I want to write code  that does the following
Given ideals I,J in CC[x1,...,xn]
check if Radical(I+J)=Radical(I)+Radical(J)
also maybe throw in an example of yes and no just to see it working

Radical(I)={f:there is an m such that f^m is in I} (f is a polynomial
of CC[x1,...,xn]
also Radical(I)=I(V(I)) by Nullstellensatz

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