Hi,
In order to treat tensor fields on a parallelizable domain N of some smooth
manifold as elements of a free module (cf.
#15916<http://trac.sagemath.org/ticket/15916>and this
post <https://groups.google.com/forum/#!topic/sage-devel/1QzUpHLUw_E>), one
has first to introduce the commutative ring C^oo(N) of smooth functions N
--> *R*, as a new class, ScalarFieldRing say. Browsing through Sage
reference manual, a natural guess would be to make it a subclass of
CommutativeRing:
from sage.rings.ring import CommutativeRing
class ScalarFieldRing(CommutativeRing):
def __init__(self, domain):
CommutativeRing.__init__(self, base_ring)
self.domain = domain
The issue here is that CommutativeRing.__init__ requires the argument
"base_ring" and in the present context, I don't know what to put here: the
ring C^oo(N) does not depend upon any other ring. Shall I put self, i.e.
write CommutativeRing.__init__(self, self) ?
A second solution could be to declare ScalarFieldRing as a subclass of
Ring, in the category of commutative rings:
from sage.rings.ring import Ring
from sage.categories.commutative_rings import CommutativeRings
class ScalarFieldRing(Ring):
def __init__(self, domain):
Ring.__init__(self, None, category=CommutativeRings())
self.domain = domain
Here the argument "base" of Ring.__init__ is set to None, which was not
possible for the argument "base_ring" of CommutativeRing.__init__ : this
triggered the error message "TypeError: base ring None is no commutative
ring".
A third solution is to declare ScalarFieldRing directly as a subclass of
Parent, in the category of commutative rings:
from sage.structure.parent import Parent
from sage.categories.commutative_rings import CommutativeRings
class ScalarFieldRing(Parent):
def __init__(self, domain):
Parent.__init__(self, category=CommutativeRings())
self.domain = domain
Which solution is preferable (and why) ? (the three of them seem to work,
at least in the few tests I've performed). Thank you for your help.
Eric.
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