I am thinking of calculation $Soc(R)$ for given algebra $R$. But the definition of socle is too abstract to calculate. https://en.m.wikipedia.org/wiki/Socle_(mathematics)
Does anyone tell me how to calculate socle algorithmically？ For instance, what is the $soc(R)$ of following algebras $R$？
(1) $R=\mathbb{C}[x,y]/(x^2+y^3,xy^2,y^4)$
(2) $R=\mathbb{C}\langle x,y \rangle /(x^2+1,y^2-1,xy+yx)$ (noncommutative algebra)