#16764 is ready for review. I follwed suggestions, so that E.has_cm() means the same over number fields as always over QQ, namely that the j-invariant is a CM j-invariant, not necessarily that the extra endomorhisms are defined over the base field. E.has_rational_cm() means that this is True *and* that E.cm_discriminant() is a square in the base field so that the extra endos are defined over it. And the E.cm_discriminant() function does what it says when E.has_cm(), raises a ValueError if not E.has_cm() (which is what used to happen over QQ).
The only changes over QQ are: a new has_rational_cm() function which always returns False (but with some instructive examples), and the type of E.cm_discriminant() is now a proper Integer (was an int). On 1 August 2014 15:32, Justin C. Walker <[email protected]> wrote: > > On Jul 31, 2014, at 7:37, William Stein <[email protected]> wrote: > >> On Wed, Jul 30, 2014 at 7:51 AM, John Cremona <[email protected]> wrote: >>> I am implementing a method for elliptic curves over number fields to >>> detect CM. I want to distingish between E.has_cm() and >>> E.has_potential_cm(). The latter only depends on the j-invariant, and >>> will return either (False, None) or (True, (d,f)) if j(E) is the >>> j-invariant of the order with discriminant d*f^2 (of index f in the >>> maximal order with discriminant d). The former, E.has_cm(), will only >>> retrun True (with (d,f) as above if in addition d is a square in >>> E.base_field() so that the additional endomorphisms are defined over >>> the base field. >>> >>> With this convention, elliptic curves over Q never have CM, they can >>> only have potential CM (iff the j-invariant is one of the 13 famous >>> values). >>> >>> BUT the class EllipticCurve_rational_field already has a method >>> has_cm() which returns the same as what I want to call >>> has_potential_cm() (but without the discriminant), so this is >>> inconsistent with what I want to do over other number fields. >> >> If a mathematician says "let E/Q be an elliptic curve with CM" that >> *means* something. >> Sage shouldn't be inconsistent with that... Also, I've never >> seen the phrase "potential CM" in any paper (though maybe you have). > > For the record, I've seen it in the wild, e.g., the recent "CM lifting" book > by Chai-Conrad-Oort, and here: > <http://arxiv.org/pdf/hep-th/0312319.pdf> > > Justin > > -- > Justin C. Walker > Curmudgeon-at-large > Director > Institute for the Absorption of Federal Funds > ---- > 186,000 Miles per Second > Not just a good idea: it's the law! > ---- > > -- > You received this message because you are subscribed to the Google Groups > "sage-nt" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send an email to [email protected]. > Visit this group at http://groups.google.com/group/sage-nt. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-nt" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send an email to [email protected]. Visit this group at http://groups.google.com/group/sage-nt. For more options, visit https://groups.google.com/d/optout.
