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MathGroup Archive 2004

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Re: Simple question or how Mathematica getting on my nerves.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg45894] Re: Simple question or how Mathematica getting on my nerves.
  • From: vb at cybertester.com (Vladimir Bondarenko)
  • Date: Thu, 29 Jan 2004 05:34:41 -0500 (EST)
  • References: <butdvt$9se$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

gtsavdar at auth.gr (George) wrote in message news:<butdvt$9se$1 at smc.vnet.net>...
> Although the 2 results must be the same they aren't. WHY???????
> And not only this, but they differ by 10^21!!!!!! WHY???????? 


Hello,

I have a remark to the answers given by Msr Hanlon, Rowe, Noffke,
Kozlowski and Treat whose many comment I agree with, and two 
questions about the Mathematica overall design.

There are at least 2 commercial applications where the things go
smoothly in the case at hand. I respect the request of our
moderator Steven Christensen and not name those applications
but the fact remains:

> evalf(int(2687176093959399272413585923303421161600*(1-f)^67*f^61, f = .6214 .. .5242));
> evalf(int(2687176093959399272413585923303421161600*(1-f)^67*f^61, f = 6214/10000 .. 5242/10000));

-.1398383104
-.1398383104

APPROX(INT(2687176093959399272413585923303421161600*(1-f)^67*f^61, f,
6214/10000,5242/10000))
APPROX(INT(2687176093959399272413585923303421161600*(1-f)^67*f^61, f,
0.6214, 0.5242))

-0.1398383104
-0.1398383104


while for Mathematica we see


Integrate[2687176093959399272413585923303421161600*(1 - f)^67*f^61,
{f, 0.6214, 0.5242}]

-9.37972 10^21 (* Mathematica 5.0 *)
-9.2522 10^21  (* Mathematica 4.2.1 *)
-7.82732 10^21 (* Mathematica 3.0 *)
1.03892 10^23  (* Mathematica 2.2 *)

I believe all of you would agree that treating the above results
yielded by those application as pure coincidence would set before
us a formidable challenge as the chances such random behavior
would be some 1/10^20; thus, it's not by chance. 

My questions are,

1) Why exactly none Mathematica version can operate in a similar way?

2) Suppose, the above behavior is a feature. Had Mathematica been
   designed in a way supporting the behavior of those two
   systems, what would be the headaches inferred from such
   hypothetical design?


Best wishes,

Vladimir Bondarenko

GEMM architect
Co-founder, CEO, Mathematical Director
Cyber Tester, LLC

http://www.cybertester.com/
http://www.CAS-testing.org/ 

.......................................................................


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