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Merge branch 'u/dkrenn/coercion/pushout' of trac.sagemath.org:sage in…
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* 'u/dkrenn/coercion/pushout' of trac.sagemath.org:sage:
  Trac #18182, comment 20, 7: rename CartesianProductPolys --> CartesianProductPoly
  Trac #18182, comment 20, 2: rewrite OUTPUT-block
  add two doctests
  CartesianProductPolys: check whether other has a construction
  remove superfluous import in doctest, superfluous empty line in docstring, and fix spacing in a line (pep 8)
  fix ReSt-error
  improve language
  fix typos
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@dkrenn
dkrenn committed Oct 8, 2015
2 parents b306679 + bc70cb9 commit 592a551
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10 changes: 5 additions & 5 deletions src/sage/categories/modules.py
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Original file line number Diff line number Diff line change
Expand Up @@ -582,11 +582,11 @@ class CartesianProducts(CartesianProductsCategory):
"""
The category of modules constructed as cartesian products of modules
This construction gives the direct product of modules. See
discussion on:
This construction gives the direct product of modules. The
implementation is based on the following resources:
- http://groups.google.fr/group/sage-devel/browse_thread/thread/35a72b1d0a2fc77a/348f42ae77a66d16#348f42ae77a66d16
- http://en.wikipedia.org/wiki/Direct_product
- http://groups.google.fr/group/sage-devel/browse_thread/thread/35a72b1d0a2fc77a/348f42ae77a66d16#348f42ae77a66d16
- http://en.wikipedia.org/wiki/Direct_product
"""
def extra_super_categories(self):
"""
Expand All @@ -606,7 +606,7 @@ def extra_super_categories(self):
class ParentMethods:
def base_ring(self):
"""
Return the base ring this cartesian product.
Return the base ring of this cartesian product.
EXAMPLES::
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67 changes: 41 additions & 26 deletions src/sage/categories/pushout.py
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Original file line number Diff line number Diff line change
Expand Up @@ -300,7 +300,9 @@ def common_base(self, other_functor, self_bases, other_bases):
OUTPUT:
Raise a :class:`~sage.structure.coerce_exceptions.CoercionException`.
Nothing, since a
:class:`~sage.structure.coerce_exceptions.CoercionException`
is raised.
.. NOTE::
Expand Down Expand Up @@ -643,7 +645,6 @@ class MultivariateConstructionFunctor(ConstructionFunctor):
TESTS::
sage: from sage.categories.pushout import pushout
sage: from sage.sets.cartesian_product import CartesianProduct
sage: A = cartesian_product((QQ['z'], QQ))
sage: B = cartesian_product((ZZ['t']['z'], QQ))
sage: pushout(A, B)
Expand Down Expand Up @@ -680,7 +681,7 @@ def common_base(self, other_functor, self_bases, other_bases):
.. NOTE::
Overload this function in derived class, see
e.e. :class:`MultivariateConstructionFunctor`.
e.g. :class:`MultivariateConstructionFunctor`.
TESTS::
Expand All @@ -690,7 +691,7 @@ def common_base(self, other_functor, self_bases, other_bases):
...
CoercionException: No common base ("join") found for
The cartesian_product functorial construction(Integer Ring) and FractionField(Integer Ring):
(Multivariate) functors are inkompatibel.
(Multivariate) functors are incompatible.
sage: pushout(cartesian_product([ZZ]), cartesian_product([ZZ, QQ])) # indirect doctest
Traceback (most recent call last):
...
Expand All @@ -702,7 +703,7 @@ def common_base(self, other_functor, self_bases, other_bases):
if self != other_functor:
self._raise_common_base_exception_(
other_functor, self_bases, other_bases,
'(Multivariate) functors are inkompatibel')
'(Multivariate) functors are incompatible')
if len(self_bases) != len(other_bases):
self._raise_common_base_exception_(
other_functor, self_bases, other_bases,
Expand Down Expand Up @@ -3387,10 +3388,10 @@ def pushout(R, S):
Ambient free module of rank 2 over the principal ideal domain Univariate Polynomial Ring in x over Real Field with 53 bits of precision
Some more tests related to univariate/multivariate
constructions. We construct a parent for a generalization to
polynomials, where we not only specify a coefficient ring `C` but
also an additive monoid `E` for its exponents. Its elements are
then
constructions. We consider a generalization of polynomial rings,
where in addition to the coefficient ring `C` we also specify
an additive monoid `E` for the exponents of the indeterminate.
In particular, the elements of such a parent are given by
.. MATH::
Expand Down Expand Up @@ -3514,51 +3515,56 @@ def pushout(R, S):
(Univariate Polynomial Ring in x over Integer Ring,
Univariate Polynomial Ring in y over Rational Field,
Univariate Polynomial Ring in z over Univariate Polynomial Ring in t over Rational Field)
sage: pushout(ZZ, cartesian_product([ZZ, QQ]))
Traceback (most recent call last):
...
CoercionException: 'NoneType' object is not iterable
::
sage: from sage.categories.pushout import PolynomialFunctor
sage: from sage.sets.cartesian_product import CartesianProduct
sage: class CartesianProductPolys(CartesianProduct):
sage: class CartesianProductPoly(CartesianProduct):
....: def __init__(self, polynomial_rings):
....: sort = sorted(polynomial_rings, key=lambda P: P.variable_name())
....: super(CartesianProductPolys, self).__init__(sort, Sets().CartesianProducts())
....: super(CartesianProductPoly, self).__init__(sort, Sets().CartesianProducts())
....: def vars(self):
....: return tuple(P.variable_name() for P in self.cartesian_factors())
....: def _pushout_(self, other):
....: if isinstance(other, CartesianProductPolys):
....: if isinstance(other, CartesianProductPoly):
....: s_vars = self.vars()
....: o_vars = other.vars()
....: if s_vars == o_vars:
....: return
....: return pushout(CartesianProductPolys(
....: return pushout(CartesianProductPoly(
....: self.cartesian_factors() +
....: tuple(f for f in other.cartesian_factors()
....: if f.variable_name() not in s_vars)),
....: CartesianProductPolys(
....: CartesianProductPoly(
....: other.cartesian_factors() +
....: tuple(f for f in self.cartesian_factors()
....: if f.variable_name() not in o_vars)))
....: C = other.construction()[0]
....: if isinstance(C, PolynomialFunctor):
....: return pushout(self, CartesianProductPolys((other,)))
....: C = other.construction()
....: if C is None:
....: return
....: elif isinstance(C[0], PolynomialFunctor):
....: return pushout(self, CartesianProductPoly((other,)))
::
sage: pushout(CartesianProductPolys((ZZ['x'],)),
....: CartesianProductPolys((ZZ['y'],)))
sage: pushout(CartesianProductPoly((ZZ['x'],)),
....: CartesianProductPoly((ZZ['y'],)))
The cartesian product of
(Univariate Polynomial Ring in x over Integer Ring,
Univariate Polynomial Ring in y over Integer Ring)
sage: pushout(CartesianProductPolys((ZZ['x'], ZZ['y'])),
....: CartesianProductPolys((ZZ['x'], ZZ['z'])))
sage: pushout(CartesianProductPoly((ZZ['x'], ZZ['y'])),
....: CartesianProductPoly((ZZ['x'], ZZ['z'])))
The cartesian product of
(Univariate Polynomial Ring in x over Integer Ring,
Univariate Polynomial Ring in y over Integer Ring,
Univariate Polynomial Ring in z over Integer Ring)
sage: pushout(CartesianProductPolys((QQ['a,b']['x'], QQ['y'])),
....: CartesianProductPolys((ZZ['b,c']['x'], SR['z'])))
sage: pushout(CartesianProductPoly((QQ['a,b']['x'], QQ['y'])),
....: CartesianProductPoly((ZZ['b,c']['x'], SR['z'])))
The cartesian product of
(Univariate Polynomial Ring in x over
Multivariate Polynomial Ring in a, b, c over Rational Field,
Expand All @@ -3567,17 +3573,26 @@ def pushout(R, S):
::
sage: pushout(CartesianProductPolys((ZZ['x'],)), ZZ['y'])
sage: pushout(CartesianProductPoly((ZZ['x'],)), ZZ['y'])
The cartesian product of
(Univariate Polynomial Ring in x over Integer Ring,
Univariate Polynomial Ring in y over Integer Ring)
sage: pushout(QQ['b,c']['y'], CartesianProductPolys((ZZ['a,b']['x'],)))
sage: pushout(QQ['b,c']['y'], CartesianProductPoly((ZZ['a,b']['x'],)))
The cartesian product of
(Univariate Polynomial Ring in x over
Multivariate Polynomial Ring in a, b over Integer Ring,
Univariate Polynomial Ring in y over
Multivariate Polynomial Ring in b, c over Rational Field)
::
sage: pushout(CartesianProductPoly((ZZ['x'],)), ZZ)
Traceback (most recent call last):
...
CoercionException: No common base ("join") found for
The cartesian_product functorial construction(...) and None(Integer Ring):
(Multivariate) functors are incompatible.
AUTHORS:
- Robert Bradshaw
Expand Down
4 changes: 2 additions & 2 deletions src/sage/sets/cartesian_product.py
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Original file line number Diff line number Diff line change
Expand Up @@ -236,7 +236,7 @@ def construction(self):
OUTPUT:
A pair whose first entry is a cartesian product functor and
its second a list of the cartesian factors.
its second entry is a list of the cartesian factors.
EXAMPLES::
Expand Down Expand Up @@ -264,7 +264,7 @@ def _coerce_map_from_(self, S):
S_factors = S.cartesian_factors()
R_factors = self.cartesian_factors()
if len(S_factors) == len(R_factors):
if all(r.has_coerce_map_from(s) for r,s in zip(R_factors, S_factors)):
if all(r.has_coerce_map_from(s) for r, s in zip(R_factors, S_factors)):
return True

an_element = Sets.CartesianProducts.ParentMethods.an_element
Expand Down

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