I have the following code

P.<x0,x1,y0,y1,y2,y3> = PolynomialRing(QQ,order='degrevlex')
I = Ideal(x0^4-y0,x0^3*x1-y1,x0*x1^3-y2,x1^4-y3)
print I
R.<y0,y1,y2,y3> = PolynomialRing(QQ,order='degrevlex')
I1=Ideal(1)
J=I.intersection(I1)
print J
but gives error
File "/usr/local/sage/sage-4.6/local/lib/python2.6/site-packages/sage/
rings/polynomial/multi_polynomial_ideal.py", line 369, in wrapper
    return func(*args, **kwds)
  File "/usr/local/sage/sage-4.6/local/lib/python2.6/site-packages/
sage/rings/polynomial/multi_polynomial_ideal.py", line 1327, in
intersection
    raise ValueError, "other must be an ideal in the ring of self, but
it isn't."
ValueError: other must be an ideal in the ring of self, but it isn't.

becuase I doesnt lie in R
so how do I change this so that sage will be happy for I, an ideal in
P, intersecting with any ideal in R
(also R is supposed to be a subring of P where the x0 and x1 are
removed)

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