Thank you all for your help!
I got the same error as William, but it pointed me into the right
direction. I found a way how to get the unique bounding interval of the
root in sympy and convert this interval to a sage interval. It is not the
prettiest solution but the following works for me:
from sage.all import *
from sympy import sympify
from sage.symbolic.expression_conversions import polynomial
expr = sympify("CRootOf(x**2 + 1, 0)")
complex_interval = expr._get_interval()
real_from = Rational(str(complex_interval.ax))._sage_()
real_to = Rational(str(complex_interval.bx))._sage_()
im_from = Rational(str(complex_interval.ay))._sage_()
im_to = Rational(str(complex_interval.by))._sage_()
sage_interval = CIF(RIF(real_from, real_to), RIF(im_from, im_to))
min_poly = polynomial(expr.expr._sage_(), base_ring=QQ)
algebraic_number = QQbar.polynomial_root(min_poly, sage_interval)
William Stein schrieb am Samstag, 1. April 2023 um 21:21:05 UTC+2:
> Thanks Vincent! What version of Sage are you using? With sage-9.8 I get:
>
> ---
>
> from sympy import sympify
> exp = sympify("CRootOf(x**5 + x + 1, 0)")
> sage_poly = QQ['x'](list(map(QQ, reversed(exp.poly.rep.rep))))
> sage_approx = RIF(exp.n()) + RIF(-1e-30, 1e-30)
> QQbar.polynomial_root(sage_poly, sage_approx)
>
> Outputs:
>
> ValueError: Refining interval that does not bound unique root!
>
> ----
>
>
>
> On Sat, Apr 1, 2023 at 12:02 PM vdelecroix <20100.d...@gmail.com> wrote:
> >
> > Dear Marcel,
> >
> > It is a pity that this does not work more directly. Here is a work
> around to achieve what you want to do
> >
> > sage: exp = sympify("CRootOf(x**5 + x + 1, 0)")
> > sage: sage_poly = QQ['x'](list(map(QQ, reversed(exp.poly.rep.rep))))
> > sage: sage_approx = RIF(exp.n()) + RIF(-1e-30, 1e-30)
> > sage: QQbar.polynomial_root(sage_poly, sage_approx)
> > -0.7548776662466928?
> >
> > This will be fixed in https://github.com/sagemath/sage/pull/35414 and
> hopefully included in the next sage version.
> >
> > Vincent
> > Le vendredi 31 mars 2023 à 15:00:34 UTC+2, Marcel Moosbrugger a écrit :
> >>
> >> I am trying to convert "complex_root_of" expressions to algebraic
> numbers (elements in the field QQbar). However, I get a "ValueError" with
> the message "to many values to unpack".
> >>
> >> A minimal example would be:
> >>
> >> from sage.all import *
> >> from sympy import sympify
> >>
> >> exp1 = sympify("CRootOf(x**2 + 1, 0)")._sage_()
> >> exp2 = sympify("CRootOf(x**2 + 1, 1)")._sage_()
> >> print(exp1)
> >> print(exp2)
> >> exp1 = QQbar(exp1)
> >> exp2 = QQbar(exp2)
> >> print(exp1)
> >> print(exp2)
> >>
> >> The context I am working in is: I have a tool that is currently written
> in python and sympy. I am trying to use the output of that tool to do some
> further computation using sage, and the output of the first tool may
> contain CRootOf expressions.
> >>
> >>
> > --
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> .
>
>
>
> --
> William (http://wstein.org)
>
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