www.GetXFactor.com

Leading Technology, Science,
Agriculture News and information
Part of the Identityscape.com network...

getxfactor.com jmoodmusic.com smartbusinesschoices.com mintdepot.com lowfaresalways.com evangelicalview.com shoppingpodder.com soproudlywehail.com webnews.ws currenthumor.com

 

 

An exact simplification challenge - 68 (Sqrt, Log)
   Science and Technology news... Forum Index -> Math - Symbolic Forum  
View previous topic :: View next topic  
Author Message
Vladimir Bondarenko
Guest
PostPosted: Thu Jul 24, 2008 4:51 am    Post subject: An exact simplification challenge - 68 (Sqrt, Log) Reply with quote
Hello,

(48 + Sqrt[3] ArcCosh[2642885282] - 11 Sqrt[3] Log[2] -
10 Sqrt[3] Log[7] + Log[(2 - Sqrt[3])^(3 Sqrt[-22 + 10
I Sqrt[3]])] + Log[(2 + Sqrt[3])^(15 I)] + Sqrt[3] Log[
578509309952 (7 + 4 Sqrt[3])])/144

?

Best wishes,

Vladimir Bondarenko

Co-founder, CEO, Mathematical Director

http://www.cybertester.com/ Cyber Tester, LLC

-------------------------------------------------------

"We must understand that technologies
like these are the way of the future."

-------------------------------------------------------
Back to top
Guest
PostPosted: Thu Jul 24, 2008 1:09 pm    Post subject: Re: An exact simplification challenge - 68 (Sqrt, Log) Reply with quote
Vladimir Bondarenko schrieb:
[quote]
(48 + Sqrt[3] ArcCosh[2642885282] - 11 Sqrt[3] Log[2] -
10 Sqrt[3] Log[7] + Log[(2 - Sqrt[3])^(3 Sqrt[-22 + 10
I Sqrt[3]])] + Log[(2 + Sqrt[3])^(15 I)] + Sqrt[3] Log[
578509309952 (7 + 4 Sqrt[3])])/144

?
[/quote]
Instantaneous result on Derive 6.10: SQRT(3)*LN(SQRT(3)+2)/9 + 1/3.

(I didn>t participate in the Meijer G challenges since Derive has zero
intrinsic knowledge of Meijer G and hypergeometric pFq functions.)

Martin.
Back to top
Vladimir Bondarenko
Guest
PostPosted: Thu Jul 24, 2008 3:05 pm    Post subject: Re: An exact simplification challenge - 68 (Sqrt, Log) Reply with quote
On Jul 24, 6:09 am, cliclic...@freenet.de wrote:
[quote]Vladimir Bondarenko schrieb:



(48 + Sqrt[3] ArcCosh[2642885282] - 11 Sqrt[3] Log[2] -
10 Sqrt[3] Log[7]  + Log[(2 - Sqrt[3])^(3 Sqrt[-22 + 10
I Sqrt[3]])] + Log[(2 + Sqrt[3])^(15 I)] + Sqrt[3] Log[
578509309952 (7 + 4 Sqrt[3])])/144

                        ?

Instantaneous result on Derive 6.10: SQRT(3)*LN(SQRT(3)+2)/9 + 1/3.

(I didn>t participate in the Meijer G challenges since Derive has zero
intrinsic knowledge of Meijer G and hypergeometric pFq functions.)

Martin.
[/quote]
I know that Derive 6.10 cracks this easily (and this is pleasant
for me, so that it was not in vain that I invested my time into
Derive improvement), while Maple 12 and Mathematica 6.0.3 not,
but I expected that someone, maybe you, a Derive fan like me, will
announce this :)

Now so you would not sit without a challenge, I propose you to
simplify this

SQRT(3)*LN(SQRT(3)/2-1/2)/72-SQRT(3)*LN(3*SQRT(3)-5)/18+5*SQRT~
(3)*LN(SQRT(3)+1)/72+1/3-#i*ATAN((COS(-10*SQRT(3)*ACOT(SQRT(3)~
/9)-15*LN(14*SQRT(3)+14))*(COS(-6*SQRT(3)*ACOT(SQRT(3)/9)-3*LN~
(SQRT(3)/2-1/2))*(COS(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT~
(3)/9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*LN(2))*SIN(33*LN(7~
)))+SIN(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(5~
1*LN(2))*SIN(33*LN(7))-COS(51*LN(2))*COS(33*LN(7))))-SIN(-6*SQ~
RT(3)*ACOT(SQRT(3)/9)-3*LN(SQRT(3)/2-1/2))*(COS(18*LN(14*SQRT(~
3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(COS(51*LN(2))*COS(33*LN(7))~
-SIN(51*LN(2))*SIN(33*LN(7)))+SIN(18*LN(14*SQRT(3)-14)-4*SQRT(~
3)*ACOT(SQRT(3)/9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*LN(2))~
*SIN(33*LN(7)))))+SIN(-10*SQRT(3)*ACOT(SQRT(3)/9)-15*LN(14*SQR~
T(3)+14))*(COS(-6*SQRT(3)*ACOT(SQRT(3)/9)-3*LN(SQRT(3)/2-1/2))~
*(COS(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(COS(51*~
LN(2))*COS(33*LN(7))-SIN(51*LN(2))*SIN(33*LN(7)))+SIN(18*LN(14~
*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(51*LN(2))*COS(33*~
LN(7))+COS(51*LN(2))*SIN(33*LN(7))))+SIN(-6*SQRT(3)*ACOT(SQRT(~
3)/9)-3*LN(SQRT(3)/2-1/2))*(COS(18*LN(14*SQRT(3)-14)-4*SQRT(3)~
*ACOT(SQRT(3)/9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*LN(2))*S~
IN(33*LN(7)))+SIN(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/~
9))*(SIN(51*LN(2))*SIN(33*LN(7))-COS(51*LN(2))*COS(33*LN(7))))~
))/(COS(-10*SQRT(3)*ACOT(SQRT(3)/9)-15*LN(14*SQRT(3)+14))*(COS~
(-6*SQRT(3)*ACOT(SQRT(3)/9)-3*LN(SQRT(3)/2-1/2))*(COS(18*LN(14~
*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(COS(51*LN(2))*COS(33*~
LN(7))-SIN(51*LN(2))*SIN(33*LN(7)))+SIN(18*LN(14*SQRT(3)-14)-4~
*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*~
LN(2))*SIN(33*LN(7))))+SIN(-6*SQRT(3)*ACOT(SQRT(3)/9)-3*LN(SQR~
T(3)/2-1/2))*(COS(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/~
9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*LN(2))*SIN(33*LN(7)))+~
SIN(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(51*LN~
(2))*SIN(33*LN(7))-COS(51*LN(2))*COS(33*LN(7)))))+SIN(-10*SQRT~
(3)*ACOT(SQRT(3)/9)-15*LN(14*SQRT(3)+14))*(SIN(-6*SQRT(3)*ACOT~
(SQRT(3)/9)-3*LN(SQRT(3)/2-1/2))*(COS(18*LN(14*SQRT(3)-14)-4*S~
QRT(3)*ACOT(SQRT(3)/9))*(COS(51*LN(2))*COS(33*LN(7))-SIN(51*LN~
(2))*SIN(33*LN(7)))+SIN(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQ~
RT(3)/9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*LN(2))*SIN(33*LN~
(7))))-COS(-6*SQRT(3)*ACOT(SQRT(3)/9)-3*LN(SQRT(3)/2-1/2))*(CO~
S(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(51*LN(2~
))*COS(33*LN(7))+COS(51*LN(2))*SIN(33*LN(7)))+SIN(18*LN(14*SQR~
T(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(51*LN(2))*SIN(33*LN(7~
))-COS(51*LN(2))*COS(33*LN(7)))))))/72

:-)

Best wishes,

Vladimir Bondarenko

Co-founder, CEO, Mathematical Director

http://www.cybertester.com/ Cyber Tester, LLC

-------------------------------------------------------

"We must understand that technologies
like these are the way of the future."

-------------------------------------------------------
Back to top
Guest
PostPosted: Thu Jul 24, 2008 3:43 pm    Post subject: Re: An exact simplification challenge - 68 (Sqrt, Log) Reply with quote
On 24 juil, 17:05, Vladimir Bondarenko <v...@cybertester.com> wrote:
[quote]On Jul 24, 6:09 am, cliclic...@freenet.de wrote:





Vladimir Bondarenko schrieb:

(48 + Sqrt[3] ArcCosh[2642885282] - 11 Sqrt[3] Log[2] -
10 Sqrt[3] Log[7]  + Log[(2 - Sqrt[3])^(3 Sqrt[-22 + 10
I Sqrt[3]])] + Log[(2 + Sqrt[3])^(15 I)] + Sqrt[3] Log[
578509309952 (7 + 4 Sqrt[3])])/144

                        ?

Instantaneous result on Derive 6.10: SQRT(3)*LN(SQRT(3)+2)/9 + 1/3.

(I didn>t participate in the Meijer G challenges since Derive has zero
intrinsic knowledge of Meijer G and hypergeometric pFq functions.)

Martin.

I know that Derive 6.10 cracks this easily (and this is pleasant
for me, so that it was not in vain that I invested my time into
Derive improvement), while Maple 12 and Mathematica 6.0.3 not,
but I expected that someone, maybe you, a Derive fan like me, will
announce this :)

Now so you would not sit without a challenge, I propose you to
simplify this

SQRT(3)*LN(SQRT(3)/2-1/2)/72-SQRT(3)*LN(3*SQRT(3)-5)/18+5*SQRT~
(3)*LN(SQRT(3)+1)/72+1/3-#i*ATAN((COS(-10*SQRT(3)*ACOT(SQRT(3)~
/9)-15*LN(14*SQRT(3)+14))*(COS(-6*SQRT(3)*ACOT(SQRT(3)/9)-3*LN~
(SQRT(3)/2-1/2))*(COS(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT~
(3)/9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*LN(2))*SIN(33*LN(7~
)))+SIN(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(5~
1*LN(2))*SIN(33*LN(7))-COS(51*LN(2))*COS(33*LN(7))))-SIN(-6*SQ~
RT(3)*ACOT(SQRT(3)/9)-3*LN(SQRT(3)/2-1/2))*(COS(18*LN(14*SQRT(~
3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(COS(51*LN(2))*COS(33*LN(7))~
-SIN(51*LN(2))*SIN(33*LN(7)))+SIN(18*LN(14*SQRT(3)-14)-4*SQRT(~
3)*ACOT(SQRT(3)/9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*LN(2))~
*SIN(33*LN(7)))))+SIN(-10*SQRT(3)*ACOT(SQRT(3)/9)-15*LN(14*SQR~
T(3)+14))*(COS(-6*SQRT(3)*ACOT(SQRT(3)/9)-3*LN(SQRT(3)/2-1/2))~
*(COS(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(COS(51*~
LN(2))*COS(33*LN(7))-SIN(51*LN(2))*SIN(33*LN(7)))+SIN(18*LN(14~
*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(51*LN(2))*COS(33*~
LN(7))+COS(51*LN(2))*SIN(33*LN(7))))+SIN(-6*SQRT(3)*ACOT(SQRT(~
3)/9)-3*LN(SQRT(3)/2-1/2))*(COS(18*LN(14*SQRT(3)-14)-4*SQRT(3)~
*ACOT(SQRT(3)/9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*LN(2))*S~
IN(33*LN(7)))+SIN(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/~
9))*(SIN(51*LN(2))*SIN(33*LN(7))-COS(51*LN(2))*COS(33*LN(7))))~
))/(COS(-10*SQRT(3)*ACOT(SQRT(3)/9)-15*LN(14*SQRT(3)+14))*(COS~
(-6*SQRT(3)*ACOT(SQRT(3)/9)-3*LN(SQRT(3)/2-1/2))*(COS(18*LN(14~
*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(COS(51*LN(2))*COS(33*~
LN(7))-SIN(51*LN(2))*SIN(33*LN(7)))+SIN(18*LN(14*SQRT(3)-14)-4~
*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*~
LN(2))*SIN(33*LN(7))))+SIN(-6*SQRT(3)*ACOT(SQRT(3)/9)-3*LN(SQR~
T(3)/2-1/2))*(COS(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/~
9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*LN(2))*SIN(33*LN(7)))+~
SIN(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(51*LN~
(2))*SIN(33*LN(7))-COS(51*LN(2))*COS(33*LN(7)))))+SIN(-10*SQRT~
(3)*ACOT(SQRT(3)/9)-15*LN(14*SQRT(3)+14))*(SIN(-6*SQRT(3)*ACOT~
(SQRT(3)/9)-3*LN(SQRT(3)/2-1/2))*(COS(18*LN(14*SQRT(3)-14)-4*S~
QRT(3)*ACOT(SQRT(3)/9))*(COS(51*LN(2))*COS(33*LN(7))-SIN(51*LN~
(2))*SIN(33*LN(7)))+SIN(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQ~
RT(3)/9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*LN(2))*SIN(33*LN~
(7))))-COS(-6*SQRT(3)*ACOT(SQRT(3)/9)-3*LN(SQRT(3)/2-1/2))*(CO~
S(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(51*LN(2~
))*COS(33*LN(7))+COS(51*LN(2))*SIN(33*LN(7)))+SIN(18*LN(14*SQR~
T(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(51*LN(2))*SIN(33*LN(7~
))-COS(51*LN(2))*COS(33*LN(7)))))))/72

:-)

Best wishes,

Vladimir Bondarenko

Co-founder, CEO, Mathematical Director

http://www.cybertester.com/ Cyber Tester, LLC

-------------------------------------------------------

"We must understand that technologies
like these are the way of the future."

-------------------------------------------------------- Masquer le texte des messages précédents -

- Afficher le texte des messages précédents -
[/quote]
Bonsoir,

I do not ever agree with : ""We must *understand* that technologies
like these are the way of the future."
I believe that with these technologies a lot of sane people
will not even understand a word about anything belonging
to their world,

Alain
Back to top
Guest
PostPosted: Thu Jul 24, 2008 3:51 pm    Post subject: Re: An exact simplification challenge - 68 (Sqrt, Log) Reply with quote
Vladimir Bondarenko schrieb:
[quote]On Jul 24, 6:09?am, cliclic...@freenet.de wrote:
Vladimir Bondarenko schrieb:

(48 + Sqrt[3] ArcCosh[2642885282] - 11 Sqrt[3] Log[2] -
10 Sqrt[3] Log[7] ?+ Log[(2 - Sqrt[3])^(3 Sqrt[-22 + 10
I Sqrt[3]])] + Log[(2 + Sqrt[3])^(15 I)] + Sqrt[3] Log[
578509309952 (7 + 4 Sqrt[3])])/144

?

Instantaneous result on Derive 6.10: SQRT(3)*LN(SQRT(3)+2)/9 + 1/3.

(I didn>t participate in the Meijer G challenges since Derive has zero
intrinsic knowledge of Meijer G and hypergeometric pFq functions.)

I know that Derive 6.10 cracks this easily (and this is pleasant
for me, so that it was not in vain that I invested my time into
Derive improvement), while Maple 12 and Mathematica 6.0.3 not,
but I expected that someone, maybe you, a Derive fan like me, will
announce this :)

Now so you would not sit without a challenge, I propose you to
simplify this

SQRT(3)*LN(SQRT(3)/2-1/2)/72-SQRT(3)*LN(3*SQRT(3)-5)/18+5*SQRT~
(3)*LN(SQRT(3)+1)/72+1/3-#i*ATAN((COS(-10*SQRT(3)*ACOT(SQRT(3)~
/9)-15*LN(14*SQRT(3)+14))*(COS(-6*SQRT(3)*ACOT(SQRT(3)/9)-3*LN~
(SQRT(3)/2-1/2))*(COS(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT~
(3)/9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*LN(2))*SIN(33*LN(7~
)))+SIN(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(5~
1*LN(2))*SIN(33*LN(7))-COS(51*LN(2))*COS(33*LN(7))))-SIN(-6*SQ~
RT(3)*ACOT(SQRT(3)/9)-3*LN(SQRT(3)/2-1/2))*(COS(18*LN(14*SQRT(~
3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(COS(51*LN(2))*COS(33*LN(7))~
-SIN(51*LN(2))*SIN(33*LN(7)))+SIN(18*LN(14*SQRT(3)-14)-4*SQRT(~
3)*ACOT(SQRT(3)/9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*LN(2))~
*SIN(33*LN(7)))))+SIN(-10*SQRT(3)*ACOT(SQRT(3)/9)-15*LN(14*SQR~
T(3)+14))*(COS(-6*SQRT(3)*ACOT(SQRT(3)/9)-3*LN(SQRT(3)/2-1/2))~
*(COS(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(COS(51*~
LN(2))*COS(33*LN(7))-SIN(51*LN(2))*SIN(33*LN(7)))+SIN(18*LN(14~
*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(51*LN(2))*COS(33*~
LN(7))+COS(51*LN(2))*SIN(33*LN(7))))+SIN(-6*SQRT(3)*ACOT(SQRT(~
3)/9)-3*LN(SQRT(3)/2-1/2))*(COS(18*LN(14*SQRT(3)-14)-4*SQRT(3)~
*ACOT(SQRT(3)/9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*LN(2))*S~
IN(33*LN(7)))+SIN(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/~
9))*(SIN(51*LN(2))*SIN(33*LN(7))-COS(51*LN(2))*COS(33*LN(7))))~
))/(COS(-10*SQRT(3)*ACOT(SQRT(3)/9)-15*LN(14*SQRT(3)+14))*(COS~
(-6*SQRT(3)*ACOT(SQRT(3)/9)-3*LN(SQRT(3)/2-1/2))*(COS(18*LN(14~
*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(COS(51*LN(2))*COS(33*~
LN(7))-SIN(51*LN(2))*SIN(33*LN(7)))+SIN(18*LN(14*SQRT(3)-14)-4~
*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*~
LN(2))*SIN(33*LN(7))))+SIN(-6*SQRT(3)*ACOT(SQRT(3)/9)-3*LN(SQR~
T(3)/2-1/2))*(COS(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/~
9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*LN(2))*SIN(33*LN(7)))+~
SIN(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(51*LN~
(2))*SIN(33*LN(7))-COS(51*LN(2))*COS(33*LN(7)))))+SIN(-10*SQRT~
(3)*ACOT(SQRT(3)/9)-15*LN(14*SQRT(3)+14))*(SIN(-6*SQRT(3)*ACOT~
(SQRT(3)/9)-3*LN(SQRT(3)/2-1/2))*(COS(18*LN(14*SQRT(3)-14)-4*S~
QRT(3)*ACOT(SQRT(3)/9))*(COS(51*LN(2))*COS(33*LN(7))-SIN(51*LN~
(2))*SIN(33*LN(7)))+SIN(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQ~
RT(3)/9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*LN(2))*SIN(33*LN~
(7))))-COS(-6*SQRT(3)*ACOT(SQRT(3)/9)-3*LN(SQRT(3)/2-1/2))*(CO~
S(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(51*LN(2~
))*COS(33*LN(7))+COS(51*LN(2))*SIN(33*LN(7)))+SIN(18*LN(14*SQR~
T(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(51*LN(2))*SIN(33*LN(7~
))-COS(51*LN(2))*COS(33*LN(7)))))))/72

[/quote]
A bit harder, but still easy - it needs some juggling with the
simplification settings:

[Trigonometry:=Collect, Logarithm:=Collect]
1/3-SQRT(3)*LN((2-SQRT(3))^(1/9))
Logarithm:=Auto
1/3-SQRT(3)*LN(2-SQRT(3))/9

Martin.

PS: But Derive (under my command) failed to fully simplify your
monster challenge

SQRT(6)*SQRT(-SQRT(16*pi^2*LN(35*SQRT(2)+20*SQRT(6)+28*SQRT(3)+49)^2-
pi^2*LN(~
35*SQRT(2)+20*SQRT(6)+28*SQRT(3)+49)*LN(3967654484264881281965698789310658220~
572212595135191362121484088486083360*SQRT(2)+32395763207048357347710948248549~
50687594346152507722273751834468297053056*SQRT(3)+229072638454175499028284157~
8360115154299405761187724567354303143178465280*SQRT(6)+5611110782457822952710~
[...........................................................................]
2*pi^2)+LN(2)*LN(1853020188851841)*(144*LN(2)^2+47*pi^2)+2304*LN(2)^4+2209*pi~
^2*LN(2)^2)-
LN(SQRT(3)-1)*LN(184141500186093409798577801761927946149371551404~
77097961418915840*SQRT(3)+318942434104267658870956964797945820754099234494920~
25397756297216)-48*LN(SQRT(3)-1)^2+LN(3)*LN(447127149604363042816-25814898018~
6069073920*SQRT(3))-48*LN(SQRT(3)+1)^2+12*LN(3)^2+48*LN(2)^2)/12

The result of the automatic simplification is recalcitrant:
SQRT(6)*SQRT(-SQRT(-pi^2*LN(2-
SQRT(3))*(12*LN(SQRT(2)+1)+LN(2))-4*pi^2*LN(SQR~
T(15*SQRT(2)+21)+2*SQRT(5*SQRT(2)+7))^2-144*LN(2)^2*LN(11*SQRT(3)-19)^2-4*pi^~
2*LN(12-6*SQRT(3))*LN(3*SQRT(3)-5)+144*LN(SQRT(3)-1)^4+576*LN(SQRT(3)+1)*LN(S~
QRT(3)-1)^3+4*LN(SQRT(3)-1)^2*(216*LN(SQRT(3)+1)^2-18*LN(3)^2+252*LN(2)^2+65*~
pi^2)+LN(SQRT(3)-1)*(576*LN(SQRT(3)+1)^3-16*LN(SQRT(3)+1)*(9*LN(3)^2+4*(36*LN~
(2)^2-5*pi^2))+32*pi^2*LN(3)-377*pi^2*LN(2))
+144*LN(SQRT(3)+1)^4-4*LN(SQRT(3)~
+1)^2*(18*LN(3)^2-72*LN(2)^2-25*pi^2)+5*pi^2*LN(SQRT(3)+1)*(4*LN(3)-47*LN(2))~
+9*pi^2*LN(SQRT(2)+1)^2+9*LN(3)^4+72*LN(2)^2*LN(3)^2-24*pi^2*LN(2)*LN(3)+144*~
LN(2)^4+138*pi^2*LN(2)^2)-12*LN(SQRT(3)-1)^2-24*LN(SQRT(3)+1)*LN(SQRT(3)-1)-1~
2*LN(SQRT(3)+1)^2+3*LN(3)^2+12*LN(2)^2)/6+SQRT(6)*SQRT(SQRT(-pi^2*LN(2-
SQRT(3~
))*(12*LN(SQRT(2)+1)+LN(2))-4*pi^2*LN(SQRT(15*SQRT(2)+21)+2*SQRT(5*SQRT(2)+7)~
)^2-144*LN(2)^2*LN(11*SQRT(3)-19)^2-4*pi^2*LN(12-6*SQRT(3))*LN(3*SQRT(3)-5)+1~
44*LN(SQRT(3)-1)^4+576*LN(SQRT(3)+1)*LN(SQRT(3)-1)^3+4*LN(SQRT(3)-1)^2*(216*L~
N(SQRT(3)+1)^2-18*LN(3)^2+252*LN(2)^2+65*pi^2)+LN(SQRT(3)-1)*(576*LN(SQRT(3)+~
1)^3-16*LN(SQRT(3)+1)*(9*LN(3)^2+4*(36*LN(2)^2-5*pi^2))
+32*pi^2*LN(3)-377*pi^~
2*LN(2))
+144*LN(SQRT(3)+1)^4-4*LN(SQRT(3)+1)^2*(18*LN(3)^2-72*LN(2)^2-25*pi^2~
)+5*pi^2*LN(SQRT(3)+1)*(4*LN(3)-47*LN(2))
+9*pi^2*LN(SQRT(2)+1)^2+9*LN(3)^4+72~
*LN(2)^2*LN(3)^2-24*pi^2*LN(2)*LN(3)+144*LN(2)^4+138*pi^2*LN(2)^2)-12*LN(SQRT~
(3)-1)^2-24*LN(SQRT(3)+1)*LN(SQRT(3)-1)-12*LN(SQRT(3)+1)^2+3*LN(3)^2+12*LN(2)~
^2)/6

Do you know how to proceed?
Back to top
David W. Cantrell
Guest
PostPosted: Thu Jul 24, 2008 8:46 pm    Post subject: Re: An exact simplification challenge - 68 (Sqrt, Log) Reply with quote
Vladimir Bondarenko <vb@cybertester.com> wrote:
[quote]On Jul 24, 6:09=A0am, cliclic...@freenet.de wrote:
Vladimir Bondarenko schrieb:



(48 + Sqrt[3] ArcCosh[2642885282] - 11 Sqrt[3] Log[2] -
10 Sqrt[3] Log[7] =A0+ Log[(2 - Sqrt[3])^(3 Sqrt[-22 + 10
I Sqrt[3]])] + Log[(2 + Sqrt[3])^(15 I)] + Sqrt[3] Log[
578509309952 (7 + 4 Sqrt[3])])/144

=A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 ?

Instantaneous result on Derive 6.10: SQRT(3)*LN(SQRT(3)+2)/9 + 1/3.

(I didn>t participate in the Meijer G challenges since Derive has zero
intrinsic knowledge of Meijer G and hypergeometric pFq functions.)

Martin.

I know that Derive 6.10 cracks this easily (and this is pleasant
for me, so that it was not in vain that I invested my time into
Derive improvement), while Maple 12 and Mathematica 6.0.3 not,
but I expected that someone, maybe you, a Derive fan like me, will
announce this :)

Now so you would not sit without a challenge, I propose you to
simplify this

SQRT(3)*LN(SQRT(3)/2-1/2)/72-SQRT(3)*LN(3*SQRT(3)-5)/18+5*SQRT~
(3)*LN(SQRT(3)+1)/72+1/3-#i*ATAN((COS(-10*SQRT(3)*ACOT(SQRT(3)~
/9)-15*LN(14*SQRT(3)+14))*(COS(-6*SQRT(3)*ACOT(SQRT(3)/9)-3*LN~
(SQRT(3)/2-1/2))*(COS(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT~
(3)/9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*LN(2))*SIN(33*LN(7~
)))+SIN(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(5~
1*LN(2))*SIN(33*LN(7))-COS(51*LN(2))*COS(33*LN(7))))-SIN(-6*SQ~
RT(3)*ACOT(SQRT(3)/9)-3*LN(SQRT(3)/2-1/2))*(COS(18*LN(14*SQRT(~
3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(COS(51*LN(2))*COS(33*LN(7))~
-SIN(51*LN(2))*SIN(33*LN(7)))+SIN(18*LN(14*SQRT(3)-14)-4*SQRT(~
3)*ACOT(SQRT(3)/9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*LN(2))~
*SIN(33*LN(7)))))+SIN(-10*SQRT(3)*ACOT(SQRT(3)/9)-15*LN(14*SQR~
T(3)+14))*(COS(-6*SQRT(3)*ACOT(SQRT(3)/9)-3*LN(SQRT(3)/2-1/2))~
*(COS(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(COS(51*~
LN(2))*COS(33*LN(7))-SIN(51*LN(2))*SIN(33*LN(7)))+SIN(18*LN(14~
*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(51*LN(2))*COS(33*~
LN(7))+COS(51*LN(2))*SIN(33*LN(7))))+SIN(-6*SQRT(3)*ACOT(SQRT(~
3)/9)-3*LN(SQRT(3)/2-1/2))*(COS(18*LN(14*SQRT(3)-14)-4*SQRT(3)~
*ACOT(SQRT(3)/9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*LN(2))*S~
IN(33*LN(7)))+SIN(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/~
9))*(SIN(51*LN(2))*SIN(33*LN(7))-COS(51*LN(2))*COS(33*LN(7))))~
))/(COS(-10*SQRT(3)*ACOT(SQRT(3)/9)-15*LN(14*SQRT(3)+14))*(COS~
(-6*SQRT(3)*ACOT(SQRT(3)/9)-3*LN(SQRT(3)/2-1/2))*(COS(18*LN(14~
*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(COS(51*LN(2))*COS(33*~
LN(7))-SIN(51*LN(2))*SIN(33*LN(7)))+SIN(18*LN(14*SQRT(3)-14)-4~
*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*~
LN(2))*SIN(33*LN(7))))+SIN(-6*SQRT(3)*ACOT(SQRT(3)/9)-3*LN(SQR~
T(3)/2-1/2))*(COS(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/~
9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*LN(2))*SIN(33*LN(7)))+~
SIN(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(51*LN~
(2))*SIN(33*LN(7))-COS(51*LN(2))*COS(33*LN(7)))))+SIN(-10*SQRT~
(3)*ACOT(SQRT(3)/9)-15*LN(14*SQRT(3)+14))*(SIN(-6*SQRT(3)*ACOT~
(SQRT(3)/9)-3*LN(SQRT(3)/2-1/2))*(COS(18*LN(14*SQRT(3)-14)-4*S~
QRT(3)*ACOT(SQRT(3)/9))*(COS(51*LN(2))*COS(33*LN(7))-SIN(51*LN~
(2))*SIN(33*LN(7)))+SIN(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQ~
RT(3)/9))*(SIN(51*LN(2))*COS(33*LN(7))+COS(51*LN(2))*SIN(33*LN~
(7))))-COS(-6*SQRT(3)*ACOT(SQRT(3)/9)-3*LN(SQRT(3)/2-1/2))*(CO~
S(18*LN(14*SQRT(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(51*LN(2~
))*COS(33*LN(7))+COS(51*LN(2))*SIN(33*LN(7)))+SIN(18*LN(14*SQR~
T(3)-14)-4*SQRT(3)*ACOT(SQRT(3)/9))*(SIN(51*LN(2))*SIN(33*LN(7~
))-COS(51*LN(2))*COS(33*LN(7)))))))/72
[/quote]
Your new expression simplifies to the same thing as the original expression
in this thread.

David
Back to top
Display posts from previous:   
   Science and Technology news... Forum Index -> Math - Symbolic Forum  
Page 1 of 1
All times are GMT

 
Jump to:  
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum