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MathGroup Archive 2002

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Re: Simplify with assumptions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg32445] Re: [mg32409] Simplify with assumptions
  • From: BobHanlon at aol.com
  • Date: Mon, 21 Jan 2002 02:54:57 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 1/19/02 2:18:10 AM, dsnead6 at charter.net writes:

>Using Mathematic 4.1, Why won't the 2nd expression simplify?
>
>Simplify[1 - c^2,  s^2 + c^2 == 1]
>gives
>s^2
>
>But
>Simplify[1 - s^2,  s^2 + c^2 == 1]
>gives
>1 - s^2
>
>Why doesn't this 2nd expression yield c^2?
>
>The leaf count of both s^2 and c^2 are 3.
>While the leaf count for both 1 - s^2 and 1 - c^2 are 7.

I don't know why but, as in your example, Mathematica's behavior 
is sometimes dependent on the canonical order of the variable names.  
For this simplification, it appears to stop its search when it has a form 
which has eliminated the first (in canonical order) variable.  One 
work-around is to replace some or all of the variable names with 
dummy names to alter the variables' order, solve the problem, and 
restore the original names.  For example,

Simplify[{1-c^2,1-s^2}, s^2+c^2==1]

{s^2, 1 - s^2}

Simplify[{1-c^2,1-s^2} /. c ->  t,
 
    s^2+c^2==1 /. c -> t] /. t -> c

{1 - c^2, c^2}

the desired simplifications being

First[Sort[#,
 
        LeafCount[#1]<LeafCount[#2]&
        ]]& /@ Transpose[{%, %%}]

{s^2, c^2}


Bob Hanlon
Chantilly, VA  USA


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