@@ -11,8 +11,8 @@ Nikolaus Conference 2010, Aachen: Sage-Combinat demo
1111
1212::
1313
14- sage: %hide
15- sage: pretty_print_default(False)
14+ sage: %hide # not tested
15+ sage: pretty_print_default(False) # not tested
1616
1717
1818Tableaux and the like
@@ -22,6 +22,7 @@ Tableaux and the like
2222
2323 sage: s = Permutation([5,3,2,6,4,8,9,7,1])
2424 sage: s
25+ [5, 3, 2, 6, 4, 8, 9, 7, 1]
2526
2627 sage: (p,q) = s.robinson_schensted()
2728 sage: p.pp()
@@ -39,6 +40,7 @@ Counting & the like
3940::
4041
4142 sage: Partitions(100000).cardinality()
43+ 27493510569...
4244
4345Species::
4446
@@ -65,11 +67,12 @@ Lattice points of polytopes
6567
6668::
6769
68- sage: A= random_matrix(ZZ,3,6 ,x=7)
69- sage: L= LatticePolytope(A)
70+ sage: A = random_matrix(ZZ,6,3 ,x=7)
71+ sage: L = LatticePolytope(A)
7072 sage: L.plot3d()
73+ Graphics3d Object
7174
72- sage: L.npoints() # should be cardinality!
75+ sage: L.npoints() # should be cardinality! # random
7376 28
7477
7578This example used PALP and J-mol
@@ -80,7 +83,8 @@ Graphs up to an isomorphism
8083::
8184
8285 sage: show(graphs(5, lambda G: G.size() <= 4))
83- 86+ <html>...
87+
8488Symmetric functions
8589+++++++++++++++++++
8690
@@ -89,69 +93,76 @@ Usual bases::
8993 sage: Sym = SymmetricFunctions(QQ); Sym
9094 Symmetric Functions over Rational Field
9195 sage: Sym.inject_shorthands()
92- 96+ Defining ...
97+
9398 sage: m(( ( h[2,1] * ( 1 + 3 * p[2,1]) ) + s[2](s[3])))
99+ 3*m[1, 1, 1] + ...
94100
95101Macdonald polynomials::
96102
97- sage: J = MacdonaldPolynomialsJ(QQ)
98- sage: P = MacdonaldPolynomialsP(QQ)
99- sage: Q = MacdonaldPolynomialsQ(QQ)
103+ sage: Sym = SymmetricFunctions(FractionField(QQ['q','t']))
104+ sage: J = Sym.macdonald().J()
105+ sage: P = Sym.macdonald().P()
106+ sage: Q = Sym.macdonald().Q()
100107 sage: J
101- Macdonald polynomials in the J basis over Fraction Field of Multivariate Polynomial Ring in q, t over Rational Field
108+ Symmetric Functions over Fraction Field of Multivariate Polynomial Ring in q, t over Rational Field in the Macdonald J basis
109+ 102110 sage: P(J[2,2] + 3 * Q[3,1])
111+ (...)*McdP[2, 2] + ...
103112
104113Root systems
105114++++++++++++
106115
107116::
108117
109118 sage: L = RootSystem(['A',2,1]).weight_space()
110- sage: L.plot(size=[[-1..1],[-1..1]],alcovewalks=[[0,2,0,1,2,1,2,0,2,1]])
119+ sage: L.plot(alcove_walk=[0,2,0,1,2,1,2,0,2,1])
120+ Graphics object consisting of 148 graphics primitives
111121
112122 sage: W = WeylGroup(["B", 3])
113123 sage: W.cayley_graph(side = "left").plot3d(color_by_label = True)
114- 124+ Graphics3d Object
125+
115126GAP at work
116127+++++++++++
117128
118129::
119130
131+ sage: W = WeylGroup(["B", 3])
120132 sage: print(W.character_table()) # Thanks GAP!
121133 CT1
122- 123- 2 4 4 3 3 4 3 1 1 3 4
124- 3 1 . . . . . 1 1 . 1
125- 126- 1a 2a 2b 4a 2c 2d 6a 3a 4b 2e
127- 134+ ...
128135 X.1 1 1 1 1 1 1 1 1 1 1
129136 X.2 1 1 1 -1 -1 -1 -1 1 1 -1
130137 X.3 1 1 -1 -1 1 -1 1 1 -1 1
131138 X.4 1 1 -1 1 -1 1 -1 1 -1 -1
132139 X.5 2 2 . . -2 . 1 -1 . -2
133140 X.6 2 2 . . 2 . -1 -1 . 2
134- X.7 3 -1 1 1 1 -1 . . -1 - 3
135- X.8 3 -1 -1 - 1 1 1 . . 1 -3
136- X.9 3 -1 -1 1 -1 -1 . . 1 3
137- X.10 3 -1 1 -1 - 1 1 . . -1 3
141+ X.7 3 -1 - 1 1 - 1 -1 . . 1 3
142+ X.8 3 -1 1 1 1 -1 . . - 1 -3
143+ X.9 3 -1 1 -1 -1 1 . . - 1 3
144+ X.10 3 -1 - 1 -1 1 1 . . 1 - 3
138145
139146 sage: type(W.character_table())
147+ <class 'sage.interfaces.interface.AsciiArtString'>
140148
141- sage: G = gap(W); G
149+ sage: G = W.gap(); G
150+ <matrix group of size 48 with 3 generators>
142151
143- sage: G.Ch
152+ sage: G.Ch # not tested
144153
145154 sage: T = G.CharacterTable(); T
155+ CharacterTable( <matrix group of size 48 with 3 generators> )
146156
147- sage: T.Irr()[10,10]
157+ sage: T.Irr()[4,4]
158+ -2
148159
149160Coxeter3 at work
150161++++++++++++++++
151162
152163::
153164
154- sage: W3 = CoxeterGroup(W , implementation="coxeter3")
165+ sage: W3 = CoxeterGroup(["B", 3] , implementation="coxeter3")
155166 sage: KL = matrix([ [ W3.kazhdan_lusztig_polynomial(u,v) if u.bruhat_le(v) else 0 for u in W3 ]
156167 ....: for v in W3])
157168 sage: show(KL)
@@ -170,10 +181,9 @@ Crystals
170181
171182::
172183
173- sage: latex.jsmath_avoid_list(['tikzpicture'])
174- sage: K = KirillovReshetikhinCrystal(['A',3,1], 2,2)
184+ sage: K = crystals.KirillovReshetikhin(['A',3,1], 2,2)
175185 sage: G = K.digraph()
176- sage: G.set_latex_options(format = "dot2tex", edge_labels = True, color_by_label = {0:"black", 1:"blue", 2:"red", 3:"green"}, edge_options = lambda (u,v,label) :({"backward":label == 0}))
186+ sage: G.set_latex_options(format = "dot2tex", edge_labels = True, color_by_label = {0:"black", 1:"blue", 2:"red", 3:"green"}, edge_options= lambda u_v_label :({"backward": u_v_label[2] == 0}))
177187 sage: view(G, viewer="pdf", tightpage=True)
178188
179189* :ref: `demo-GAP3-Semigroupe `
0 commit comments