#8675: Remove AmbientSpace._constructor and fix consequences
----------------------------------+-----------------------------------------
Reporter: novoselt | Owner: AlexGhitza
Type: defect | Status: new
Priority: major | Milestone: sage-4.4
Component: algebraic geometry | Keywords:
Author: Andrey Novoseltsev | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Currently in schemes/generic/ambient_space we see
{{{
...
# Derived classes must overload all of the following functions
...
def _constructor(self):
"""
TEST::
sage: from sage.schemes.generic.ambient_space import AmbientSpace
sage: A = AmbientSpace(5, ZZ)
sage: A._constructor()
Traceback (most recent call last):
...
NotImplementedError
"""
raise NotImplementedError
...
# End overloads
...
def base_extend(self, S, check=True):
"""
...
"""
if is_CommutativeRing(S):
R = self.base_ring()
if S == R:
return self
if check:
if not S.has_coerce_map_from(R):
raise ValueError, "No natural map from the base ring (=%s)
to S (=%s)"%(R, S)
return self._constructor(self.__n, S, self.variable_names())
else:
raise NotImplementedError
...
}}}
I have the following problems with it:
* _constructor function has no documentation and a very strange name
(because !__init!__ IS a constructor, why do we need another one?)
* Its usage in the same class calls it with arguments different from
specified.
* With these arguments _constructor still would not quite make sense for
toric varieties, where dimension and base ring are not sufficient for
creation (and if we do take extra information from self, why do we need to
pass dimension explicitly?)
* Digging further, I have found the following as a consequence of using
_constructor:
{{{
sage: A = AffineSpace(2)
sage: (A^2).variable_names()
('x0', 'x1', 'x0', 'x1')
}}}
I propose the following solution, making !AmbientSpace behave closer to
!FreeModule's like ZZ^n:
* Remove _constructor
* Make base_extend check if extension is possible and call change_ring
* Make change_ring mandatory for overriding - it should create "exactly
the same" ambient space but with a new ring, even if it is not a base
extension.
* Powers of affine ambient spaces use default indexed variables rather
than trying to cook up something from variables of the base:
{{{
sage: A = AffineSpace(2)
sage: (A^2).variable_names()
('x0', 'x1', 'x2', 'x3')
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8675>
Sage <http://www.sagemath.org>
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