Re: seruous solve bug? only when used with simplifying

• To: mathgroup at smc.vnet.net
• Subject: [mg48672] Re: [mg48634] seruous solve bug? only when used with simplifying
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Thu, 10 Jun 2004 02:43:09 -0400 (EDT)
• References: <200406090816.EAA15571@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```On 9 Jun 2004, at 17:16, sean kim wrote:

> hello group,
>
> i think i have a serious Solve[], Simplify[], FullSimplify[] bug...
>
>
> Take a system of equations as below. (apb is actually (a+b). i defined
> it as apb to keep Mathematica crunching away at it)
>
> sys =
> {c1[t] == (c*(16*a^4 + 8*a^3*kd + 4*a^2*apb*kd + 2*a*apb^2*kd +
> apb^3*kd))/(apb^4*kd),
> c2[t] == (2*(8*a^3 + 4*a^2*apb + 2*a*apb^2 + apb^3)*b*c)/(apb^4*d),
> c3[t] == (2*(8*a^3 + 4*a^2*apb + 2*a*apb^2 + apb^3)*b*c)/(apb^4*kd)}
>
> sys1 = sys /.{apb -> (a + b)}
> sys2 = sys/.{apb -> (a + b)}//Simplify
> sys3 = sys/.{apb -> (a + b)}//FullSimplify
>
> and then use
>
> TrueQ[sys1 == sys1]
> TrueQ[sys1 == sys2]
> TrueQ[sys1 == sys3]
> TrueQ[sys2 == sys3]
>
> then it gives,
>
> Out[18]=True
> Out[19]=False
> Out[20]=False
> Out[21]=False
>
> Simplify and FullSimplify changed the system so much that they are not
> equal?
>
> Basically, unless I define the (a+b) as a single constant apb, the
> Mathematica
> will do soemthing with it then it messes it up. I think...
>
> Why is this happening? and how do i prevent it from happening again
> with other more obsucre systems?  Above I got lucky in finding the
> cause (a+b)
>
> thanks in advance for any and all comments.
>
> Sean
>
>

There is no bug here at all, just that TrueQ is not for that purpose!
For example:

TrueQ[(a+b)^2==a^2+2 a b + b^2]

False

Now think about that, if TrueQ did what you think it does that would be
some bug! TrueQ is not meant to check if something is true or not, it
is used to "force" Mathematica to give an answer True or Flase in all
cases, even when Mathematica does not know what the answer is. If you
just evaluate

(a + b)^2 == a^2 + 2*a*b + b^2

Mathematica will return the same thing as output

(a + b)^2 == a^2 + 2*b*a + b^2

since does not perform the necessary simplifications to decide if both
sides are equal.
If you now use TrueQ you will force it to give a True or False answer
without any additional simplifications and it will of course return
False. On the other hand

Simplify[%]

True

without nay need for TrueQ.
Anyway, to summarise: TrueQ is basically used for programming and not
for the purpose you have intended. No serious bug or even a very
unserious one.

Andrzej Kozlowski
Chiba, Japan
http://www.mimuw.edu.pl/~akoz/

```

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