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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
Koch-Beuttenmueller
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?
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,

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

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
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.bug-list.org/ASME.doc a talk titled Automating the Simplification of Mathematical Expressions by Albert D. Rich, the Derive co-author, gave at the Visit-ME conference in Vienna, Austria. Sincerely, 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
Peter Luschny
science forum beginner

Joined: 13 May 2005
Posts: 36

Posted: Fri Jul 21, 2006 10:50 am    Post subject: Re: How does a CAS simplify complicated expressions?

 Quote: 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.bug-list.org/ASME.doc a talk titled Automating the Simplification of Mathematical Expressions by Albert D. Rich, the Derive co-author, gave at the Visit-ME conference in Vienna, Austria.

Rule-based Simplification of Expressions
Jšurgen Billing and Stefan Wehmeier

Peter

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