The reason why the precompile is of that form is that that’s the most natural way to make it usable for both e(a, b) = e(c, d) and more complex equations like e(a, b) * e(c, d) = e(f, g), or e(a, b) * e(c, d) = e(f, g) + e(h, i), etc. You’re correct that simply negating the G1 points that are on the “right” side of the equation is the way to do it.
Between bn128 and alt_bn128 the
aandbparameters are the exact same; only theG2generator point is different (if I’m not mistaken)
Given that, as we proved last year, there can only be one order-N subgroup of G2, that would basically mean that the alt_bn128 generator is a multiple of the bn128 generator, and I would presume the generators are constructed in such a way that we don’t know what the cofactor is. If this is true, then the pairing precompile for alt_bn128 should be exactly the same as the pairing precompile for bn128, as although it does care that the G2 points are on the right subgroup, it doesn’t care what the generator is.