"William Stein" <[EMAIL PROTECTED]> writes:

> On 5/17/07, Prof. J. E. Cremona <[EMAIL PROTECTED]> wrote:
>>
>> Problem:  when executing the following, the last line takes forever and
>> had to be killed:
>>
>> R = PolynomialRing(QQ, ['a','b','c','d','e'], 5)
>> K = R.fraction_field()
>> a,b,c,d,e = K.gens()
>>
>> ig = 12*a*e-3*b*d+c^2
>> jg = 72*a*c*e+9*b*c*d-27*a*d^2-27*e*b^2-2*c^3
>> hg = 8*a*c-3*b^2
>> deltag = 4*ig^3-jg^2
>>
>> Ky.<y> = PolynomialRing(K,'y')
>> phipoly = y^3-3*ig*y+jg
>>
>> What am I missing?
>
> Nothing --  You have found a subtle bug in SAGE's coercion code.

Such problems are legion.  I've given up trying to fix them, because
the details of munging every _coerce_ are too messy.  I vote +1 to
David Roe's commutative diagram approach precisely because of these
issues.

Nick

PS.  I also was doing elliptic curve calculations over the fraction
field of a polynomial ring in SAGE...

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