How does a CAS simplify complicated expressions?

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

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

xyz91234@yahoo.com wrote:

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

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:

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

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

Vladimir Bondarenko wrote:

Google