Changeset 8419:6054b29ac8d6

Timestamp:

11/11/07 13:49:40 (6 years ago)

Author:

David Roe <roed@…>

Branch:

default

Message:

Added sections of morphisms.

Location:

sage/categories

Files:

• category_types.py (modified) (2 diffs)
• morphism.pxd (modified) (1 diff)
• morphism.pyx (modified) (1 diff)

sage/categories/category_types.py

@@ -283 +283 @@
         return Sets, tuple([])
 
+#############################################################
+# Pointed Sets
+#############################################################
+
+class PointedSets(Category_uniq):
+    """
+    The category of pointed sets.
+
+    EXAMPLES:
+        sage: PointedSets()
+        Category of pointed sets
+    """
+    def __call__(self, X, pt):
+        import sage.sets.all
+        return sage.sets.all.Set(X, pt)
+
+    def __reduce__(self):
+        return PointedSets, tuple([])
+
+#############################################################
+# Sets with Partial Maps
+#############################################################
+
+class SetsWithPartialMaps(Category_uniq):
+    """
+    The category whose objects are sets and whose morphisms are
+    maps that are allowed to raise a ValueError on some inputs.
+
+    This category is equivalent to the category of pointed sets,
+    via the equivalence sending an object X to X union {error},
+    a morphism f to the morphism of pointed sets that sends x
+    to f(x) if f does not raise an error on x, or to error if it
+    does.
+
+    EXAMPLES:
+        sage: SetsWithPartialMaps()
+        Category of Sets with 
+    """
+    def __call__(self, X, pt):
+        import sage.sets.all
+        return sage.sets.all.Set(X, pt)
+
+    def __reduce__(self):
+        return SetsWithPartialMaps, tuple([])
+
+    def __repr__(self):
+        return "Category with objects Sets and morphisms partially defined maps"
 
 #############################################################
@@ -295 +342 @@
         sage: S = SymmetricGroup(3)
         sage: GSets(S)
-        Category of G-sets for SymmetricGroup(3)
+        Category of G-sets for Symmetric group of order 3! as a permutation group
     """
     def __init__(self, G):

sage/categories/morphism.pxd

@@ -16 +16 @@
     cdef Element _call_c_impl(self, Element x) 
 
+cdef class Section(Morphism):
+    cdef Morphism _morphism
+
 cdef class FormalCoercionMorphism(Morphism):
     cdef Element _call_c(self, x)

sage/categories/morphism.pyx

@@ -164 +164 @@
         return generic_power(self, n)
 
+cdef class Section(Morphism):
+    def __init__(self, morphism):
+        from sage.categories.homset import Hom
+        from sage.categories.category_types import SetsWithPartialMaps
+        Morphism.__init__(self, Hom(morphism.codomain(), morphism.domain(), SetsWithPartialMaps()))
+        self._morphism = morphism
+
+    def _repr_type(self):
+        return "Section"
+
 cdef class FormalCoercionMorphism(Morphism):
     def __init__(self, parent):