I have added a new ticket for adding a default gcd and lcm for field
elements.

http://trac.sagemath.org/sage_trac/ticket/9819

For the case of field elements gcd and lcm methods are not of great
interest. However, they can be addecuated for some reasons.

- Some algorithms may accept as input either polynomials or rational
functions. In these algorithms we may reduce a list of polynomials and
rational functions to a common denominator. If all the inputs are
polynomials, the denominators are the one element of the base field.
In this case, lcm would fail.

See the problem raised in #9063 for a case of this problem.

I propose to add a lcm and gcd funtion for field elements.

By default, if both elements are zero, their gcd is 0. Otherwise 1

if one of the elements is zero, their lcm is zero. 1 Otherwise.

However, I can imaging that this approach may lead to further
problems. Does anyone have a case where this approcah can lead to
problems?


Luis

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