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Science Forum Index » Math - Symbolic Forum » An exact simplification challenge - 62 (ln)...
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| Vladimir Bondarenko... |
 Posted: Sat Jul 05, 2008 10:03 pm |
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Guest
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Hello,
1/48*ln(1180872205318713601+835002744095575440*2^(1/2))+
1/48*ln((-5/19+2/19*I*2^(1/2)-2/19*I*3^(1/2)+2/19*3^(1/2
)*2^(1/2))^(3*3^(1/2)+3*I)*(201-82*3^(1/2)*2^(1/2)-138*I
*2^(1/2)+116*I*3^(1/2))^(4*3^(1/2))*(55-16*I*2^(1/2)-12*
I*3^(1/2)+24*3^(1/2)*2^(1/2))^(-2*3^(1/2))*(-3+10*I*2^(1
/2)+26/3*I*3^(1/2)-2/3*3^(1/2)*2^(1/2))^(3*I)*(-27+90*I*
2^(1/2)+78*I*3^(1/2)-6*3^(1/2)*2^(1/2))^(-3^(1/2)))
?
Best wishes,
Vladimir Bondarenko
VM and GEMM architect
Co-founder, CEO, Mathematical Director
http://www.cybertester.com/ Cyber Tester, LLC
http://maple.bug-list.org/ Maple Bugs Encyclopaedia
http://www.CAS-testing.org/ CAS Testing
--------------------------------------------------------
"We must understand that technologies
like these are the way of the future."
-------------------------------------------------------- |
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| Vladimir Bondarenko... |
| Posted: Sat Jul 05, 2008 11:55 pm |
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Guest
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Great! Compressed 5:1. Is some extra compression available?
;)
On Jul 6, 2:41 am, Axel Vogt <&nore... at (no spam) axelvogt.de> wrote:
Quote: Vladimir Bondarenko wrote:
Hello,
1/48*ln(1180872205318713601+835002744095575440*2^(1/2))+
1/48*ln((-5/19+2/19*I*2^(1/2)-2/19*I*3^(1/2)+2/19*3^(1/2
)*2^(1/2))^(3*3^(1/2)+3*I)*(201-82*3^(1/2)*2^(1/2)-138*I
*2^(1/2)+116*I*3^(1/2))^(4*3^(1/2))*(55-16*I*2^(1/2)-12*
I*3^(1/2)+24*3^(1/2)*2^(1/2))^(-2*3^(1/2))*(-3+10*I*2^(1
/2)+26/3*I*3^(1/2)-2/3*3^(1/2)*2^(1/2))^(3*I)*(-27+90*I*
2^(1/2)+78*I*3^(1/2)-6*3^(1/2)*2^(1/2))^(-3^(1/2)))
?
-1/96*3^(1/2)*ln(4250272665676801+1735166549767840*6^(1/2))
+ln(1+2^(1/2)) |
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| Vladimir Bondarenko... |
| Posted: Sun Jul 06, 2008 1:23 am |
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Guest
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On Jul 6, 3:21 am, Axel Vogt <&nore... at (no spam) axelvogt.de> wrote:
Quote: Vladimir Bondarenko wrote:
Great! Compressed 5:1. Is some extra compression available?
;)
On Jul 6, 2:41 am, Axel Vogt <&nore... at (no spam) axelvogt.de> wrote:
Vladimir Bondarenko wrote:
Hello,
1/48*ln(1180872205318713601+835002744095575440*2^(1/2))+
1/48*ln((-5/19+2/19*I*2^(1/2)-2/19*I*3^(1/2)+2/19*3^(1/2
)*2^(1/2))^(3*3^(1/2)+3*I)*(201-82*3^(1/2)*2^(1/2)-138*I
*2^(1/2)+116*I*3^(1/2))^(4*3^(1/2))*(55-16*I*2^(1/2)-12*
I*3^(1/2)+24*3^(1/2)*2^(1/2))^(-2*3^(1/2))*(-3+10*I*2^(1
/2)+26/3*I*3^(1/2)-2/3*3^(1/2)*2^(1/2))^(3*I)*(-27+90*I*
2^(1/2)+78*I*3^(1/2)-6*3^(1/2)*2^(1/2))^(-3^(1/2)))
?
-1/96*3^(1/2)*ln(4250272665676801+1735166549767840*6^(1/2))
+ln(1+2^(1/2))
-1/48*3^(1/2)*ln(46099201+18819920*6^(1/2))+ln(1+2^(1/2))
But what should it be good for?
PS: please do not answer on top of posts, but at the bottom,
so threads can be read in sequel. Thanks.- Hide quoted text -
- Show quoted text -
Attempt #1...
AV> -1/96*3^(1/2)*ln(4250272665676801+1735166549767840*6^(1/2))
AV> +ln(1+2^(1/2))
Attempt #2...
AV> -1/48*3^(1/2)*ln(46099201+18819920*6^(1/2))+ln(1+2^(1/2))
Great! Compressed 7:1. Is even more compression available?
;))
AV> But what should it be good for?
1) For fun )))
2) For thinking on how further full automated simplification
can be done... that is again, for fun ))))) |
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| Andreas Dieckmann... |
| Posted: Sun Jul 06, 2008 2:47 am |
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Guest
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my simplest form is arcsinh(1)-arcsinh(sqrt(2))/sqrt(3)
Andreas |
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| Axel Vogt... |
| Posted: Sun Jul 06, 2008 4:41 am |
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Vladimir Bondarenko wrote:
Quote: Hello,
1/48*ln(1180872205318713601+835002744095575440*2^(1/2))+
1/48*ln((-5/19+2/19*I*2^(1/2)-2/19*I*3^(1/2)+2/19*3^(1/2
)*2^(1/2))^(3*3^(1/2)+3*I)*(201-82*3^(1/2)*2^(1/2)-138*I
*2^(1/2)+116*I*3^(1/2))^(4*3^(1/2))*(55-16*I*2^(1/2)-12*
I*3^(1/2)+24*3^(1/2)*2^(1/2))^(-2*3^(1/2))*(-3+10*I*2^(1
/2)+26/3*I*3^(1/2)-2/3*3^(1/2)*2^(1/2))^(3*I)*(-27+90*I*
2^(1/2)+78*I*3^(1/2)-6*3^(1/2)*2^(1/2))^(-3^(1/2)))
?
-1/96*3^(1/2)*ln(4250272665676801+1735166549767840*6^(1/2))
+ln(1+2^(1/2)) |
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| ... |
| Posted: Sun Jul 06, 2008 5:14 am |
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Guest
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Vladimir Bondarenko schrieb:
Quote: Hello,
1/48*ln(1180872205318713601+835002744095575440*2^(1/2))+
1/48*ln((-5/19+2/19*I*2^(1/2)-2/19*I*3^(1/2)+2/19*3^(1/2
)*2^(1/2))^(3*3^(1/2)+3*I)*(201-82*3^(1/2)*2^(1/2)-138*I
*2^(1/2)+116*I*3^(1/2))^(4*3^(1/2))*(55-16*I*2^(1/2)-12*
I*3^(1/2)+24*3^(1/2)*2^(1/2))^(-2*3^(1/2))*(-3+10*I*2^(1
/2)+26/3*I*3^(1/2)-2/3*3^(1/2)*2^(1/2))^(3*I)*(-27+90*I*
2^(1/2)+78*I*3^(1/2)-6*3^(1/2)*2^(1/2))^(-3^(1/2)))
?
For the imaginary part to be reduded to zero, the Derive 6.10 default
settings need to be changed to Trigonometry := Collect. Within a
second or so, simplification then gives
SQRT(3)*LN(1835457113162089-749322228668160*SQRT(6))/96
- SQRT(3)*LN(7*SQRT(3)+8*SQRT(2))/24 + LN(SQRT(2)+1).
A repeat simplification of this result produces
SQRT(3)*LN(SQRT(3)-SQRT(2))/3 + LN(SQRT(2)+1).
It is a rare occurence that the initial result of a Derive
simplification is not stable.
Martin. |
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| Axel Vogt... |
| Posted: Sun Jul 06, 2008 5:21 am |
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Guest
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Vladimir Bondarenko wrote:
Quote: Great! Compressed 5:1. Is some extra compression available?
;)
On Jul 6, 2:41 am, Axel Vogt <&nore... at (no spam) axelvogt.de> wrote:
Vladimir Bondarenko wrote:
Hello,
1/48*ln(1180872205318713601+835002744095575440*2^(1/2))+
1/48*ln((-5/19+2/19*I*2^(1/2)-2/19*I*3^(1/2)+2/19*3^(1/2
)*2^(1/2))^(3*3^(1/2)+3*I)*(201-82*3^(1/2)*2^(1/2)-138*I
*2^(1/2)+116*I*3^(1/2))^(4*3^(1/2))*(55-16*I*2^(1/2)-12*
I*3^(1/2)+24*3^(1/2)*2^(1/2))^(-2*3^(1/2))*(-3+10*I*2^(1
/2)+26/3*I*3^(1/2)-2/3*3^(1/2)*2^(1/2))^(3*I)*(-27+90*I*
2^(1/2)+78*I*3^(1/2)-6*3^(1/2)*2^(1/2))^(-3^(1/2)))
?
-1/96*3^(1/2)*ln(4250272665676801+1735166549767840*6^(1/2))
+ln(1+2^(1/2))
-1/48*3^(1/2)*ln(46099201+18819920*6^(1/2))+ln(1+2^(1/2))
But what should it be good for?
PS: please do not answer on top of posts, but at the bottom,
so threads can be read in sequel. Thanks. |
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| Vladimir Bondarenko... |
| Posted: Sun Jul 06, 2008 8:13 am |
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Guest
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On Jul 6, 8:14 am, cliclic... at (no spam) freenet.de wrote:
Quote: Vladimir Bondarenko schrieb:
Hello,
1/48*ln(1180872205318713601+835002744095575440*2^(1/2))+
1/48*ln((-5/19+2/19*I*2^(1/2)-2/19*I*3^(1/2)+2/19*3^(1/2
)*2^(1/2))^(3*3^(1/2)+3*I)*(201-82*3^(1/2)*2^(1/2)-138*I
*2^(1/2)+116*I*3^(1/2))^(4*3^(1/2))*(55-16*I*2^(1/2)-12*
I*3^(1/2)+24*3^(1/2)*2^(1/2))^(-2*3^(1/2))*(-3+10*I*2^(1
/2)+26/3*I*3^(1/2)-2/3*3^(1/2)*2^(1/2))^(3*I)*(-27+90*I*
2^(1/2)+78*I*3^(1/2)-6*3^(1/2)*2^(1/2))^(-3^(1/2)))
?
For the imaginary part to be reduded to zero, the Derive 6.10 default
settings need to be changed to Trigonometry := Collect. Within a
second or so, simplification then gives
SQRT(3)*LN(1835457113162089-749322228668160*SQRT(6))/96
- SQRT(3)*LN(7*SQRT(3)+8*SQRT(2))/24 + LN(SQRT(2)+1).
A repeat simplification of this result produces
SQRT(3)*LN(SQRT(3)-SQRT(2))/3 + LN(SQRT(2)+1).
It is a rare occurence that the initial result of a Derive
simplification is not stable.
Martin.
M> It is a rare occurence that the initial result
M> of a Derive simplification is not stable.
A nice catch, great!
Still, I agree with you that such cases in Derive are
fairly rare.
Vladimir
--
Vladimir Bondarenko
VM and GEMM architect
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."
---------------------------------------------- |
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| Vladimir Bondarenko... |
| Posted: Sun Jul 06, 2008 8:15 am |
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Guest
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On Jul 6, 5:47 am, Andreas Dieckmann <adieckm... at (no spam) aol.com> wrote:
Quote: my simplest form is arcsinh(1)-arcsinh(sqrt(2))/sqrt(3)
Andreas
AD> arcsinh(1)-arcsinh(sqrt(2))/sqrt(3)
Perfect! It is precisely what I expected.
Could you please show how you got your result?
Best wishes,
Vladimir Bondarenko
VM and GEMM architect
Co-founder, CEO, Mathematical Director
http://www.cybertester.com/ Cyber Tester, LLC
http://maple.bug-list.org/ Maple Bugs Encyclopaedia
http://www.CAS-testing.org/ CAS Testing
-----------------------------------------------------
"We must understand that technologies
like these are the way of the future."
----------------------------------------------------- |
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| Andreas Dieckmann... |
| Posted: Sun Jul 06, 2008 8:53 am |
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Guest
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46099201 + 18819920*sqrt(6) = (sqrt(2)+sqrt(3))^16
Andreas |
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| Andreas Dieckmann... |
| Posted: Sun Jul 06, 2008 11:58 am |
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Guest
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I tried repeated square roots...
Andreas |
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| Axel Vogt... |
| Posted: Sun Jul 06, 2008 2:21 pm |
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Guest
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Andreas Dieckmann wrote:
Quote: 46099201 + 18819920*sqrt(6) = (sqrt(2)+sqrt(3))^16
Andreas
How you got that? Sprich ...
Axel |
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