Merge branch 'u/dkrenn/asy/growthGroup-exponential' of trac.sagemath.…

…org:sage into t/19073/asy/groups-coercion

* 'u/dkrenn/asy/growthGroup-exponential' of trac.sagemath.org:sage:
  fixup due to changes in #18587 (coming from #18223)
  fix code after changes by previous merge
  add a doctest dealing with coercion while comparing
  code-simplify CartesianProduct assignment
  rename CartesianProductPosets to CartesianProductPoset

src/sage/categories/posets.py

@@ -683,9 +683,8 @@ def is_antichain_of_poset(self, o):
             """
             return all(not self.lt(x,y) for x in o for y in o)
 
-        CartesianProductPosets = LazyImport(
-            'sage.combinat.posets.cartesian_product', 'CartesianProductPosets')
-        CartesianProduct = CartesianProductPosets
+        CartesianProduct = LazyImport(
+            'sage.combinat.posets.cartesian_product', 'CartesianProductPoset')
 
     class ElementMethods:
         pass

src/sage/combinat/posets/cartesian_product.py

@@ -18,7 +18,7 @@
 from sage.sets.cartesian_product import CartesianProduct
 
 
-class CartesianProductPosets(CartesianProduct):
+class CartesianProductPoset(CartesianProduct):
     r"""
     A class implementing cartesian products of posets (and elements
     thereof). Compared to :class:`CartesianProduct` you are able to
@@ -83,7 +83,7 @@ class CartesianProductPosets(CartesianProduct):
 
     def __init__(self, sets, category, order=None, **kwargs):
         r"""
-        See :class:`CartesianProductPosets` for details.
+        See :class:`CartesianProductPoset` for details.
 
         TESTS::
 
@@ -111,7 +111,7 @@ def __init__(self, sets, category, order=None, **kwargs):
         if not isinstance(category, tuple):
             category = (category,)
         category = Category.join(category + (Posets(),))
-        super(CartesianProductPosets, self).__init__(
+        super(CartesianProductPoset, self).__init__(
             sets, category, **kwargs)
 
 
@@ -132,7 +132,7 @@ def le(self, left, right):
         .. NOTE::
 
             This method uses the order defined on creation of this
-            cartesian product. See :class:`CartesianProductPosets`.
+            cartesian product. See :class:`CartesianProductPoset`.
 
         EXAMPLES::
 
@@ -315,15 +315,15 @@ def _le_(self, other):
 
             .. NOTE::
 
-                This method calls :meth:`CartesianProductPosets.le`. Override
+                This method calls :meth:`CartesianProductPoset.le`. Override
                 it in inherited class to change this.
 
                 It can be assumed that this element and ``other`` have
                 the same parent.
 
             TESTS::
 
-                sage: QQ.CartesianProduct = sage.combinat.posets.cartesian_product.CartesianProductPosets  # needed until #19269 is fixed
+                sage: QQ.CartesianProduct = sage.combinat.posets.cartesian_product.CartesianProductPoset  # needed until #19269 is fixed
                 sage: def le_sum(left, right):
                 ....:     return (sum(left) < sum(right) or
                 ....:             sum(left) == sum(right) and left[0] <= right[0])
@@ -358,7 +358,8 @@ def __le__(self, other):
 
             TESTS::
 
-                sage: QQ.CartesianProduct = sage.combinat.posets.cartesian_product.CartesianProductPosets  # needed until #19269 is fixed
+                sage: from sage.combinat.posets.cartesian_product import CartesianProductPoset
+                sage: QQ.CartesianProduct = CartesianProductPoset  # needed until #19269 is fixed
                 sage: def le_sum(left, right):
                 ....:     return (sum(left) < sum(right) or
                 ....:             sum(left) == sum(right) and left[0] <= right[0])
@@ -367,6 +368,25 @@ def __le__(self, other):
                 True
                 sage: C((1/3, 2)) <= C((2, 2))
                 True
+
+            The following example tests that the coercion gets involved in
+            comparisons; it can be simplified once #18182 is in merged.
+            ::
+
+                sage: class MyCP(CartesianProductPoset):
+                ....:     def _coerce_map_from_(self, S):
+                ....:         if isinstance(S, self.__class__):
+                ....:             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)):
+                ....:                     return True
+                sage: QQ.CartesianProduct = MyCP
+                sage: A = cartesian_product((QQ, ZZ), order=le_sum)
+                sage: B = cartesian_product((QQ, QQ), order=le_sum)
+                sage: A((1/2, 4)) <= B((1/2, 5))
+                True
             """
             from sage.structure.element import have_same_parent
             if have_same_parent(self, other):
@@ -402,7 +422,7 @@ def __ge__(self, other):
 
             TESTS::
 
-                sage: QQ.CartesianProduct = sage.combinat.posets.cartesian_product.CartesianProductPosets  # needed until #19269 is fixed
+                sage: QQ.CartesianProduct = sage.combinat.posets.cartesian_product.CartesianProductPoset  # needed until #19269 is fixed
                 sage: def le_sum(left, right):
                 ....:     return (sum(left) < sum(right) or
                 ....:             sum(left) == sum(right) and left[0] <= right[0])
@@ -437,7 +457,7 @@ def __lt__(self, other):
 
             TESTS::
 
-                sage: QQ.CartesianProduct = sage.combinat.posets.cartesian_product.CartesianProductPosets  # needed until #19269 is fixed
+                sage: QQ.CartesianProduct = sage.combinat.posets.cartesian_product.CartesianProductPoset  # needed until #19269 is fixed
                 sage: def le_sum(left, right):
                 ....:     return (sum(left) < sum(right) or
                 ....:             sum(left) == sum(right) and left[0] <= right[0])
@@ -472,7 +492,7 @@ def __gt__(self, other):
 
             TESTS::
 
-                sage: QQ.CartesianProduct = sage.combinat.posets.cartesian_product.CartesianProductPosets  # needed until #19269 is fixed
+                sage: QQ.CartesianProduct = sage.combinat.posets.cartesian_product.CartesianProductPoset  # needed until #19269 is fixed
                 sage: def le_sum(left, right):
                 ....:     return (sum(left) < sum(right) or
                 ....:             sum(left) == sum(right) and left[0] <= right[0])

src/sage/rings/asymptotic/growth_group_cartesian.py

@@ -364,9 +364,9 @@ def create_object(self, version, args, **kwds):
 CartesianProductGrowthGroups = CartesianProductFactory('CartesianProductGrowthGroups')
 
 
-from sage.combinat.posets.cartesian_product import CartesianProductPosets
+from sage.combinat.posets.cartesian_product import CartesianProductPoset
 from sage.rings.asymptotic.growth_group import GenericGrowthGroup
-class GenericProduct(CartesianProductPosets, GenericGrowthGroup):
+class GenericProduct(CartesianProductPoset, GenericGrowthGroup):
     r"""
     A cartesian product of growth groups.
 
@@ -394,10 +394,10 @@ class GenericProduct(CartesianProductPosets, GenericGrowthGroup):
     .. SEEALSO::
 
         :class:`~sage.sets.cartesian_product.CartesianProduct`,
-        :class:`~sage.combinat.posets.cartesian_product.CartesianProductPosets`.
+        :class:`~sage.combinat.posets.cartesian_product.CartesianProductPoset`.
     """
 
-    __classcall__ = CartesianProductPosets.__classcall__
+    __classcall__ = CartesianProductPoset.__classcall__
 
 
     def __init__(self, sets, category, **kwds):
@@ -411,7 +411,7 @@ def __init__(self, sets, category, **kwds):
             Growth Group x^ZZ * y^ZZ
         """
         order = kwds.pop('order')
-        CartesianProductPosets.__init__(self, sets, category, order, **kwds)
+        CartesianProductPoset.__init__(self, sets, category, order, **kwds)
 
         vars = sum(iter(factor.variable_names()
                         for factor in self.cartesian_factors()),
@@ -423,7 +423,7 @@ def __init__(self, sets, category, **kwds):
         GenericGrowthGroup.__init__(self, sets[0], Vars, self.category(), **kwds)
 
 
-    __hash__ = CartesianProductPosets.__hash__
+    __hash__ = CartesianProductPoset.__hash__
 
 
     def _element_constructor_(self, data):
@@ -647,7 +647,7 @@ def _coerce_map_from_(self, S):
             sage: B.has_coerce_map_from(A) # indirect doctest
             False
         """
-        if CartesianProductPosets.has_coerce_map_from(self, S):
+        if CartesianProductPoset.has_coerce_map_from(self, S):
             return True
 
         elif isinstance(S, GenericProduct):
@@ -880,7 +880,7 @@ def variable_names(self):
         return tuple(v for v, _ in groupby(vars))
 
 
-    class Element(CartesianProductPosets.Element):
+    class Element(CartesianProductPoset.Element):
 
         def _repr_(self):
             r"""

src/sage/sets/cartesian_product.py

@@ -4,8 +4,6 @@
 AUTHORS:
 
 - Nicolas Thiery (2010-03): initial version
-- Daniel Krenn (2015-06): cartesian products for posets with different orders
-
 """
 #*****************************************************************************
 #       Copyright (C) 2008 Nicolas Thiery <nthiery at users.sf.net>,