The documentation for the nth_root method for finite fields (repeated
in each of the files sage/structure/element.pyx, sage/rings/
finite_field_element.py, and sage/rings/finite_field_givaro.pyx) says
this:
INPUT:
n -- integer >= 1 (must fit in C int type)
extend -- bool (default: True); if True, return a square
root in an extension ring, if necessary. Otherwise,
raise a ValueError if the square is not in the base
ring.
all -- bool (default: False); if True, return all square
roots of self, instead of just one.
OUTPUT:
If self has an nth root, returns one (if all == False) or a
list of
all of them (if all == True). Otherwise, raises a
ValueError (if
extend = False) or a NotImplementedError (if extend =
True).
The entirety of the code dealing with 'extend' is this:
if extend:
raise NotImplementedError
Should the 'extend' option be removed altogether, or should it be left
in with a big warning saying that it's not implemented? (Or is
someone out there willing to implement it?)
(The same goes for the square_root method in finite_field_element.py.
The code for the sqrt method in finite_field_givaro.pyx is similar,
but the extend option, while present, isn't documented.)
I can open up a ticket for this, but it would be nice to have a
suggestion about which direction to go in the short term -- remove the
option or document the fact that it's not implemented -- to go on the
ticket.
John
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