#4722: BUG - number field K.hilbert_class_polynomial() is a *lie*
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Reporter: was | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-3.2.2
Component: number theory | Keywords:
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I'm in a talk right now, and the speaker (Marco from Holland) just pointed
out that
Sage's K.hilbert_class_polynomial() function, for K quadratic imaginary,
is a *LIE*.
It returns a poly that defines that Hilbert class field, but it is *not*
the Hilbert Class Polynomial.
Observe:
{{{
sage: K.<a> =QuadraticField(-97)
sage: K.hilbert_class_polynomial()
x^4 + 9*x^2 - 6*x + 1
sage: magma(K.discriminant()).HilbertClassPolynomial()
$.1^4 - 750062398364686994581728000*$.1^3 -
20542159225989612130996373047535232000000*$.1^2 +
208224136957169320201407896480139264000000000*$.1 -
1121692648948590091501551223636881408000000000000
}}}
Solution: change the name of this function and add documentation
clarifying this, say including the above example.
The difference is *very* important, given the use of the Hilbert class
polynomial in computing elliptic curves with a given number of rational
points.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4722>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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