# [Maxima] Declarations - how to compare two equations?

Stavros Macrakis macrakis at alum.mit.edu
Mon Jan 23 11:41:47 CST 2012

```Though this is a good approach for equivalence of *expressions*, I don't
think it works well for equations, even for simple cases. The
equations* a*= 1, 200*
*a *= 200, *a* + 37 = 38, and (a-1)^201 = 0 all have the same solution set,
but LHS-RHS and LHS/RHS are different for all *a* <> 1.  Even if you happen
to test the a=1 case, you still don't know that the solution sets are the
same.  Of course, it is much worse in the multivariate case.

-s

On Sun, Jan 22, 2012 at 14:56, Richard Fateman <fateman at eecs.berkeley.edu>wrote:

> On 1/22/2012 11:22 AM, Gerd Kortemeyer wrote:
> ....
>
>> . Is there any better way to compare two equations (that LON-CAPA does
>> not "know" the first thing about) inside MAXIMA, and if not, how could I
>> begin to address the issue? Thanks! - Gerd.
>>
>
> say that you want to tell if  A=B   and C=D    express the same truth.
>
> let e1 = A-B  and e2= C-D.
> let  X=[x1,x2,...,xn]  be the set of variables that occur in e1 and e2.
>
> Choose n random floating point numbers for x1, ..., xn, and evaluate e1
> and e2.
>
> If the results are the same, approximately, then you say "yes".
>
> This can also be done with values chosen from a finite field, followed by
> evaluation using modular arithmetic.  This is called hash-coding of
> expressions.
> The results would be identical.
>
> Details to consider:
>  how many times to repeat the test.
>  what to do with overflow, underflow, divide by zero.
>  how close is equal.
>
> These ideas are not original with me,  but (especially) the floating point
> evaluation
> has been proposed and maybe used in student test grading.
>
>
>
>
>
>
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