base_extend() not implemented in MPolynomialRing

[vbraun]

The base class Ring defines base_extend(), but the implementation needs to be overridden in the derived class MPolynomialRing:

sage: sage: P.<x,y,z> = PolynomialRing(QQ,'x, y, z'); P
Multivariate Polynomial Ring in x, y, z over Rational Field
sage: P.base_extend(CC)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/home/vbraun/opt/sage-4.5.3/devel/sage-main/<ipython console> in <module>()

/home/vbraun/Sage/sage/local/lib/python2.6/site-packages/sage/rings/ring.so in sage.rings.ring.Ring.base_extend (sage/rings/ring.c:3190)()

TypeError: no base extension defined

The patch implements the override and adds documentation.

[vbraun]

Initial patch

[vbraun]

Andrey, I wrote this patch a while a go to be able to extend the base field of the toric coordinate ring. It might be useful...

[novoselt]

I am not quite sure it is the right approach. It seems to me that we have two methods: change_ring that constructs "the same object but over different ring" and base_extend which does the same, but only if there is a natural coercion. Given this description, it seems to me that there should be only one implementation of base_extend in the base class:

def base_extend(self, R):
    if R.has_coerce_map(self.base_ring()):
        return self.change_ring(R)
    else:
        raise TypeError("%s cannot be extened to %s!" % (self.base_ring(), R))

and then each derived class should implement change_ring only. (If the detailed error message breaks a lot of doctests I am fine with keeping the current one.) Thoughts?

There is also discrepancy between actual argument names and their description in documentation (base_ring vs. R).