Re: expression normalization

["Ruud H.G. van Tol" <rvtol@isolution.nl>]

On 2022-10-22 16:59, Ruud H.G. van Tol wrote:
> ? (a-b)/(c-d)
> %1 = 1/(c - d)*a - 1/(c - d)*b
> ? ((a-b)/(c-d))
> %2 = 1/(c - d)*a - 1/(c - d)*b
>
> ? (b-a)/(d-c)
> %3 = -1/(-c + d)*a + 1/(-c + d)*b
> ? ((b-a)/(d-c))
> %4 = -1/(-c + d)*a + 1/(-c + d)*b
>
> I wondered why these don't all "normalize"
> to the same internal (?) format.
>
> And if there is no special reason for that:
> if it is worth the effort to make it so.
>
> -- Ruud
>
> ? a/b-c/d
> %5 = 1/b*a - 1/d*c
> ? b/a-c/d
> %6 = (c*a - d*b)/(-d*a)
> ? b/a-d/c
> %7 = (-d*a + c*b)/(c*a)

? a/b-d/c
%8 = 1/b*a - d/c
? w/x-z/y
%9 = (-z*x + w*y)/(y*x)

Least multiplication/division steps, could be a goal?
And then alphabetical order preservation?

I'm really only guessing here, didn't benchmark anything,
and also didn't think through any commutativity and distributivity 
implications.

? type(a/b-c/d)
%16 = "t_POL"
? type(b/a-d/c)
%17 = "t_RFRAC"

-- Ruud