
>
> ****
>
> Using preferably tanh-sinh quadrature and to over 300 digits accuracy!****
>
> ****
>
> I can do the same with python mpmath and on mathematica. I wanted to check
> the answers from a third source.****
>
> ****
>
> But Maxima cannot compute up to 1e+13!****
>
> ****
>
> Can I do that or is Maxima limited to certain accuracy?****
>
> ****
>
> Thanks****
>
> Vick****
>
> ****
>
> ****
>
>
> _______________________________________________
> Maxima mailing list
> Maxima at math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima****
>
> ** **
>