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xyz91234@yahoo.com science forum beginner
Joined: 13 Jun 2006
Posts: 6

Posted: Tue Jul 18, 2006 12:59 am Post subject:
How does a CAS simplify complicated expressions?



Hello,
How does CAS simplify expressions such as: sqrt(4 + (1058 * 2^(1/3)) +
(92 * 2^(2/3)))
to this:
2 + (23 * 2^(2/3))
Thanks 

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KochBeuttenmueller science forum beginner
Joined: 18 Jul 2006
Posts: 1

Posted: Tue Jul 18, 2006 8:31 am Post subject:
Re: How does a CAS simplify complicated expressions?



xyz91234@yahoo.com wrote:
Quote:  Hello,
How does CAS simplify expressions such as: sqrt(4 + (1058 * 2^(1/3)) +
(92 * 2^(2/3)))
to this:
2 + (23 * 2^(2/3))
Thanks
It depends on CAS and what is 2^(1/3) really? 


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Vladimir Bondarenko science forum Guru
Joined: 23 Apr 2005
Posts: 601

Posted: Tue Jul 18, 2006 10:50 am Post subject:
Re: How does a CAS simplify complicated expressions?



In Derive 6 http://www.derive.com you can use
the Display Step feature in the main menu.
At the first step, Derive applies the rule
If u = 2*SQRT(x*y) and x>y>0 then
SQRT(x + u + y) = SQRT(x) + SQRT(y)
So you get
SQRT(4 + 1058*2^(1/3) + 92*2^(2/3)) >
SQRT(4) + SQRT(2368574224^(1/3))
At the second step, Derive reduces SQRT(4) and
SQRT(2368574224^(1/3)) to 2 and 23*2^(2/3),
respectively, so you obtain your desired data
2 + (23 * 2^(2/3))
Best wishes,
Vladimir Bondarenko
VM and GEMM architect
Cofounder, CEO, Mathematical Director
http://www.cybertester.com/ Cyber Tester, LLC
http://maple.buglist.org/ Maple Bugs Encyclopaedia
http://www.CAStesting.org/ CAS Testing
xyz91234@yahoo.com wrote:
Quote:  Hello,
How does CAS simplify expressions such as: sqrt(4 + (1058 * 2^(1/3)) +
(92 * 2^(2/3)))
to this:
2 + (23 * 2^(2/3))
Thanks 


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Vladimir Bondarenko science forum Guru
Joined: 23 Apr 2005
Posts: 601

Posted: Fri Jul 21, 2006 6:41 am Post subject:
Re: How does a CAS simplify complicated expressions?



xyz91234> How does CAS simplify expressions...
If you are interested in simplification matters, for starters,
you could derive much pleasure from these famous classic works
Essays in Algebraic Simplification
by Richard J. Fateman
http://groups.google.com/group/sci.math.symbolic/msg/0711802858f3b44b
Algebraic Simplification: A Guide for the Perplexed
by Joel Moses
http://groups.google.com/group/sci.math.symbolic/msg/e81b8db8dd551d70
In case you are especially interested in Derive processing,
I uploaded here
http://maple.buglist.org/ASME.doc a talk titled
Automating the Simplification of Mathematical Expressions
by Albert D. Rich, the Derive coauthor, gave at the VisitME
conference in Vienna, Austria.
Sincerely,
Vladimir Bondarenko
VM and GEMM architect
Cofounder, CEO, Mathematical Director
http://www.cybertester.com/ Cyber Tester, LLC
http://maple.buglist.org/ Maple Bugs Encyclopaedia
http://www.CAStesting.org/ CAS Testing 

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Peter Luschny science forum beginner
Joined: 13 May 2005
Posts: 36


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Google


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