If i have an element alpha=3^(1/3)+(7^(1/2)*2^(1/4))
and an ideal I=<a^3-3, b^2-7,c^4-2, alpha-(a+b*c)>
how do i show the minimum polynomial of alpha lies in the ideal I
then use it to construct the minumum polynomial of alpha

So far I have:
P.<a,b,c> = PolynomialRing(QQ)
alpha=3^(1/3)+(7^(1/2)*2^(1/4))
I = Ideal(a^3-3,b^2-7,c^4-2,alpha-(a+b*c))
al=alpha.minpoly()
but im not sure if QQ should be RR or not and about the implementation
of the minpoly() command

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