Add positive root function of two algebraic numbers

[bobot]

I mainly wanted to understand how the library was built, so the approach is surely very naive. But I though it was sad that the algebraic numbers only provide operations that the rational provides. So this MR adds an implementation of the positive root of a positive algebraic number.

[disteph]

Looks good to me. Will see if @dddejan has comments.

[nafur]

I'd suggest some improvements, mostly about comments/documentation.
I'm aware that my request go beyond the current average of libpoly, but libpoly should really improve in this respect... :-)

[dddejan]

Can you please add some tests.

The standard way is to add tests in Python. There is some work to add the new functionality to the Python API but this also helps make sure that the new API is useful.

You can follow what's already done in https://github.com/SRI-CSL/libpoly/tree/master/python to add the API. Then you can add the tests in https://github.com/SRI-CSL/libpoly/tree/master/test/python/tests.

[bobot]

Thank you for the review, improving documentation is always important. Three tests are added (other tests in the file algebraic_number.py are failing).

[dddejan]

Looks good, thanks!

[bobot]

What remains to be done for the PR to be merged ?

Playing with the new function I have seen that the degree of the polynomials can quickly grow even if we stay in the same simple extension (sorry I'm using words that I don't really understand), which should mean that any applications of field operations that use a uniq algebraic number of degree 2 and rationals should be representable with degree 2 .

For example : is represented with even if it is representable with as computed by .

Is it a known limitation?

[bobot]

One can play with which are computed by libpoly using a polynomial of degree even if their minimal polynome is of degree 2 (as any )