fixed doctests for added methods in hopf_algebras_with_basis.py and bialgebras.py

Author: alauve

src/sage/categories/bialgebras.py

@@ -171,11 +171,13 @@ def convolution_product(self, *maplist):
                 sage: m[[]].convolution_product([]), m[[1,3],[2]].convolution_product([])
                 (m{}, 0)
 
-                sage: x = GroupAlgebra(SymmetricGroup(7),QQ).an_element(); x
-                () + 3*(1,2) + 3*(1,2,3,4,5,6,7)
+                sage: QS = SymmetricGroupAlgebra(QQ,5)
+                sage: x = QS.sum_of_terms(zip(Permutations(5)[3:6],[1,2,3])); x
+                [1, 2, 4, 5, 3] + 2*[1, 2, 5, 3, 4] + 3*[1, 2, 5, 4, 3]
+                sage: x.convolution_product([Antipode])
+                2*[1, 2, 4, 5, 3] + [1, 2, 5, 3, 4] + 3*[1, 2, 5, 4, 3]
                 sage: x.convolution_product([Id, Antipode, Antipode, Antipode])
-                4*() + 3*(1,6,4,2,7,5,3)
-
+                3*[1, 2, 3, 4, 5] + [1, 2, 4, 5, 3] + 2*[1, 2, 5, 3, 4]
             """
             # be flexible on how the maps are entered...
             if len(maplist)==1 and isinstance(maplist[0], (list,tuple)):
@@ -223,15 +225,15 @@ def coproduct_iterated(self, n=1):
                 sage: p([]).coproduct_iterated(3)
                 p[] # p[] # p[] # p[]
 
-                sage: S = NonCommutativeSymmetricFunctions(QQ).S()
-                sage: S[4].coproduct_iterated(0)
-                S[4]
-                sage: S[4].coproduct_iterated(2)
-                S[] # S[] # S[4] + S[] # S[1] # S[3] + S[] # S[2] # S[2] + S[] # S[3] # S[1] + S[] # S[4] # S[] + S[1] # S[] # S[3] + S[1] # S[1] # S[2] + S[1] # S[2] # S[1] + S[1] # S[3] # S[] + S[2] # S[] # S[2] + S[2] # S[1] # S[1] + S[2] # S[2] # S[] + S[3] # S[] # S[1] + S[3] # S[1] # S[] + S[4] # S[] # S[]
+                sage: Psi = NonCommutativeSymmetricFunctions(QQ).Psi()
+                sage: Psi[2,2].coproduct_iterated(0)
+                Psi[2, 2]
+                sage: Psi[2,2].coproduct_iterated(3)
+                Psi[] # Psi[] # Psi[] # Psi[2, 2] + 2*Psi[] # Psi[] # Psi[2] # Psi[2] + Psi[] # Psi[] # Psi[2, 2] # Psi[] + 2*Psi[] # Psi[2] # Psi[] # Psi[2] + 2*Psi[] # Psi[2] # Psi[2] # Psi[] + Psi[] # Psi[2, 2] # Psi[] # Psi[] + 2*Psi[2] # Psi[] # Psi[] # Psi[2] + 2*Psi[2] # Psi[] # Psi[2] # Psi[] + 2*Psi[2] # Psi[2] # Psi[] # Psi[] + Psi[2, 2] # Psi[] # Psi[] # Psi[]
 
                 sage: m = SymmetricFunctionsNonCommutingVariables(QQ).m()
-                sage: m[[1,3],[2]].convolution_product([Antipode,Antipode])
-                3*m{{1}, {2, 3}} + 3*m{{1, 2}, {3}} + 6*m{{1, 2, 3}} - 2*m{{1, 3}, {2}}
+                sage: m[[1,3],[2]].coproduct_iterated(2)
+                m{} # m{} # m{{1, 3}, {2}} + m{} # m{{1}} # m{{1, 2}} + m{} # m{{1, 2}} # m{{1}} + m{} # m{{1, 3}, {2}} # m{} + m{{1}} # m{} # m{{1, 2}} + m{{1}} # m{{1, 2}} # m{} + m{{1, 2}} # m{} # m{{1}} + m{{1, 2}} # m{{1}} # m{} + m{{1, 3}, {2}} # m{} # m{}
 
                 sage: m[[]].coproduct_iterated(3), m[[1,3],[2]].coproduct_iterated(0)
                 (m{} # m{} # m{} # m{}, m{{1, 3}, {2}})

src/sage/categories/hopf_algebras_with_basis.py

@@ -309,14 +309,15 @@ def adams_operator(self, n):
                 5*S[1, 1, 1, 1] + 10*S[1, 1, 2] + 10*S[1, 2, 1] + 10*S[1, 3] + 10*S[2, 1, 1] + 10*S[2, 2] + 10*S[3, 1] + 5*S[4]
 
 
-                sage: x = GroupAlgebra(SymmetricGroup(7),QQ).an_element(); x
-                () + 2*(6,7) + 3*(5,6) + (1,2,3,4,5,6,7)
+                sage: QS = SymmetricGroupAlgebra(QQ,5)
+                sage: x = QS.sum_of_terms(zip(Permutations(5)[3:6],[1,2,3])); x
+                [1, 2, 4, 5, 3] + 2*[1, 2, 5, 3, 4] + 3*[1, 2, 5, 4, 3]
                 sage: x.adams_operator(2)
-                6*() + (1,3,5,7,2,4,6)
+                3*[1, 2, 3, 4, 5] + 2*[1, 2, 4, 5, 3] + [1, 2, 5, 3, 4]
                 sage: x.antipode()
-                () + 2*(6,7) + 3*(5,6) + (1,7,6,5,4,3,2)
+                2*[1, 2, 4, 5, 3] + [1, 2, 5, 3, 4] + 3*[1, 2, 5, 4, 3]
                 sage: x.adams_operator(-2)
-                6*() + (1,6,4,2,7,5,3)
+                3*[1, 2, 3, 4, 5] + [1, 2, 4, 5, 3] + 2*[1, 2, 5, 3, 4]
 
             TESTS::
 
@@ -328,12 +329,13 @@ def adams_operator(self, n):
                 sage: m[[1,3],[2]].adams_operator(-2)
                 3*m{{1}, {2, 3}} + 3*m{{1, 2}, {3}} + 6*m{{1, 2, 3}} - 2*m{{1, 3}, {2}}
 
-                sage: x = GroupAlgebra(SymmetricGroup(7),QQ).an_element(); x
-                () + 2*(6,7) + 3*(5,6) + (1,2,3,4,5,6,7)
+                sage: G = AlternatingGroup(5); QG = GroupAlgebra(G,QQ)
+                sage: x = QG.sum_of_terms(zip(G[3:6],[1,2,3])); x
+                (3,5,4) + 3*(1,2,4,3,5) + 2*(1,3,5,2,4)
                 sage: x.adams_operator(-3)
-                () + 2*(6,7) + 3*(5,6) + (1,5,2,6,3,7,4)
-                sage: x.adams_operator(0)
-                7*()
+                () + 3*(1,4,5,2,3) + 2*(1,5,4,3,2)
+                sage: x.adams_operator(0), x.adams_operator(10)
+                (6*(), 5*() + (3,5,4))
             """
             if n < 0:
                 T = lambda x: x.antipode()