I've always seen it stated that a Pythagorean Triple is threeintegers where .positive

Why the restriction that are positive?

Similarly with Euclid's formula for generating such triples giving the restriction for...

If we let we generate the same |absolute| values with -ve

According to the restrictions is not a Pythagorean Triple but the result

still holds true.

Are the restrictions merely convention or is there another reason?

Thanks