LIPS compares complex numbers for order

[jpellegrini]

Hello,
It seems that LIPS accepts <, >, <=, >= for complex numbers:

lips> (< 1+1i 2+2i)
#t
lips> (< 2+2i 1+1i)
#f
lips> (< 1+2i 2+1i)
#t
lips> (< 1+2i 0)
#f

[jpellegrini]

(Does it implement a partial order? Then, does it use the norm or is it a lexicographic order? It would then be nice to document this -- or perhaps not allow the comparison)

[jcubic]

Yes, I think that it should throw an error for comparing complex numbers. I was asking (on StackOverflow or Math Exchange) about comparing complex numbers and long ago someone replied that it doesn't make sense to compare them.

I think that the reason why comparison works is because all operators use polymorphism so every number type gets those for free even if the result doesn't make sense.

[jcubic]

Added type checking to the compare operations. Also, the comparison was implemented for complex numbers so I've deleted it and thrown an error instead.

It looked like this:

LComplex.prototype.cmp = function(n) {
    const [a, b] = this.coerce(n);
    const [re_a, re_b] = a.__re__.coerce(b.__re__);
    const re_cmp = re_a.cmp(re_b);
    if (re_cmp !== 0) {
        return re_cmp;
    } else {
        const [im_a, im_b] = a.__im__.coerce(b.__im__);
        return im_a.cmp(im_b);
    }
};

It was a naive complex comparison that I'd implemented before I knew that it didn't make sense to compare complex numbers.