# Let $Y = \{ (1,1),(0,0\} \subset \mathbb A_k^2$. Find the $\mathbb I(Y)$.

Let $Y = \{ (1,1),(0,0\} \subset \mathbb A_k^2$. Find the $\mathbb I(Y)$.

As if $f(x,y) \in \mathbb I(Y)$ then as $f(0,0)=0$ hence constant term of $f$ is zero and as $f(1,1)=0$ therefore sum of the coefficients of $f(x,y)$ is zero. But how can we describe this set properly?

#### Solutions Collecting From Web of "Let $Y = \{ (1,1),(0,0\} \subset \mathbb A_k^2$. Find the $\mathbb I(Y)$."

Note that $f\in (x,y)\cap (x-1,y-1)$. Now try to show this: $$(x,y)\cap (x-1,y-1)=(x-y,x(x-1),y(y-1)).$$

Furthermore, $$(x-y,x(x-1),y(y-1))=(x-y,x^2-y).$$