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

[Stavros M. <mac...@gm...>]

equal tries to do the "right thing" , but for "interesting" cases, you may
need to think a bit about what you intend.

For example,

is(equal(float(%pi),%pi)) => true

But

is(equal(bfloat(%pi),%pi)) => false

for all values of fpprec.

And

is(equal(bfloat(%pi),float(%pi))))

is true for fpprec = 3-7,11,12,14,15, and false otherwise.





On Sun, Nov 23, 2025, 16:38 David Scherfgen via Maxima-discuss <
max...@li...> wrote:

> 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
> _______________________________________________
> Maxima-discuss mailing list
> Max...@li...
> https://lists.sourceforge.net/lists/listinfo/maxima-discuss
>