Ticket #3662: trac_3662-4.patch

a/sage/combinat/combinatorial_algebra.py

@@ -317 +317 @@
-        """
-        return self._element_class(self, {self._one:self.base_ring()(1)})
-
+    def _coerce_impl(self, x):
+        """
+        EXAMPLES:
+            sage: s = SFASchur(QQ)
+            sage: s._coerce_impl(2)
+            2*s[]
+        """
+        try:
+            R = x.parent()
+            if R.__class__ is self.__class__:
+                #Only perform the coercion if we can go from the base
+                #ring of x to the base ring of self
+                if self.base_ring().has_coerce_map_from( R.base_ring() ):
+                    return self(x)
+        except AttributeError:
+            pass
+        
+        # any ring that coerces to the base ring
+        return self._coerce_try(x, [self.base_ring()])
-            
-    def multiply(self,left,right):
-        """

a/sage/combinat/free_module.py

@@ +1 @@
+"""
+Free modules
+"""
-#*****************************************************************************
-#       Copyright (C) 2007 Mike Hansen <mhansen@gmail.com>, 
-#
@@ -22 +25 @@
-from sage.combinat.finite_class import FiniteCombinatorialClass
-from sage.combinat.combinat import CombinatorialClass
-
-# TODO:
-# Rewrite all tests in a more self contained way
-
-class CombinatorialFreeModuleElement(ModuleElement):
-    def __init__(self, M, x):
-        """
-        Create a combinatorial module element x.  This should never
-        be called directly, but only through the parent combinatorial
-        module's __call__ method.
+
+        TESTS:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: B = F.basis()
+            sage: f = B['a'] + 3*B['c']; f
+            B('a') + 3*B('c')
+            sage: f == loads(dumps(f))
+            True
-
-        """
-        ModuleElement.__init__(self, M)
@@ -39 +47 @@
-    def __iter__(self):
-        """
-        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: B = F.basis()
+            sage: f = B['a'] + 3*B['c']
+            sage: [i for i in sorted(f)]
+            [('a', 1), ('c', 3)]
+
-            sage: s = SFASchur(QQ)
-            sage: a = s([2,1]) + s([3])
-            sage: [i for i in sorted(a)]
@@ -53 +67 @@
-        element is in the support of self.
-        
-        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: B = F.basis()
+            sage: f = B['a'] + 3*B['c']
+            sage: 'a' in f
+            True
+            sage: 'b' in f
+            False
+
-            sage: s = SFASchur(QQ)
-            sage: a = s([2,1]) + s([3])
-            sage: Partition([2,1]) in a
@@ -69 +91 @@
-        coefficients as values.
-
-        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: B = F.basis()
+            sage: f = B['a'] + 3*B['c']
+            sage: d = f.monomial_coefficients()
+            sage: d['a']
+            1
+            sage: d['c']
+            3
+
-            sage: s = SFASchur(QQ)
-            sage: a = s([2,1])+2*s([3,2])
-            sage: d = a.monomial_coefficients()
@@ -104 +135 @@
-    def _latex_(self):
-        """
-        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: B = F.basis()
+            sage: f = B['a'] + 3*B['c']
+            sage: latex(f)
+            B_{a} + 3B_{c}
+
-            sage: QS3 = SymmetricGroupAlgebra(QQ,3)
-            sage: a = 2 + QS3([2,1,3])
-            sage: latex(a) #indirect doctest
@@ -145 +182 @@
-    def _add_(self, y):
-        """
-        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: B = F.basis()
+            sage: B['a'] + 3*B['c']
+            B('a') + 3*B('c')
+
-            sage: s = SFASchur(QQ)
-            sage: s([2,1]) + s([5,4]) # indirect doctest
-            s[2, 1] + s[5, 4]
@@ -181 +223 @@
-    def _neg_(self):
-        """
-        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: B = F.basis()
+            sage: f = B['a'] + 3*B['c']
+            sage: -f
+            -B('a') - 3*B('c')
+
-            sage: s = SFASchur(QQ)
-            sage: -s([2,1]) # indirect doctest
-            -s[2, 1]
@@ -191 +239 @@
-    def _sub_(self, y):
-        """
-        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: B = F.basis()
+            sage: B['a'] - 3*B['c']
+            B('a') - 3*B('c')
+
-            sage: s = SFASchur(QQ)
-            sage: s([2,1]) - s([5,4]) # indirect doctest
-            s[2, 1] - s[5, 4]
@@ -234 +287 @@
-            Traceback (most recent call last):
-            ...
-            TypeError: list objects are unhashable
+
-            sage: a._coefficient_fast(p)
-            1
-            sage: a._coefficient_fast(p, 2)
@@ -255 +309 @@
-
-    def coefficient(self, m):
-        """
-
-        # NT: coefficient_fast should be the default, just with appropriate assertions
-        # that can be turned on or of
-        
-        EXAMPLES:
-            sage: s = SFASchur(QQ)
-            sage: z = s([4]) - 2*s([2,1]) + s([1,1,1]) + s([1])
@@ -267 +317 @@
-            sage: z.coefficient([2,1])
-            -2
-        """
+        # NT: coefficient_fast should be the default, just with appropriate assertions
+        # that can be turned on or off
-        p = self.parent()
-        if isinstance(m, p._combinatorial_class.object_class):
-            return self._monomial_coefficients.get(m, p.base_ring().zero_element())
@@ -281 +333 @@
-        Returns True if and only self == 0.
-
-        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: B = F.basis()
+            sage: f = B['a'] - 3*B['c']
+            sage: f.is_zero()
+            False
+            sage: F(0).is_zero()
+            True
+
-            sage: s = SFASchur(QQ)
-            sage: s([2,1]).is_zero()
-            False
@@ -301 +361 @@
-        nonzero coefficients.
-        
-        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: B = F.basis()
+            sage: f = B['a'] - 3*B['c']
+            sage: len(f)
+            2
+            
-            sage: s = SFASchur(QQ)
-            sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1])
-            sage: len(z)
@@ -314 +380 @@
-        nonzero coefficients.
-        
-        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: B = F.basis()
+            sage: f = B['a'] - 3*B['c']
+            sage: f.length()
+            2
+
-            sage: s = SFASchur(QQ)
-            sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1])
-            sage: z.length()
-            4
-        """
-
-
+
-
-    def support(self):
-        """
-        # NT: ???
-        Returns a pair [mons, cffs] of lists of the monomials
-        of self (mons) and their respective coefficients (cffs).
-        
-        EXAMPLES:
-            sage: s = SFASchur(QQ)
-            sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1])
-            sage: z.support()
-            [[[1], [1, 1, 1], [2, 1], [4]], [1, 1, 1, 1]]
-        """
-        v = self._monomial_coefficients.items()
-        v.sort()
-        mons = [ m for (m, _) in v ]
-        cffs = [ x for (_, x) in v ]
-        return [mons, cffs]
-
-    def monomials(self):
-        """
-        Returns a list of the combinatorial objects indexing
-        the basis elements of self which non-zero coefficients.
-
-        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: B = F.basis()
+            sage: f = B['a'] - 3*B['c']
+            sage: f.support()
+            ['a', 'c']
+
-            sage: s = SFASchur(QQ)
-            sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1])
-monomials
+support
-            [[1], [1, 1, 1], [2, 1], [4]]
-        """
-        v = self._monomial_coefficients.items()
-        v.sort()
-        mons = [ m for (m, _) in v ]
-        return mons
+
+    def monomials(self):
+        """
+        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: B = F.basis()
+            sage: f = B['a'] + 2*B['c']
+            sage: f.monomials()
+            [B('a'), B('c')]
+        """
+        P = self.parent()
+        one = P.base_ring()(1)
+        v = self._monomial_coefficients.items()
+        v.sort()
+        return [P._from_dict({key:one}) for key,value in v]
+
+    def terms(self):
+        """
+        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: B = F.basis()
+            sage: f = B['a'] + 2*B['c']
+            sage: f.terms()
+            [B('a'), 2*B('c')]
+        """
+        P = self.parent()
+        v = self._monomial_coefficients.items()
+        v.sort()
+        return [P._from_dict({key:value}) for key,value in v]
-    
-    def coefficients(self):
-        """
@@ -362 +450 @@
-        basiselements in self.
-
-        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: B = F.basis()
+            sage: f = B['a'] - 3*B['c']
+            sage: f.coefficients()
+            [1, -3]
+
-            sage: s = SFASchur(QQ)
-            sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1])
-            sage: z.coefficients()
@@ -378 +472 @@
-        then in returns a vector over new_BR.
-
-        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: B = F.basis()
+            sage: f = B['a'] - 3*B['c']
+            sage: vector(f)
+            (1, 0, -3)
+
-            sage: QS3 = SymmetricGroupAlgebra(QQ, 3)
-            sage: a = 2*QS3([1,2,3])+4*QS3([3,2,1])
-            sage: a._vector_()
@@ -389 +489 @@
-        """
-        parent = self.parent()
-        if parent.get_order() is None:
-
+
+
-        else:
-            cc = parent.get_order()
-            
@@ -403 +504 @@
-        Returns a vector version of self.
-
-        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: B = F.basis()
+            sage: f = B['a'] - 3*B['c']
+            sage: f.to_vector()
+            (1, 0, -3)
+
-            sage: QS3 = SymmetricGroupAlgebra(QQ, 3)
-            sage: a = 2*QS3([1,2,3])+4*QS3([3,2,1])
-            sage: a.to_vector()
@@ -418 +525 @@
-        of self.
-
-        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: B = F.basis()
+            sage: f = B['a'] - 3*B['c']
+            sage: f.map_coefficients(lambda x: x+5)
+            6*B('a') + 2*B('c')
+
-            sage: s = SFASchur(QQ)
-            sage: a = s([2,1])+2*s([3,2])
-            sage: a.map_coefficients(lambda x: x*2)
@@ -429 +542 @@
-        return self.parent()._from_dict(z_elt)
-
-
-basis
+support
-        """
-        Returns a new element of self.parent() obtained
-        by applying the function f to all of the combinatorial
-        objects indexing the basis elements.
-
-        FIXME: rename to map_support?
-
-        EXAMPLES:
-            sage: s = SFASchur(QQ)
-            sage: a = s([2,1])+2*s([3,2])
-basis
+support
-            s[2, 1] + 2*s[2, 2, 1]
-        """
-        res = self.parent()(0)
@@ -450 +561 @@
-        res._monomial_coefficients = z_elt
-        return res
-
-
+_monomial
-        """
-        Returns a new element of self.parent() obtained
-        by applying the function f to a monomial coefficient
-        (m,c) pair.  f returns a (new_m, new_c) pair.
-
-        FIXME: map_monomial?
-
-        EXAMPLES:
-            sage: s = SFASchur(QQ)
-            sage: f = lambda m,c: (m.conjugate(), 2*c)
-            sage: a = s([2,1]) + s([1,1,1])
-c
+onomial
-            2*s[2, 1] + 2*s[3]
-        """
-        z_elt = {}
@@ -471 +580 @@
-            z_elt[new_m] = new_c
-        return self.parent()._from_dict(z_elt)
-
-
+_monomial
-
-    def _l_action(self, x):
+        """
+        Returns the action of a scalar on self when self is on the left (and the
+        scalar is on the right).
+
+        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: B = F.basis()
+            sage: B['a']*1/2
+            1/2*B('a')
+
+        """
+        x = self.base_ring()(x)
+        return self.map_coefficients(lambda c: c*x)
+
+    def _r_action(self, x):
+        """
+        Returns the action of a scalar on self when self is on the right (and the
+        scalar is on the left).
+
+        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: B = F.basis()
+            sage: 1/2*B['a']
+            1/2*B('a')
+
+        """        
-        x = self.base_ring()(x)
-        return self.map_coefficients(lambda c: x*c)
-
-    def _r_action(self, x):
-        x = self.base_ring()(x)
-        return self.map_coefficients(lambda c: c*x)
-
-    def __div__(self, x):
-        """
-        Division by coefficients
-
-        EXAMPLES:
- 
+
-            sage: x = F._from_dict({1:2, 2:3})
-            sage: x/2
-            B(1) + 3/2*B(2)
+
+            sage: F = CombinatorialFreeModule(QQ, [1,2,3])
+            sage: B = F.basis()
+            sage: f = 2*B[2] + 4*B[3]
+            sage: f/2
+            B(2) + 2*B(3)
+
-        """
-
-
-
+
+
+
+
+
-
-
-
-
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
-    def __init__(self, R, element_class):
+        """
+        """
-        #Make sure R is a ring with unit element
-        if not isinstance(R, Ring):
-            raise TypeError, "Argument R must be a ring."
@@ -521 +682 @@
-    # Should be an attribute?
-    def basis(self):
-        """
-a list of the basis element
+the basi
-
-        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: F.basis()
+            Finite family {'a': B('a'), 'c': B('c'), 'b': B('b')}
+
-            sage: QS3 = SymmetricGroupAlgebra(QQ,3)
-            sage: list(QS3.basis())
-            [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]
-
-            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
-            sage: F.basis()
-            Finite family {'a': B('a'), 'c': B('c'), 'b': B('b')}
-
-        """
-        return Family(self._combinatorial_class, self.term)
@@ -540 +701 @@
-        Coerce x into self.
-
-        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ,[0,1])
+            sage: F(0)
+            0
+            sage: F(1)
+            Traceback (most recent call last):
+            ...
+            TypeError: do not know how to make x (= 1) an element of Free module generated by [0, 1] over Rational Field
+
-            sage: QS3 = SymmetricGroupAlgebra(QQ,3)
-            sage: QS3(2)
-            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
@@ -556 +722 @@
-        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:
-                return self._coerce_start(x)
-            except TypeError:
-                pass
-
-
-
-
-
-
+
-        if hasattr(x, 'parent') and x.parent().__class__ is self.__class__:
-            P = x.parent()
-            #same base ring
@@ -580 +738 @@
-            else:
-                return eclass(self, dict([ (e1,R(e2)) for e1,e2 in x._monomial_coefficients.items()]))
-        #x is an element of the basis combinatorial class
+        elif x in R:
+            if x == 0:
+                return self.zero()
+            else:
+                raise TypeError, "do not know how to make x (= %s) an element of %s"%(x, self)
-        elif isinstance(self._combinatorial_class.object_class, type) and isinstance(x, self._combinatorial_class.object_class):
-            return eclass(self, {x:R(1)}) 
-        elif x in self._combinatorial_class:
@@ -594 +757 @@
-
-    def _an_element_impl(self):
-        """
-unit
+zero
-
-        EXAMPLES:
-            sage: F = CombinatorialFreeModule(QQ, ['a', 'b', 'c'])
@@ -620 +783 @@
-        elements.
-
-        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a', 'b', 'c'])
+            sage: F.combinatorial_class()
+            Combinatorial class with elements in ['a', 'b', 'c']
+
-            sage: s = SFASchur(QQ)
-            sage: s.combinatorial_class()
-            Partitions
-        """
-        return self._combinatorial_class
-
-    def _coerce_impl(self, x):
-        """
-        EXAMPLES:
-            sage: s = SFASchur(QQ)
-            sage: s._coerce_impl(2)
-            2*s[]
-        """
-        try:
-            R = x.parent()
-            if R.__class__ is self.__class__:
-                #Only perform the coercion if we can go from the base
-                #ring of x to the base ring of self
-                if self.base_ring().has_coerce_map_from( R.base_ring() ):
-                    return self(x)
-        except AttributeError:
-            pass
-        
-        # any ring that coerces to the base ring
-        return self._coerce_try(x, [self.base_ring()])
-                                
-    def dimension(self):
-        """
@@ -652 +799 @@
-        by the number of elements in the associated combinatorial class).
-
-        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a', 'b', 'c'])
+            sage: F.dimension()
+            3
+
-            sage: s = SFASchur(QQ)
-            sage: s.dimension()
-            +Infinity
@@ -695 +846 @@
-        Returns the prefix used when displaying elements of self.
-
-        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a', 'b', 'c'])
+            sage: F.prefix()
+            'B'
+
-            sage: X = SchubertPolynomialRing(QQ)
-            sage: X.prefix()
-            'X'
@@ -782 +937 @@
-        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
-        """
+        # TODO: cache
-        return self._from_dict({})
-    
-    def sum(self, operands):
@@ -834 +989 @@
-        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:
-        Caveat in family: the order of the indices is not preserved
-            sage: e = F.basis()
-
-e.keys()  # todo: not implemented
+list(sorted(e.keys()))
-            ['a', 'b', 'c']
-e)   # todo: not implemented
+sorted(e))
-            [B('a'), B('b'), B('c')]
-
-        Let us construct some elements, and compute with them:
@@ -854 +1009 @@
-            sage: e['a'] + 3*e['b']
-            B('a') + 3*B('b')
-    """
-
-
-    def __init__(self, R, cc, element_class = CombinatorialFreeModuleElement, prefix="B"):
+        """
+        EXAMPLES:
+            sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
+            sage: F == loads(dumps(F))
+            True
+        """
+        self._name = "Free module generated by %s"%cc
-        if isinstance(cc, list):
-            cc = FiniteCombinatorialClass(cc)
-        if not isinstance(cc, CombinatorialClass):
-            raise TypeError, "cc = (%s) must be an instance of CombinatorialClass"%cc
-        self._combinatorial_class = cc
-        self._prefix = prefix
-        self._name = "Free module generated by %s"%cc
-        CombinatorialFreeModuleInterface.__init__(self, R, element_class)
-
+

a/sage/combinat/sf/classical.py

@@ -342 +342 @@
-        return "Symmetric Function Algebra over %s, %s symmetric functions as basis"%(self.base_ring(), self._basis.capitalize())
-
-
-    def prefix(self):
-        """
-        Returns the prefix on the elements of self.
-
-        EXAMPLES:
-            sage: s = SFASchur(QQ)
-            sage: s.prefix()
-            's'
-        """
-        return self._prefix
-
-    def transition_matrix(self, basis, n):
-        """
-        Returns the transitions matrix between self and basis
-        for the homogenous component of degree n.
-        
-        EXAMPLES:
-            sage: s = SFASchur(QQ)
-            sage: m = SFAMonomial(QQ)
-            sage: s.transition_matrix(m,5)
-            [1 1 1 1 1 1 1]
-            [0 1 1 2 2 3 4]
-            [0 0 1 1 2 3 5]
-            [0 0 0 1 1 3 6]
-            [0 0 0 0 1 2 5]
-            [0 0 0 0 0 1 4]
-            [0 0 0 0 0 0 1]
-
-            sage: p = SFAPower(QQ)
-            sage: s.transition_matrix(p, 4)
-            [ 1/4  1/3  1/8  1/4 1/24]
-            [-1/4    0 -1/8  1/4  1/8]
-            [   0 -1/3  1/4    0 1/12]
-            [ 1/4    0 -1/8 -1/4  1/8]
-            [-1/4  1/3  1/8 -1/4 1/24]
-            sage: StoP = s.transition_matrix(p,4)
-            sage: a = s([3,1])+5*s([1,1,1,1])-s([4])
-            sage: a
-            5*s[1, 1, 1, 1] + s[3, 1] - s[4]
-            sage: mon, coef = a.support()
-            sage: coef
-            [5, 1, -1]
-            sage: mon
-            [[1, 1, 1, 1], [3, 1], [4]]
-            sage: cm = matrix([[-1,1,0,0,5]])
-            sage: cm * StoP
-            [-7/4  4/3  3/8 -5/4 7/24]
-            sage: p(a)
-            7/24*p[1, 1, 1, 1] - 5/4*p[2, 1, 1] + 3/8*p[2, 2] + 4/3*p[3, 1] - 7/4*p[4]
-
-
-            sage: h = SFAHomogeneous(QQ)
-            sage: e = SFAElementary(QQ)
-            sage: s.transition_matrix(m,7) == h.transition_matrix(s,7).transpose()
-            True
-
-            sage: h.transition_matrix(m, 7) == h.transition_matrix(m, 7).transpose()
-            True
-
-            sage: h.transition_matrix(e, 7) == e.transition_matrix(h, 7)
-            True
-
-            
-            sage: p.transition_matrix(s, 5)
-            [ 1 -1  0  1  0 -1  1]
-            [ 1  0 -1  0  1  0 -1]
-            [ 1 -1  1  0 -1  1 -1]
-            [ 1  1 -1  0 -1  1  1]
-            [ 1  0  1 -2  1  0  1]
-            [ 1  2  1  0 -1 -2 -1]
-            [ 1  4  5  6  5  4  1]
-           
-            sage: e.transition_matrix(m,7) == e.transition_matrix(m,7).transpose()
-            True
-
-
-        """
-        P = sage.combinat.partition.Partitions_n(n)
-        Plist = P.list()
-        m = []
-        for row_part in Plist:
-            z = basis(self(row_part))
-            m.append( map( lambda col_part: z.coefficient(col_part), Plist ) )
-        return matrix(m)
-
-
-class SymmetricFunctionAlgebraElement_classical(sfa.SymmetricFunctionAlgebraElement_generic):
-    """
-    A symmetric function.
-    """
-
+
-
-##     def __pow__(self, n):
-##         """

a/sage/combinat/sf/kschur.py

@@ -67 +67 @@
-        out = {}
-        fail = False
-        while el != 0:
-monomials
+support
-            l.sort()
-            part2 = l[0]
-            n = part2.size()
@@ -166 +166 @@
-
-        if isinstance(x, sfa.SymmetricFunctionAlgebraElement_generic):
-            x = self._s(x).restrict_parts(self.k)
-monomials
+support
-                self._s_cache(p.size())
-            return self._change_by_triangularity(x, self._self_to_s_cache, True)
-        else:

a/sage/combinat/sf/schur.py

@@ -108 +108 @@
-            s[3, 1]
-        """
-        conj = lambda part: part.conjugate()
-basis
+support
-
-
-    def scalar(self, x):

a/sage/combinat/sf/sfa.py

@@ -113 +113 @@
-sage: z.length()
-2
-sage: z.support()
-[1, 1, 1], [2, 1]], [1
+1, 1, 1], [2
-sage: z.degree()
-3
-
@@ -771 +771 @@
-            sage: a = s([3,1])+5*s([1,1,1,1])-s([4])
-            sage: a
-            5*s[1, 1, 1, 1] + s[3, 1] - s[4]
-
-
+
+
+
-            [5, 1, -1]
-            sage: mon
-            [[1, 1, 1, 1], [3, 1], [4]]
@@ -1120 +1121 @@
-        #Takes n an symmetric function f, and an n and returns the
-        #symmetric function with all of its basis partitions scaled
-        #by n
-basis
+support
-
-        #Takes in a partition and applies        
-        f = lambda part: prod( pn_pleth(p_x.map_coefficients(raise_c(i)), i) for i in part )
@@ -1154 +1155 @@
-        
-        p = SFAPower(QQ)
-        res = 0
-monomials
+support
-        for d in degrees:
-            for mu in sage.combinat.partition.Partitions(d):
-                mu_k = mu.power(k)
@@ -1190 +1191 @@
-        if len(nu) == 0:
-            s = SFASchur(self.base_ring())
-            p = SFAPower(self.base_ring())
-monomials
+support
-            degrees = uniq(degrees)
-            return p(sum([s([n]) for n in degrees]))
-

a/sage/combinat/symmetric_group_algebra.py

@@ -283 +283 @@
-        if permutation.PermutationOptions()['mult'] == 'l2r':
-            return z
-        else:
-basis
+support
-        
-  
-