How can I compute Intersect of Ideals?

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I am not sure i understand your question, but you may try:

sage: R.<x> = PolynomialRing(QQ, 1) ; R
Multivariate Polynomial Ring in x over Rational Field
sage: I = R.ideal(x^2-1) ; I
Ideal (x^2 - 1) of Multivariate Polynomial Ring in x over Rational Field
sage: J = R.ideal(x^2-2) ; J
Ideal (x^2 - 2) of Multivariate Polynomial Ring in x over Rational Field
sage: I.intersection(J)
Ideal (x^4 - 3*x^2 + 2) of Multivariate Polynomial Ring in x over Rational Field