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Forum index » Science and Technology » Math » Symbolic
How does a CAS simplify complicated expressions?
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xyz91234@yahoo.com
science forum beginner


Joined: 13 Jun 2006
Posts: 6

PostPosted: Tue Jul 18, 2006 12:59 am    Post subject: How does a CAS simplify complicated expressions? Reply with 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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Koch-Beuttenmueller
science forum beginner


Joined: 18 Jul 2006
Posts: 1

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

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

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

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
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
Back to top
Vladimir Bondarenko
science forum Guru


Joined: 23 Apr 2005
Posts: 601

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

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
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Peter Luschny
science forum beginner


Joined: 13 May 2005
Posts: 36

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

Vladimir Bondarenko wrote:

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
MuPAD Research Group, Universitity of Paderborn
http://www-math.uni-paderborn.de/~stefanw/Papers/mathPAD_Vol11_art07.pdf

Peter
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