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Re: Maple's magical bounds break even the simplest tasks.

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On 5/12/2023 3:33 PM, peter....@gmail.com wrote:
> With Maple 2023.0:
> 
> a := n -> denom(add((n-j)/j, j=1..n)):
> b := n -> denom(n*harmonic(n)):
> 
> seq(a(n), n = 1..13);
> seq(b(n), n = 1..13);
> 
>      1, 1, 2, 3, 12, 10, 20, 35, 280, 252, 2520, 2310, 27720
>      1, 1, 2, 3, 12, 10, 20, 35, 280, 252, 2520, 2310, 27720
> 
> seq(print([n, a(n)]), n=599..600);
> seq(print([n, b(n)]), n=599..600);
> 
> [599, 24518...43033600]
> [600, 44775...38628544]
> 
> [599, 1]
> [600, 1]
> 

a(n) is not the same as b(n) for large n. They give different
results starting at n=501.

b := n -> denom(n*harmonic(n)):
a := n -> denom(add((n-j)/j, j=1..n)):

b(501)
         1
a(501)
1949158278614846....34240

So if you limit the print to n=500, it works

seq(lprint([n, b(n)]), n=499..500);
[499, 4892426340611412598120499299869225038728212308035354645714708753146045919\
8933676282116072023975502328168545495423118821451779568011772436268745785346466\
134503715040454880025595359981443379389168637406283325898144000]
[500, 4882641487930189772924258301269486588650755883419283936423279335639753828\
0535808929551839879927551323512208404432272583808876008875748891396208293775773\
202234707610373970265544169261480492630390300131470759246347712]


seq(lprint([n, a(n)]), n=499..500);
[499, 4892426340611412598120499299869225038728212308035354645714708753146045919\
8933676282116072023975502328168545495423118821451779568011772436268745785346466\
134503715040454880025595359981443379389168637406283325898144000]
[500, 4882641487930189772924258301269486588650755883419283936423279335639753828\
0535808929551839879927551323512208404432272583808876008875748891396208293775773\
202234707610373970265544169261480492630390300131470759246347712]


Now

seq(lprint([n, b(n)]), n=500..501);
[500, 4882641487930189772924258301269486588650755883419283936423279335639753828\
0535808929551839879927551323512208404432272583808876008875748891396208293775773\
202234707610373970265544169261480492630390300131470759246347712]
[501, 1]


seq(lprint([n, a(n)]), n=500..501);
[500, 4882641487930189772924258301269486588650755883419283936423279335639753828\
0535808929551839879927551323512208404432272583808876008875748891396208293775773\
202234707610373970265544169261480492630390300131470759246347712]
[501, 1949158278614846216736230858790214207046209933500712150268774185884133264\
6920482606607520910150719091222438484803302428666217967615069417723037243024260\
75937513277859240329961843084290638428358894216825180009834240]


Are these supposed to give same result for any n, no matter how
large it is?

--Nasser

--Nasser

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Maple's magical bounds break even the simplest tasks. "peter....@gmail.com" <peter.luschny@gmail.com> - 2023-05-12 13:33 -0700
  Re: Maple's magical bounds break even the simplest tasks. "Nasser M. Abbasi" <nma@12000.org> - 2023-05-13 21:17 -0500

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