# Extended GCD of two zero polynomials over finite field

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?

• Looks like a random choice, just to return something that works. Clearly $s$ and $t$ are not uniquely determined when $a=b=0$. – Hans Lundmark Oct 17 '18 at 21:06