Ticket #3662: trac_3662-3.patch

a/sage/combinat/free_module.py

@@ -227 +227 @@
-
-        EXAMPLES:
-            sage: p = Partition([2,1])
+            sage: q = Partition([1,1,1])
-            sage: s = SFASchur(QQ)
-[2,1]
+p
-            sage: a._coefficient_fast([2,1])
-            Traceback (most recent call last):
-            ...
@@ -237 +238 @@
-            1
-            sage: a._coefficient_fast(p, 2)
-            1
+            sage: a._coefficient_fast(q)
+            0
+            sage: a._coefficient_fast(q, 2)
+            2
+            sage: a[p]
+            1
+            sage: a[q]
+            0
-        """
-        if default is None:
-            default = self.base_ring()(0)
-        return self._monomial_coefficients.get(m, default)
+
+    __getitem__ = _coefficient_fast
-
-    def coefficient(self, m):
-        """
@@ -470 +481 @@
-        x = self.base_ring()(x)
-        return self.map_coefficients(lambda c: c*x)
-
+    def __div__(self, x):
+        """
+        Division by coefficients
+
+        EXAMPLES:
+            sage: F = CombinatorialFreeModule (QQ, [1,2,3])
+            sage: x = F._from_dict({1:2, 2:3})
+            sage: x/2
+            B(1) + 3/2*B(2)
+        """
+        # FIXME: make this robust, especially over rings!
+        x = self.base_ring()(x)
+        return self.map_coefficients(lambda c: c/x)
-
-# NT: There is nothing combinatorial here
-# NT: It's really too bad that we can't have the ring as second optional argument
@@ -521 +545 @@
-            2*[1, 2, 3]
-            sage: QS3([2,3,1])
-            [2, 3, 1]
+            sage: F = CombinatorialFreeModule(QQ,[0,1])
+            sage: F(0)
+            0
-        """
-        R = self.base_ring()
-        eclass = self._element_class
@@ -529 +556 @@
-        if isinstance(x, int):
-            x = Integer(x)
-
+        # Workaround when the indexing set contains 0
+        if isinstance(x, Integer) and x == 0:
+            return self.zero()
-
-        if hasattr(self, '_coerce_start'):
-            try:
@@ -750 +780 @@
-            B('a')
-        """
-        return self._from_dict({i:self.base_ring().one_element()})
+
+    def zero(self):
+        # TODO: cache
+        """
+        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a', 'b', 'c'])
+            sage: F.zero()
+            0
+        """
+        return self._from_dict({})
-    
+    def sum(self, operands):
+        """
+        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, [1,2,3,4])
+            sage: F.sum(F.term(i) for i in [1,2,3])
+            B(1) + B(2) + B(3)
+        """
+        return sum(operands, self.zero())
+
-    def _from_dict(self, d, coerce=False):
-        """
-        Given a monomial coefficient dictionary d, return the element
@@ -785 +834 @@
-        We construct a free module whose basis is indexed by the letters a,b,c:
-
-            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
-
+  # todo: not implemented: F.basis().keys() should be ['a','b','c']
-            Free module generated by ['a', 'b', 'c'] over Rational Field
-
-        Its basis is a family, indexed by a,b,c:
-FIXME in family: we should preserve the order of the indices
+Caveat in family: the order of the indices is not preserved
-            sage: e = F.basis()
-
-
+  # todo: not implemented
-            ['a', 'b', 'c']
-
+   # todo: not implemented
-            [B('a'), B('b'), B('c')]
-
-        Let us construct some elements, and compute with them:
@@ -807 +856 @@
-    """
-
-
-
+element_class = CombinatorialFreeModuleElement, 
-        if isinstance(cc, list):
-            cc = FiniteCombinatorialClass(cc)
-        if not isinstance(cc, CombinatorialClass):
@@ -815 +864 @@
-        self._combinatorial_class = cc
-        self._prefix = prefix
-        self._name = "Free module generated by %s"%cc
-CombinatorialFreeModuleElement
+element_class
-    pass

a/sage/combinat/sf/sfa.py

@@ -354 +354 @@
-        f = lambda m,c: (m, c*prod([expr_k(k) for k in m]))
-        return self(p_x.map_mc(f))
-
-
+
+
+
+
+
+
-    def _apply_multi_module_morphism(self, x, y, f, orthogonal=False):
-        """
-        INPUT:
@@ -380 +385 @@
-            sage: s._apply_multi_module_morphism(a,b,f2,orthogonal=True)  #2+2
-            4
-        """
+        # broken for most coeff ring
-        res = 0
-        if orthogonal:
+            # could check which of x and y has less terms
+            # for mx, cx in x:
-            for mx, cx in x._monomial_coefficients.iteritems():
+                # if not y.has_key(mx):
-                if mx not in y._monomial_coefficients:
-                    continue
-                else:
+                    # cy = y[mx]
-                    cy = y._monomial_coefficients[mx]
+                # might as well call f(mx)
-                res += cx*cy*f(mx, mx)
-            return res
-        else: