Show that in $\mathbb{C}[X,Y]$, the ideals $(X^3-X^2,X^2Y-X^2, XY-Y, Y^2-Y)$ and $(X^2,Y)\cap (X-1, Y-1)$ coincide. Is this a radical ideal? I can show that $(X^3-X^2,X^2Y-X^2, XY-X, Y^2-Y) \subseteq (X^2,Y)\cap (X-1, Y-1)$, but I don't have an idea on how to proceed proving the inverse, nor how to investigate whether this ideal is radical. Any ideas?
2026-03-30 14:55:49.1774882549
calculate intersection of two polynomial ideals
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