Unexpected Mod(0,1) == Mod(x,x*(x-1))*Mod(1,y*(y-1))*Mod(1,x+y-1)

[Georgi Guninski <gguninski@gmail.com>]

I am experimenting with quotients of polynomial rings
and get unexpected Mod(0,1):

? mo=Mod(1,x*(x-1))*Mod(1,y*(y-1))*Mod(1,x+y-1)
%1 = Mod(Mod(0, y^2 - y), 1)
? mo=Mod(x,x*(x-1))*Mod(1,y*(y-1))*Mod(1,x+y-1)
%2 = Mod(0, 1)

In sagemath:
sage: K.<x,y>=QQ[]
sage: Kquo=K.quotient([x*(x-1),y*(y-1),x+y-1])
sage: Kquo(x)
-ybar + 1