Something strange (at least for me). I am computing with polynomials in QQbar[z]. So I do:
sage: P.<z>=QQbar[]
And I define 2 polynomials N and D. Coefficients of N and D are all
real, algebraic numbers (say like QQbar(sqrt(3))) and I consider the
rational fraction R=N/D
sage: R.parent()
Fraction Field of Univariate Polynomial Ring in z over Algebraic Field
Now, I want to look at R on the imaginary axis. I do (may be this is not
a good idea):
sage: PP.<x>=QQbar[]
sage: RIaxe=R(z=QQbar(I)*x)
sage: RIaxe.parent()
Fraction Field of Univariate Polynomial Ring in x over Algebraic Field
it seems ok.
I take the numerator:
sage: pp=RIaxe.numerator()
sage: print pp
0.05638275005921478?*I*x^3 - 0.4022786138875136?*x^2 - 1/2*I*x + 1
okay.
sage: pp.parent()
Univariate Polynomial Ring in x over Algebraic Field
okay.
-----
Now starts my problem; I want to extract from pp the polynomial which
has real coefficients:
sage: l=[s for s in pp.coefficients() if s.imag()==0]
sage: print l
[1, -0.4022786138875136?]
okay. Now let us construct a polynomial from l:
sage: print sum([l[i]*z^i for i in range(0,len(l))])
(-0.4022786138875136? + 0.?e-18*I)*z + 1
^^^^^
Why? an imaginary part?
----------------------
Now if I use the radical_expression method:
sage: l=[QQbar(pp.coefficients()[i].radical_expression())*x^i for i in
range(0,pp.degree()+1) if pp.coefficients()[i].imag()==0]
sage: -0.4022786138875136?*x^2 + 1
which is ok, (but... a bit slow).
Why ?
Yours,
t.
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