Checking equivilence of equalities



Edd Barrett <vext01 at gmail.com> writes:
> On Tue, Feb 07, 2012 at 04:00:23PM -0500, Stavros Macrakis wrote:
>> You could certainly do something like
>> 
>>         is  (  equal(   lhs(eq1)-rhs(eq1)  , lhs(eq2)-rhs(eq2) ) )
>> 
>> as you suggest, but that does NOT test that the truth-values of the
>> equations are the same.
>> 
>> After all, 2*x=0 and x=0 are equivalent equations, but 2*x is not equal to
>> x.  Logically, what you want is something like
>> 
>>         is  (  equal(   zerop(lhs(eq1)-rhs(eq1))  , zerop(
>> lhs(eq2)-rhs(eq2) ) ) )
>> 
>> but Maxima doesn't support any such zerop function.
>> 
>> You could define zerop(q) := signum(q)^2 , which is perfectly correct, but
>> the <is> system won't be able to do anything useful with that.
>> 
>>            -s
>
> I am quite suprised that this functionality does not exist. I would have
> thought that equality equivilence would be a commonly used feature in a
> CAS system.
>
> I will raise a feature request and see what the developers say.

Stavros is one of the core developers of Maxima.

Also, look at the zeroequiv function, and maybe at past discussions of
the topic. You might find this thread [1] interesting (it basically
consists of people correctly telling me that I'm being very
naive...). Less promising is [2].

Rupert

[1] http://thread.gmane.org/gmane.comp.mathematics.maxima.general/25976/focus=25978
[2] http://article.gmane.org/gmane.comp.mathematics.maxima.general/10928
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