#6413: Retrieving the multiplication-by-p isogeny on elliptic curves over fields
of characteristic p fails.
--------------------------------+-------------------------------------------
Reporter: hlaw | Owner: tba
Type: defect | Status: new
Priority: major | Milestone: sage-4.1
Component: algebraic geometry | Keywords:
Reviewer: | Author:
Merged: |
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{{{
sage: p = 11
sage: E = EllipticCurve(GF(p), [1,1])
sage: E.multiplication_by_m(p)
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call
last)
/Users/hlaw/.sage/temp/resid_tg082.upc.es/80890/_Users_hlaw__sage_init_sage_0.py
in <module>()
/Users/hlaw/src/sage-4.0.1/local/lib/python2.5/site-
packages/sage/schemes/elliptic_curves/ell_generic.pyc in
multiplication_by_m(self, m, x_only)
2133 # and hence 2*my+a1*mx+a3 = (1/m)*(2*y+a1*x+a3)*d(mx)/dx
2134
-> 2135 my = ((2*y+a1*x+a3)*mx.derivative(x)/m - a1*mx-a3)/2
2136
2137 return mx, my
/Users/hlaw/src/sage-4.0.1/local/lib/python2.5/site-
packages/sage/structure/element.so in
sage.structure.element.RingElement.__div__
(sage/structure/element.c:10361)()
/Users/hlaw/src/sage-4.0.1/local/lib/python2.5/site-
packages/sage/structure/coerce.so in
sage.structure.coerce.CoercionModel_cache_maps.bin_op
(sage/structure/coerce.c:6105)()
/Users/hlaw/src/sage-4.0.1/local/lib/python2.5/site-
packages/sage/structure/element.so in
sage.structure.element.RingElement.__div__
(sage/structure/element.c:10342)()
/Users/hlaw/src/sage-4.0.1/local/lib/python2.5/site-
packages/sage/rings/fraction_field_element.so in
sage.rings.fraction_field_element.FractionFieldElement._div_
(sage/rings/fraction_field_element.c:5805)()
/Users/hlaw/src/sage-4.0.1/local/lib/python2.5/site-
packages/sage/rings/fraction_field_element.so in
sage.rings.fraction_field_element.FractionFieldElement.__init__
(sage/rings/fraction_field_element.c:1954)()
ZeroDivisionError: fraction field element division by zero
}}}
One can see from the line that causes the error that the calculation of
the ''y''-component of the isogeny involves a division by ''m'', which in
this case is the characteristic of the ground field.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6413>
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