Maxima has two equality operations: a = b and equal (a, b). The first is
strict syntactic (structural) equality. The second is semantic
(mathematical value) equality (though not very powerful). You want the
second.
-s
On Nov 26, 2011 5:14 AM, "Oliver Kullmann" <O.Kullmann at swansea.ac.uk> wrote:
> Hello,
>
> I encountered the example
>
> is((y1-y2)^2+(x1-x2)^2 = (y2-y1)^2+(x2-x1)^2);
> false
>
> Is this to be expected? I understand that standard simplification
> only performs very simple operations, but that it doesn't recognise
> that simple equation?
>
> I know that applying "expand" and/or "radcan" often helps,
> and so it does here:
>
> is(expand((y1-y2)^2+(x1-x2)^2 = (y2-y1)^2+(x2-x1)^2));
> true
>
> Now two remarks:
>
> 1) The above comes from working with the Euclidian norm. As far as I know,
> there is no built-in function for this norm, or the more general p-norms.
> And as far as I know, having such functions provided by Maxima itself could
> enhance the possibilities for handling equations correctly.
>
> 2) Before Maxima I used MuPad, which was open at the beginning; when
> they went commercial I stopped using it. This was (is) likely not a
> very powerful computer-algebra system, but nevertheless several times
> I had nice surprises by using its "simplify"-function: it came up with
> interesting simplifications, which I could actually use for papers.
>
> It is really a pity that Maxima doesn't have such a function:
> In it would be collected heuristical knowledge, analysing the expression,
> and applying the given simplification-functions in all kinds of different
> ways.
>
>
> Thanks for your attention.
>
> Oliver
>
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