Good day, please help understand the following, as I am feeling my self an idiot and not able to figure out what to do:
The study is in a closed algebraic field K.
I have $(x,y)/(x^{2},xy,y^{2},(x-a)^{3}-(y-b)^{2})$
when $a=b=0$ then the previous expression becomes $$(\bar{x},\bar{y})$$ where $\bar{x},\bar{y}$ represent the residue classes of x,y.
When $a\neq0,b\neq0$, the expression becomes: $=\left\{\begin{matrix} \bar{x}=\bar{y},charK\neq2,3\\ \bar{x},charK=3\\ \bar{y},charK=2 \end{matrix}\right.$
May I ask how we calculated the residue classes in these situations.
Thanks in advanced.