# [Maxima] Checking equivilence of equalities

Stavros Macrakis macrakis at alum.mit.edu
Wed Feb 8 05:01:31 CST 2012

```Could you give some examples of non-trivial situations where this
functionality is useful?  That might help in thinking about approaches.
Your current example is easily handled with 'solve' but of course that
won't work when Maxima can't solve the equations.

-s
On Feb 8, 2012 5:32 AM, "Edd Barrett" <vext01 at gmail.com> wrote:

> 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.
>
> Cheers
>
> --
> Best Regards
> Edd Barrett
>
> http://www.theunixzoo.co.uk
>
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