I have given a polynomial in two variables y^10+10 * y^8 * x^3 + 1 in
Q[x][y] and a polynomial defining a number field such as x^5 + 137.
I want to factor the polynomial over the number field and then evaluate it
given numerical interval values for x and y.
I used to do the following:
Rx=PolynomialRing(RationalField(),'x')
Rxy=PolynomialRing(Rx,'y')
x = var('x')
y = var('y')
# Polynomial in Q[x][y]
poly = Rxy(y^10+10 * y^8 * x^3 + 1)
nf = NumberField(x^5 + 137, 'x')
#polynomial in Q(a)[y] where a is a "root" of nf
poly_nf = poly.change_ring(nf)
factors = poly_nf.factor()
#pick first factor
factor, multiplicity = factors[0]
# Lift polynomial back to Q[x][y]
lifted = factor.map_coefficients(lambda c:Rx(c.lift()), Rxy)
# Evaluate
val = lifted.substitute(x = RIF(-2.67512520581, -2.67512520582), y =
RIF(1.00001, 1.00002))
# We expect this to be an interval
type(val)
<type 'sage.rings.real_mpfi.RealIntervalFieldElement'>
But in sage 6.10, this now gives as result:
<type 'sage.rings.polynomial.polynomial_element.Polynomial_generic_dense'>
Something has changed. Was I using it incorrectly and this improved or is
this a regression?
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