#8723: Change to return type of E.multiplcation_by_m(m,True)
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Reporter: cremona | Owner: cremona
Type: defect | Status: new
Priority: minor | Milestone: sage-4.4
Component: elliptic curves | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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As reported to sage-nt:
If E is an elliptic curve over K and m is a nonzero integer, then
E.multiplication_by_m(m) returns a tuple (X,Y) where X and Y are both in
K(x,y) and give the "formula" for the multiplcation-by-m map on E. Of
course, mathematically, X is in K(x), but it is returned with the same
parent as Y, namely K(x,y) (i.e. the fraction field of the 2-variable
polynomial ring over K).
There is an optional parameter x_only which by default is False, but if
True the return value is just X as above, an element of K(x,y) which
happens not to involve y.
I propose to change the function so that there is no change when x_only is
False (the default), but when it is True the rational function returned
would be in K(x) and not in K(x,y); in this case one would not need to
construct any bivariate polynomial rings or fields at all.
Would anyone be unhappy about this? The only issue which I can see is
that if you construct phi to be the multiplcation-by-m isogeny, then
phi.rational_maps() is currently of the form (X,Y) as above, so now one
can check that
phi.rational_maps()[0] == E.multiplication_by_m(m,True)
while after my proposed change this would be False (I think, unless
coercion would magically embed K(x) into K(x,y), which I have not
checked).
Implementation and checking would be very easy.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8723>
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