Re: An exact simplification challenge - 37 (MeijerG) - Go and surpass all CASs

On Aug 3, 10:48 am, Vladimir Bondarenko <v...@xxxxxxxxxxxxxxx> wrote:
Hi Oleksandr,

Unfortunately, after about 8000 seconds,
Mathematica 6.0.0 returns this unevaluated

Normal[Table[FullSimplify[Series[%, {z, 0, k}]],
{k, 5, 20, 5}]] // Timing

so I cannot reproduce your result...

Did you use the developer version? How
much time it took you to get the result?

No, I used the shipping version 6.0.0. The following
is the output of the Linux version, the Windows version
also succeeds is about the same time:

Mathematica 6.0 for Linux x86 (32-bit)
Copyright 1988-2007 Wolfram Research, Inc.

In[1]:= $Version

Out[1]= 6.0 for Linux x86 (32-bit) (April 29, 2007)

In[2]:= res =
MeijerG[{{1/12, 1/4, 5/12, 7/12, 3/4, 11/12}, {}}, {{-(1/6), 1/3, 1/
2, 5/6, 7/6}, {-(1/3), 0, 1/6, 1/3, 1/2, 2/3, 1}}, z] +
MeijerG[{{1/12, 1/4, 5/12, 7/12, 3/4, 5/6, 11/12}, {}}, {{1/3, 1/2,
5/6, 5/6, 7/6}, {-(1/3), -(1/6), 0, 1/6, 1/3, 1/2, 2/3, 1}},
z];

In[3]:= Normal[
Table[FullSimplify[Series[%, {z, 0, k}]], {k, 5, 20, 5}]]//
Timing

4 Sqrt[2] Pi 4 Sqrt[2] Pi 4 Sqrt[2] Pi 4 Sqrt[2]
Pi
Out[3]= {11.46, {------------, ------------, ------------,
------------}}
1/6 1/6 1/6 1/6
z z z z

What is the output of $Version in your copy of mathematica ?


Oleksandr Pavlyk
Wolfram Research


I am asking you as I know at least one
person who is positively willing to
upgrade from 5.2 to 6.1 (where he hopes
many 6.0 bugs will be fixed), so you
have an extra opportunity to motivate
him... :)

Best wishes,

Vladimir Bondarenko

VM and GEMM architect
Co-founder, CEO, Mathematical Director

http://www.cybertester.com/ Cyber Tester, LLChttp://maple.bug-list.org/ Maple Bugs Encyclopaediahttp://www.CAS-testing.org/ CAS Testing

On Jul 31, 11:33 pm, sashap <pav...@xxxxxxxxx> wrote:

Hi Vladimir,

The answer is 12*Sqrt[2]*Pi, but unlike your previous challenges, I
did
not particularly like this one. It seems too artificial. Could you
share
your path to creating this challenge ?

But, anyway, here is how you arrive to the answer:

Start with the following function of z:

In[1]:= res =
MeijerG[{{1/12, 1/4, 5/12, 7/12, 3/4, 11/12}, {}}, {{-(1/6), 1/3, 1/
2, 5/6, 7/6}, {-(1/3), 0, 1/6, 1/3, 1/2, 2/3, 1}}, z] +
MeijerG[{{1/12, 1/4, 5/12, 7/12, 3/4, 5/6, 11/12}, {}}, {{1/3, 1/2,
5/6, 5/6, 7/6}, {-(1/3), -(1/6), 0, 1/6, 1/3, 1/2, 2/3, 1}},
z];

(* series expansion around the origin to different degrees *)

In[2]:= Normal[
Table[FullSimplify[Series[%, {z, 0, k}]], {k, 5, 20, 5}]]

Out[2]= {(4 Sqrt[2] \[Pi])/z^(1/6), (4 Sqrt[2] \[Pi])/z^(1/6), (
4 Sqrt[2] \[Pi])/z^(1/6), (4 Sqrt[2] \[Pi])/z^(1/6)}

In[3]:= First[%] /. z -> 1/729

Out[3]= 12 Sqrt[2] \[Pi]

In[4]:= N[res /. z -> 1/729, 150]/Pi // RootApproximant

Out[4]= 12 Sqrt[2]

Funny enough, the Plouffe's inverter fails to recognize this numerical
value
as the derived above constant.

Post-factum one proves that res is a simple function as follows:

In[5]:= res2 = Expand[z^(1/6) res, _MeijerG]

Out[5]= MeijerG[{{1/4, 5/12, 7/12, 3/4, 11/12, 13/12}, {}}, {{0, 1/2,
2/3, 1, 4/3}, {-(1/6), 1/6, 1/3, 1/2, 2/3, 5/6, 7/6}}, z] +
MeijerG[{{1/4, 5/12, 7/12, 3/4, 11/12, 1, 13/12}, {}}, {{1/2, 2/3, 1,
1, 4/3}, {-(1/6), 0, 1/6, 1/3, 1/2, 2/3, 5/6, 7/6}}, z]

In[6]:= D[res2, z]

Out[6]= 0

Oleksandr Pavlyk
Wolfram Research Inc

On Jul 29, 2:19 am, Vladimir Bondarenko <v...@xxxxxxxxxxxxxxx> wrote:

Hello symbolic calculation fans,

None of the modern computer algebra systems is able to crack
this straightforwardly.

Is there a Whiz the Simplifier to come up with the steps to
compress (very much :) this sum

MeijerG[{{1/12,1/4,5/12,7/12,3/4,11/12}, {}},
{{-1/6,1/3,1/2,5/6,7/6}, {-1/3,0,1/6,1/3,1/2,2/3,1}}, 1/729]

+

MeijerG[{{1/12,1/4,5/12,7/12,3/4,5/6,11/12}, {}},
{{1/3,1/2,5/6,5/6,7/6}, {-1/3,-1/6,0,1/6,1/3,1/2,2/3,1}}, 1/729]

?

Best wishes,

Vladimir Bondarenko

VM and GEMM architect
Co-founder, CEO, Mathematical Director

http://www.cybertester.com/CyberTester, LLChttp://maple.bug-list.org/Maple Bugs Encyclopaediahttp://www.CAS-testing.org/CASTesting


.

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