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 PARI/gp Xorter Fellow   Posts: 90 Threads: 29 Joined: Aug 2016 11/21/2017, 03:50 PM (11/21/2017, 03:05 PM)Gottfried Wrote: (11/21/2017, 01:31 PM)Xorter Wrote: I got the following error message:   ***   at top-level: subst(exp(1/x),x,1/1000)   ***                       ^------------------   *** exp: domain error in exp: valuation < 0 My question is that how can we solve this problem? Perhaps it is meaningful for you to replace 1/x by exp(-u) where u=log(x) ? At least this gives a power series (more precisiely a puisieux-series) I tried your advice but without success: (15:42) gp > subst(f(x),x,1/1000)   ***   at top-level: subst(f(x),x,1/1000)   ***                       ^--------------   ***   in function f: exp(exp(-u(x)))   ***                           ^------   ***   in function u: log(x)   ***                  ^------   *** log: domain error in log: series valuation != 0 It looked like a simple problem, but I have not be able to solve it. Any idea? Xorter Unizo Gottfried Ultimate Fellow     Posts: 757 Threads: 116 Joined: Aug 2007 11/21/2017, 08:24 PM (This post was last modified: 11/21/2017, 08:26 PM by Gottfried.) (11/21/2017, 03:50 PM)Xorter Wrote: (11/21/2017, 03:05 PM)Gottfried Wrote: (11/21/2017, 01:31 PM)Xorter Wrote: I got the following error message:   ***   at top-level: subst(exp(1/x),x,1/1000)   ***                       ^------------------   *** exp: domain error in exp: valuation < 0 My question is that how can we solve this problem? Perhaps it is meaningful for you to replace 1/x by exp(-u) where u=log(x) ? At least this gives a power series (more precisiely a puisieux-series) I tried your advice but without success: (15:42) gp > subst(f(x),x,1/1000)   ***   at top-level: subst(f(x),x,1/1000)   ***                       ^--------------   ***   in function f: exp(exp(-u(x)))   ***                           ^------   ***   in function u: log(x)   ***                  ^------   *** log: domain error in log: series valuation != 0 It looked like a simple problem, but I have not be able to solve it. Any idea? This should go like                     subst ( Pol(exp(exp(u)),u) ,   u,    log(1/1000) )        or    subst ( Pol(exp(exp(-u)),u) ,   u,   log(1000) )        Because \$exp(x)\$ gives series and not a polynomial, to make the "subst" working, you need to convert the series into a polynomial ("Pol(exp(x))" or "Pol(exp(u),u)" first. However, "substituting" in a polynomial is not a very good idea, especially if the value to be substituted makes the functional value large.              Converting the exp()-function into a polynomial and then substituting such a large value does not give a near estimate for the true exp(1000) which is what I think your initial subst should  give.  (I hope I got your initial formula correct) Gottfried Helms, Kassel Xorter Fellow   Posts: 90 Threads: 29 Joined: Aug 2016 11/23/2017, 02:48 PM Aha, yes! It works... Thank you very much! Xorter Unizo Xorter Fellow   Posts: 90 Threads: 29 Joined: Aug 2016 05/08/2018, 08:56 PM (This post was last modified: 05/08/2018, 09:13 PM by Xorter. Edit Reason: edit2: new formula ) Hi, again! I would like to algoritmize the fractional derivatives and integrals, but here are some problems. This is my code: Code:```int1(f,a,b,h)={return(sum(k=floor(min(a*h,b*h)),ceil(max(a*h,b*h)),sign(b-a)*subst(f,x,k/h)/h));} Stein(f,n,a,h)={return(der1(int1(f,0,a,h),a,h)/gamma(1-n));}``` So e. g. D^2.5 x^2.5 = gamma(2.5-1) = Stein(x^2.5,2.5,0,1000.0), but it returns with this error message: domain error in gpow [irrational exponent]: valuation != 0 Furthermore my Stein function return with ~0 in other cases. Why? EDIT: Here is the original formula: https://wikimedia.org/api/rest_v1/media/...cc722c1f49 Oops, it looks I forgot some things from the my algorithm. It will be checked soon. EDIT2: Here is the new algorithm which is not working, too: Code:`Stein(f,n,a,h)={return(der1(int1(subst(f,x,u)/(x-u)^n,0,a,h),a,h)/gamma(1-n));}` Xorter Unizo Xorter Fellow   Posts: 90 Threads: 29 Joined: Aug 2016 07/09/2018, 08:54 AM Hi, there! Does anyone have any idea how to extend the binary bittest(x,n) to other number systems? Thanks a lot! Xorter Xorter Unizo « Next Oldest | Next Newest »

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