Extended GCD of two polynomials $a$ and $b$ results in two polynomials $s$ and $t$ so that $as + bt = \text{gcd}(a, b)$.
What convention makes most sense when both $a$ and $b$ are zero?
I found that SymPy chooses $(s, t, \text{gcd}) = (1, 0, 0)$ and this got me wondering why is it better than $(0, 0, 0)$ or some other values?