Re: [Maxima-discuss] semantics of is(equal(a, b))

[David S. <d.s...@go...>]

Rubey, Martin <mar...@tu...> schrieb am So., 23. Nov. 2025,
03:03:

> is(equal(a, b)) returns true (or false) if and only if a and b are equal
> (or not equal) for all possible values of their variables, as determined by
> evaluating ratsimp(a - b);
>
> Does this mean that is(equal(a, b)) is false if and only if the function
> (a, b) \mapsto a-b does not have any zeros?
>

Yes.

As far as I know, this is how it works:
- If ratsimp(a-b) gives 0, then is(equal(a,b)) is true.
- If ratsimp(a-b) gives a non-zero constant (no variables), then
is(equal(a,b)) is false.
- Otherwise, is(equal(a,b)) is unknown.

Of course, this is quite limited, because it only works reliably with
rational expressions due to relying on ratsimp.

To get better results, first convert trigonometric/hyperbolic functions to
exponential form using "exponentialize" and inverse
trigonometric/hyperbolic functions to logarithmic form using "logarc". You
may also want to denest roots using "sqrtdenest".

Best regards
David