# HG changeset patch # User Nathann Cohen # Date 1338373600 -7200 # Node ID 1a1f98e921da153165f4774c4e66aa97a0a89a78 # Parent e43401df8ed6360c3ac0b0db812fcd5673810c52 Two constructions for graphs.HallJankoGraph diff --git a/sage/graphs/graph_generators.py b/sage/graphs/graph_generators.py --- a/sage/graphs/graph_generators.py +++ b/sage/graphs/graph_generators.py @@ -1511,7 +1511,7 @@ return H - def HallJankoGraph(self): + def HallJankoGraph(self, from_string = True): r""" Returns the Hall-Janko graph. @@ -1525,6 +1525,13 @@ — Permutation representation on 100 points `_. + INPUT: + + - ``from_string`` (boolean) -- whether to build the graph from + its sparse6 string or through GAP. The two methods return the + same graph though doing it through GAP takes more time. It is + set to ``True`` by default. + EXAMPLES:: sage: g = graphs.HallJankoGraph() @@ -1555,41 +1562,13 @@ 3 sage: factor(g.characteristic_polynomial()) (x - 36) * (x - 6)^36 * (x + 4)^63 - """ - # Below are the lines generating the graph's sparse6 string. As it - # takes some time to run them, this method actually builds the graph - # from its sparse6 string. - - # The following construction is due to version 3 of the ATLAS of Finite - # Group Representations, specifically the page at - # http://brauer.maths.qmul.ac.uk/Atlas/v3/permrep/J2G1-p100B0 . - - # from sage.interfaces.gap import gap - # gap.eval("g1 := (1,84)(2,20)(3,48)(4,56)(5,82)(6,67)(7,55)(8,41)" - # "(9,35)(10,40)(11,78)(12,100)(13,49)(14,37)(15,94)(16,76)" - # "(17,19)(18,44)(21,34)(22,85)(23,92)(24,57)(25,75)(26,28)" - # "(27,64)(29,90)(30,97)(31,38)(32,68)(33,69)(36,53)(39,61)" - # "(42,73)(43,91)(45,86)(46,81)(47,89)(50,93)(51,96)(52,72)" - # "(54,74)(58,99)(59,95)(60,63)(62,83)(65,70)(66,88)(71,87)" - # "(77,98)(79,80);") - - # gap.eval("g2 := (1,80,22)(2,9,11)(3,53,87)(4,23,78)(5,51,18)" - # "(6,37,24)(8,27,60)(10,62,47)(12,65,31)(13,64,19)(14,61,52)" - # "(15,98,25)(16,73,32)(17,39,33)(20,97,58)(21,96,67)" - # "(26,93,99)(28,57,35)(29,71,55)(30,69,45)(34,86,82)" - # "(38,59,94)(40,43,91)(42,68,44)(46,85,89)(48,76,90)" - # "(49,92,77)(50,66,88)(54,95,56)(63,74,72)(70,81,75)" - # "(79,100,83);") - - # gap.eval("G := Group([g1,g2]);") - # edges = gap('Orbit(G,[1,5],OnSets)') - - # edge_list = [] - # for u, v in edges: - # edge_list.append((int(u),int(v))) - - # g = sage.graphs.graph.Graph(edge_list, pos={}) - # string = g.sparse6_string() + + TESTS:: + + sage: gg = graphs.HallJankoGraph(from_string = False) + sage: g == gg + True + """ string = (":~?@c__E@?g?A?w?A@GCA_?CA`OWF`W?EAW?@?_OD@_[GAgcIaGGB@OcIA" "wCE@o_K_?GB@?WGAouC@OsN_?GB@O[GB`A@@_e?@OgLB_{Q_?GC@O[GAOs" @@ -1634,7 +1613,40 @@ "HSTtl[VT}A@ocJBOwSD`_XEpo_Ha_mJrKtLbgzNSTGQspLRtDUUDp\\WG[" "HB`CQCp[WFQGgIQgkJQ{rLbc{Nc@APsdLRt@PSt\\WUtt_Wn") - g = graph.Graph(string, pos={}, loops=False, multiedges=False) + if from_string: + g = graph.Graph(string, pos={}, loops=False, multiedges=False) + else: + + # The following construction is due to version 3 of the ATLAS of Finite + # Group Representations, specifically the page at + # http://brauer.maths.qmul.ac.uk/Atlas/v3/permrep/J2G1-p100B0 . + + from sage.interfaces.gap import gap + gap.eval("g1 := (1,84)(2,20)(3,48)(4,56)(5,82)(6,67)(7,55)(8,41)" + "(9,35)(10,40)(11,78)(12,100)(13,49)(14,37)(15,94)(16,76)" + "(17,19)(18,44)(21,34)(22,85)(23,92)(24,57)(25,75)(26,28)" + "(27,64)(29,90)(30,97)(31,38)(32,68)(33,69)(36,53)(39,61)" + "(42,73)(43,91)(45,86)(46,81)(47,89)(50,93)(51,96)(52,72)" + "(54,74)(58,99)(59,95)(60,63)(62,83)(65,70)(66,88)(71,87)" + "(77,98)(79,80);") + + gap.eval("g2 := (1,80,22)(2,9,11)(3,53,87)(4,23,78)(5,51,18)" + "(6,37,24)(8,27,60)(10,62,47)(12,65,31)(13,64,19)(14,61,52)" + "(15,98,25)(16,73,32)(17,39,33)(20,97,58)(21,96,67)" + "(26,93,99)(28,57,35)(29,71,55)(30,69,45)(34,86,82)" + "(38,59,94)(40,43,91)(42,68,44)(46,85,89)(48,76,90)" + "(49,92,77)(50,66,88)(54,95,56)(63,74,72)(70,81,75)" + "(79,100,83);") + + gap.eval("G := Group([g1,g2]);") + edges = gap('Orbit(G,[1,5],OnSets)') + + edge_list = [] + for u, v in edges: + edge_list.append((int(u),int(v))) + + g = graph.Graph(edge_list, pos={}) + g.relabel() _circle_embedding(g, range(100)) g.name("Hall-Janko graph")