{DV note: I'm suspicious that there is a serious bug in the "test_support..." scripts that Jeff demonstrated below. But the discussion of how they work and the atlas tips are all good!} atlas> set G=Sp(6,R) Variable G: RealForm atlas> for p in all_parameters_gamma (G,G.rho) do prints(p, " ", support(p)) od final parameter(x=44,lambda=[3,2,1]/1,nu=[3,2,1]/1) [0,1,2] final parameter(x=44,lambda=[4,2,1]/1,nu=[3,2,1]/1) [0,1,2] final parameter(x=44,lambda=[3,3,1]/1,nu=[3,2,1]/1) [0,1,2] final parameter(x=44,lambda=[4,3,1]/1,nu=[3,2,1]/1) [0,1,2] final parameter(x=44,lambda=[3,2,2]/1,nu=[3,2,1]/1) [0,1,2] final parameter(x=44,lambda=[4,2,2]/1,nu=[3,2,1]/1) [0,1,2] final parameter(x=44,lambda=[3,3,2]/1,nu=[3,2,1]/1) [0,1,2] final parameter(x=44,lambda=[4,3,2]/1,nu=[3,2,1]/1) [0,1,2] final parameter(x=43,lambda=[3,2,1]/1,nu=[5,5,2]/2) [0,1,2] final parameter(x=43,lambda=[3,2,2]/1,nu=[5,5,2]/2) [0,1,2] final parameter(x=42,lambda=[3,2,1]/1,nu=[6,3,3]/2) [0,1,2] final parameter(x=42,lambda=[4,2,1]/1,nu=[6,3,3]/2) [0,1,2] final parameter(x=41,lambda=[3,2,1]/1,nu=[3,2,0]/1) [0,1,2] final parameter(x=41,lambda=[4,2,1]/1,nu=[3,2,0]/1) [0,1,2] final parameter(x=41,lambda=[3,3,1]/1,nu=[3,2,0]/1) [0,1,2] final parameter(x=41,lambda=[4,3,1]/1,nu=[3,2,0]/1) [0,1,2] final parameter(x=40,lambda=[3,2,1]/1,nu=[3,2,0]/1) [0,1,2] final parameter(x=40,lambda=[4,2,1]/1,nu=[3,2,0]/1) [0,1,2] final parameter(x=40,lambda=[3,3,1]/1,nu=[3,2,0]/1) [0,1,2] final parameter(x=40,lambda=[4,3,1]/1,nu=[3,2,0]/1) [0,1,2] final parameter(x=39,lambda=[3,2,1]/1,nu=[5,5,0]/2) [0,1,2] final parameter(x=38,lambda=[3,2,1]/1,nu=[5,5,0]/2) [0,1,2] final parameter(x=37,lambda=[3,2,1]/1,nu=[2,2,2]/1) [0,1,2] final parameter(x=37,lambda=[3,3,1]/1,nu=[2,2,2]/1) [0,1,2] final parameter(x=36,lambda=[3,2,1]/1,nu=[3,0,1]/1) [0,1,2] final parameter(x=36,lambda=[4,2,1]/1,nu=[3,0,1]/1) [0,1,2] final parameter(x=36,lambda=[3,2,2]/1,nu=[3,0,1]/1) [0,1,2] final parameter(x=36,lambda=[4,2,2]/1,nu=[3,0,1]/1) [0,1,2] final parameter(x=35,lambda=[3,2,1]/1,nu=[3,0,1]/1) [0,1,2] final parameter(x=35,lambda=[4,2,1]/1,nu=[3,0,1]/1) [0,1,2] final parameter(x=35,lambda=[3,2,2]/1,nu=[3,0,1]/1) [0,1,2] final parameter(x=35,lambda=[4,2,2]/1,nu=[3,0,1]/1) [0,1,2] final parameter(x=34,lambda=[3,2,1]/1,nu=[6,1,-1]/2) [0,1,2] final parameter(x=34,lambda=[4,2,1]/1,nu=[6,1,-1]/2) [0,1,2] final parameter(x=31,lambda=[3,2,1]/1,nu=[3,0,0]/1) [0,1,2] final parameter(x=31,lambda=[4,2,1]/1,nu=[3,0,0]/1) [0,1,2] final parameter(x=30,lambda=[3,2,1]/1,nu=[3,0,0]/1) [0,1,2] final parameter(x=30,lambda=[4,2,1]/1,nu=[3,0,0]/1) [0,1,2] final parameter(x=29,lambda=[3,2,1]/1,nu=[3,0,0]/1) [0,1,2] final parameter(x=29,lambda=[4,2,1]/1,nu=[3,0,0]/1) [0,1,2] final parameter(x=28,lambda=[3,2,1]/1,nu=[3,0,0]/1) [0,1,2] final parameter(x=28,lambda=[4,2,1]/1,nu=[3,0,0]/1) [0,1,2] final parameter(x=33,lambda=[3,2,1]/1,nu=[2,0,2]/1) [0,1,2] final parameter(x=32,lambda=[3,2,1]/1,nu=[2,0,2]/1) [0,1,2] final parameter(x=27,lambda=[3,2,1]/1,nu=[0,2,1]/1) [1,2] final parameter(x=27,lambda=[3,3,1]/1,nu=[0,2,1]/1) [1,2] final parameter(x=27,lambda=[3,2,2]/1,nu=[0,2,1]/1) [1,2] final parameter(x=27,lambda=[3,3,2]/1,nu=[0,2,1]/1) [1,2] final parameter(x=26,lambda=[3,2,1]/1,nu=[0,2,1]/1) [1,2] final parameter(x=26,lambda=[3,3,1]/1,nu=[0,2,1]/1) [1,2] final parameter(x=26,lambda=[3,2,2]/1,nu=[0,2,1]/1) [1,2] final parameter(x=26,lambda=[3,3,2]/1,nu=[0,2,1]/1) [1,2] final parameter(x=25,lambda=[3,2,1]/1,nu=[1,2,-1]/1) [0,1,2] final parameter(x=25,lambda=[3,3,1]/1,nu=[1,2,-1]/1) [0,1,2] final parameter(x=24,lambda=[3,2,1]/1,nu=[0,3,3]/2) [1,2] final parameter(x=23,lambda=[3,2,1]/1,nu=[0,3,3]/2) [1,2] final parameter(x=22,lambda=[3,2,1]/1,nu=[0,2,0]/1) [1,2] final parameter(x=22,lambda=[3,3,1]/1,nu=[0,2,0]/1) [1,2] final parameter(x=21,lambda=[3,2,1]/1,nu=[0,2,0]/1) [1,2] final parameter(x=21,lambda=[3,3,1]/1,nu=[0,2,0]/1) [1,2] final parameter(x=20,lambda=[3,2,1]/1,nu=[0,2,0]/1) [1,2] final parameter(x=20,lambda=[3,3,1]/1,nu=[0,2,0]/1) [1,2] final parameter(x=19,lambda=[3,2,1]/1,nu=[0,2,0]/1) [1,2] final parameter(x=19,lambda=[3,3,1]/1,nu=[0,2,0]/1) [1,2] final parameter(x=18,lambda=[3,2,1]/1,nu=[1,0,-1]/1) [0,1] final parameter(x=17,lambda=[3,2,1]/1,nu=[1,0,-1]/1) [0,1] final parameter(x=16,lambda=[3,2,1]/1,nu=[1,-1,2]/2) [0,2] final parameter(x=16,lambda=[3,2,2]/1,nu=[1,-1,2]/2) [0,2] final parameter(x=15,lambda=[3,2,1]/1,nu=[0,0,1]/1) [2] final parameter(x=15,lambda=[3,2,2]/1,nu=[0,0,1]/1) [2] final parameter(x=14,lambda=[3,2,1]/1,nu=[0,0,1]/1) [2] final parameter(x=14,lambda=[3,2,2]/1,nu=[0,0,1]/1) [2] final parameter(x=13,lambda=[3,2,1]/1,nu=[0,0,1]/1) [2] final parameter(x=13,lambda=[3,2,2]/1,nu=[0,0,1]/1) [2] final parameter(x=12,lambda=[3,2,1]/1,nu=[0,0,1]/1) [2] final parameter(x=12,lambda=[3,2,2]/1,nu=[0,0,1]/1) [2] final parameter(x=11,lambda=[3,2,1]/1,nu=[0,1,-1]/2) [1] final parameter(x=10,lambda=[3,2,1]/1,nu=[0,1,-1]/2) [1] final parameter(x=9,lambda=[3,2,1]/1,nu=[1,-1,0]/2) [0] final parameter(x=8,lambda=[3,2,1]/1,nu=[1,-1,0]/2) [0] final parameter(x=7,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] final parameter(x=6,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] final parameter(x=5,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] final parameter(x=4,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] final parameter(x=3,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] final parameter(x=2,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] final parameter(x=1,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] final parameter(x=0,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] atlas> atlas> atlas> void:for p in all_parameters_gamma (G,G.rho) do prints(p, " ", support(p), " ", tau(p)) od final parameter(x=44,lambda=[3,2,1]/1,nu=[3,2,1]/1) [0,1,2] [0,1,2] final parameter(x=44,lambda=[4,2,1]/1,nu=[3,2,1]/1) [0,1,2] [1,2] final parameter(x=44,lambda=[3,3,1]/1,nu=[3,2,1]/1) [0,1,2] [2] final parameter(x=44,lambda=[4,3,1]/1,nu=[3,2,1]/1) [0,1,2] [0,2] final parameter(x=44,lambda=[3,2,2]/1,nu=[3,2,1]/1) [0,1,2] [0] final parameter(x=44,lambda=[4,2,2]/1,nu=[3,2,1]/1) [0,1,2] [] final parameter(x=44,lambda=[3,3,2]/1,nu=[3,2,1]/1) [0,1,2] [1] final parameter(x=44,lambda=[4,3,2]/1,nu=[3,2,1]/1) [0,1,2] [0,1] final parameter(x=43,lambda=[3,2,1]/1,nu=[5,5,2]/2) [0,1,2] [1,2] final parameter(x=43,lambda=[3,2,2]/1,nu=[5,5,2]/2) [0,1,2] [1] final parameter(x=42,lambda=[3,2,1]/1,nu=[6,3,3]/2) [0,1,2] [0,2] final parameter(x=42,lambda=[4,2,1]/1,nu=[6,3,3]/2) [0,1,2] [0,2] final parameter(x=41,lambda=[3,2,1]/1,nu=[3,2,0]/1) [0,1,2] [0,1] final parameter(x=41,lambda=[4,2,1]/1,nu=[3,2,0]/1) [0,1,2] [1] final parameter(x=41,lambda=[3,3,1]/1,nu=[3,2,0]/1) [0,1,2] [1] final parameter(x=41,lambda=[4,3,1]/1,nu=[3,2,0]/1) [0,1,2] [0,1] final parameter(x=40,lambda=[3,2,1]/1,nu=[3,2,0]/1) [0,1,2] [0,1] final parameter(x=40,lambda=[4,2,1]/1,nu=[3,2,0]/1) [0,1,2] [1] final parameter(x=40,lambda=[3,3,1]/1,nu=[3,2,0]/1) [0,1,2] [1] final parameter(x=40,lambda=[4,3,1]/1,nu=[3,2,0]/1) [0,1,2] [0,1] final parameter(x=39,lambda=[3,2,1]/1,nu=[5,5,0]/2) [0,1,2] [1] final parameter(x=38,lambda=[3,2,1]/1,nu=[5,5,0]/2) [0,1,2] [1] final parameter(x=37,lambda=[3,2,1]/1,nu=[2,2,2]/1) [0,1,2] [2] final parameter(x=37,lambda=[3,3,1]/1,nu=[2,2,2]/1) [0,1,2] [2] final parameter(x=36,lambda=[3,2,1]/1,nu=[3,0,1]/1) [0,1,2] [0,2] final parameter(x=36,lambda=[4,2,1]/1,nu=[3,0,1]/1) [0,1,2] [0,2] final parameter(x=36,lambda=[3,2,2]/1,nu=[3,0,1]/1) [0,1,2] [0] final parameter(x=36,lambda=[4,2,2]/1,nu=[3,0,1]/1) [0,1,2] [0] final parameter(x=35,lambda=[3,2,1]/1,nu=[3,0,1]/1) [0,1,2] [0,2] final parameter(x=35,lambda=[4,2,1]/1,nu=[3,0,1]/1) [0,1,2] [0,2] final parameter(x=35,lambda=[3,2,2]/1,nu=[3,0,1]/1) [0,1,2] [0] final parameter(x=35,lambda=[4,2,2]/1,nu=[3,0,1]/1) [0,1,2] [0] final parameter(x=34,lambda=[3,2,1]/1,nu=[6,1,-1]/2) [0,1,2] [0,1] final parameter(x=34,lambda=[4,2,1]/1,nu=[6,1,-1]/2) [0,1,2] [0,1] final parameter(x=31,lambda=[3,2,1]/1,nu=[3,0,0]/1) [0,1,2] [0,1] final parameter(x=31,lambda=[4,2,1]/1,nu=[3,0,0]/1) [0,1,2] [0,1] final parameter(x=30,lambda=[3,2,1]/1,nu=[3,0,0]/1) [0,1,2] [0,1] final parameter(x=30,lambda=[4,2,1]/1,nu=[3,0,0]/1) [0,1,2] [0,1] final parameter(x=29,lambda=[3,2,1]/1,nu=[3,0,0]/1) [0,1,2] [0] final parameter(x=29,lambda=[4,2,1]/1,nu=[3,0,0]/1) [0,1,2] [0] final parameter(x=28,lambda=[3,2,1]/1,nu=[3,0,0]/1) [0,1,2] [0] final parameter(x=28,lambda=[4,2,1]/1,nu=[3,0,0]/1) [0,1,2] [0] final parameter(x=33,lambda=[3,2,1]/1,nu=[2,0,2]/1) [0,1,2] [0,2] final parameter(x=32,lambda=[3,2,1]/1,nu=[2,0,2]/1) [0,1,2] [0,2] final parameter(x=27,lambda=[3,2,1]/1,nu=[0,2,1]/1) [1,2] [1,2] final parameter(x=27,lambda=[3,3,1]/1,nu=[0,2,1]/1) [1,2] [2] final parameter(x=27,lambda=[3,2,2]/1,nu=[0,2,1]/1) [1,2] [] final parameter(x=27,lambda=[3,3,2]/1,nu=[0,2,1]/1) [1,2] [1] final parameter(x=26,lambda=[3,2,1]/1,nu=[0,2,1]/1) [1,2] [1,2] final parameter(x=26,lambda=[3,3,1]/1,nu=[0,2,1]/1) [1,2] [2] final parameter(x=26,lambda=[3,2,2]/1,nu=[0,2,1]/1) [1,2] [] final parameter(x=26,lambda=[3,3,2]/1,nu=[0,2,1]/1) [1,2] [1] final parameter(x=25,lambda=[3,2,1]/1,nu=[1,2,-1]/1) [0,1,2] [1] final parameter(x=25,lambda=[3,3,1]/1,nu=[1,2,-1]/1) [0,1,2] [1] final parameter(x=24,lambda=[3,2,1]/1,nu=[0,3,3]/2) [1,2] [2] final parameter(x=23,lambda=[3,2,1]/1,nu=[0,3,3]/2) [1,2] [2] final parameter(x=22,lambda=[3,2,1]/1,nu=[0,2,0]/1) [1,2] [1] final parameter(x=22,lambda=[3,3,1]/1,nu=[0,2,0]/1) [1,2] [1] final parameter(x=21,lambda=[3,2,1]/1,nu=[0,2,0]/1) [1,2] [1] final parameter(x=21,lambda=[3,3,1]/1,nu=[0,2,0]/1) [1,2] [1] final parameter(x=20,lambda=[3,2,1]/1,nu=[0,2,0]/1) [1,2] [1] final parameter(x=20,lambda=[3,3,1]/1,nu=[0,2,0]/1) [1,2] [1] final parameter(x=19,lambda=[3,2,1]/1,nu=[0,2,0]/1) [1,2] [1] final parameter(x=19,lambda=[3,3,1]/1,nu=[0,2,0]/1) [1,2] [1] final parameter(x=18,lambda=[3,2,1]/1,nu=[1,0,-1]/1) [0,1] [0,1] final parameter(x=17,lambda=[3,2,1]/1,nu=[1,0,-1]/1) [0,1] [0,1] final parameter(x=16,lambda=[3,2,1]/1,nu=[1,-1,2]/2) [0,2] [0,2] final parameter(x=16,lambda=[3,2,2]/1,nu=[1,-1,2]/2) [0,2] [0] final parameter(x=15,lambda=[3,2,1]/1,nu=[0,0,1]/1) [2] [0,2] final parameter(x=15,lambda=[3,2,2]/1,nu=[0,0,1]/1) [2] [0] final parameter(x=14,lambda=[3,2,1]/1,nu=[0,0,1]/1) [2] [0,2] final parameter(x=14,lambda=[3,2,2]/1,nu=[0,0,1]/1) [2] [0] final parameter(x=13,lambda=[3,2,1]/1,nu=[0,0,1]/1) [2] [2] final parameter(x=13,lambda=[3,2,2]/1,nu=[0,0,1]/1) [2] [] final parameter(x=12,lambda=[3,2,1]/1,nu=[0,0,1]/1) [2] [2] final parameter(x=12,lambda=[3,2,2]/1,nu=[0,0,1]/1) [2] [] final parameter(x=11,lambda=[3,2,1]/1,nu=[0,1,-1]/2) [1] [1] final parameter(x=10,lambda=[3,2,1]/1,nu=[0,1,-1]/2) [1] [1] final parameter(x=9,lambda=[3,2,1]/1,nu=[1,-1,0]/2) [0] [0] final parameter(x=8,lambda=[3,2,1]/1,nu=[1,-1,0]/2) [0] [0] final parameter(x=7,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] [0,1] final parameter(x=6,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] [0] final parameter(x=5,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] [0,1] final parameter(x=4,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] [] final parameter(x=3,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] [1] final parameter(x=2,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] [0] final parameter(x=1,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] [1] final parameter(x=0,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] [] atlas> atlas> atlas> atlas> set x=G.KGB[10] Variable x: KGBElt atlas> x Value: KGB element #10 atlas> x.w Value: <1> atlas> x.w.matrix Value: | 1, 0, 0 | | 0, 0, 1 | | 0, 1, 0 | atlas> x.w.word Value: [1] atlas> for x in G.KGB do prints(x, " ", x.w) od KGB element #0 <> KGB element #1 <> KGB element #2 <> KGB element #3 <> KGB element #4 <> KGB element #5 <> KGB element #6 <> KGB element #7 <> KGB element #8 <0> KGB element #9 <0> KGB element #10 <1> KGB element #11 <1> KGB element #12 <2> KGB element #13 <2> KGB element #14 <2> KGB element #15 <2> KGB element #16 <2.0> KGB element #17 <1.0.1> KGB element #18 <1.0.1> KGB element #19 <1.2.1> KGB element #20 <1.2.1> KGB element #21 <1.2.1> KGB element #22 <1.2.1> KGB element #23 <2.1.2> KGB element #24 <2.1.2> KGB element #25 <1.2.0.1> KGB element #26 <2.1.2.1> KGB element #27 <2.1.2.1> KGB element #28 <0.1.2.1.0> KGB element #29 <0.1.2.1.0> KGB element #30 <0.1.2.1.0> KGB element #31 <0.1.2.1.0> KGB element #32 <2.1.0.1.2> KGB element #33 <2.1.0.1.2> KGB element #34 <1.0.1.2.1.0> KGB element #35 <2.0.1.2.1.0> KGB element #36 <2.0.1.2.1.0> KGB element #37 <2.1.2.0.1.2> KGB element #38 <1.2.1.0.1.2.1> KGB element #39 <1.2.1.0.1.2.1> KGB element #40 <1.2.1.0.1.2.1.0> KGB element #41 <1.2.1.0.1.2.1.0> KGB element #42 <2.1.2.0.1.2.1.0> KGB element #43 <2.1.2.1.0.1.2.1> KGB element #44 <2.1.2.1.0.1.2.1.0> atlas> atlas> atlas> set G=Sp(4,R) Variable G: RealForm (overriding previous instance, which had type RealForm) atlas> set all=all_parameters_gamma (G,G.rho) Variable all: [Param] atlas> [[Param]]) Defined is_proper_support: (KGBElt->bool) Defined is_proper_support_dual: (KGBElt->bool) Added definition [2] of is_proper_support: (Param->bool) Added definition [2] of is_proper_support_dual: (Param->bool) Defined is_proper_support_or_dual: (Param->bool) Defined proper_support_or_dual_proper_support_subset: ([Param]->[Param]) Added definition [2] of proper_support_or_dual_proper_support_subset: ([Param],[WCell]->[([Param],[Param])]) Defined test_support: ([Param]->[[([Param],[Param])]]) Defined test_support_long: ([Param]->bool) Completely read file 'support.at'. atlas> for p in all do is_proper_support_or_dual (p) od Value: [true,true,true,true,true,true,true,true,true,true,true,true,true,true,true,true,true,true] atlas> for p in all do is_proper_support (p) od Value: [false,false,false,false,false,false,false,false,false,true,true,true,true,true,true,true,true,true] atlas> for p in all do if(is_proper_support (p)) then [p] else [] fi od Value: [[],[],[],[],[],[],[],[],[],[final parameter(x=6,lambda=[2,1]/1,nu=[0,1]/1)],[final parameter(x=6,lambda=[2,2]/1,nu=[0,1]/1)],[final parameter(x=5,lambda=[2,1]/1,nu=[0,1]/1)],[final parameter(x=5,lambda=[2,2]/1,nu=[0,1]/1)],[final parameter(x=4,lambda=[2,1]/1,nu=[1,-1]/2)],[final parameter(x=3,lambda=[2,1]/1,nu=[0,0]/1)],[final parameter(x=2,lambda=[2,1]/1,nu=[0,0]/1)],[final parameter(x=1,lambda=[2,1]/1,nu=[0,0]/1)],[final parameter(x=0,lambda=[2,1]/1,nu=[0,0]/1)]] {The for loop makes a list in which each term is either [p] if p has the desired property, or [] if not. It isn't possible to make a loop that says "for each p, put p in the list if p has the property and do nothing if it doesn't. The reason is that each step of the loop has to make the same kind of thing: in this example, a list of parameters (with one element in one case and zero elements in the other). {Atlas offers a shortcut to go through this strange kind of list of lists, remove the empty terms, and make a single list out of all the terms in the nonempty list: atlas> ##[[],[2,3],[3,5],[],[2,3]] Value: [2,3,3,5,2,3] Here's how to use it with this loop:} atlas> ##for p in all do if(is_proper_support (p)) then [p] else [] fi od Value: [final parameter(x=6,lambda=[2,1]/1,nu=[0,1]/1),final parameter(x=6,lambda=[2,2]/1,nu=[0,1]/1),final parameter(x=5,lambda=[2,1]/1,nu=[0,1]/1),final parameter(x=5,lambda=[2,2]/1,nu=[0,1]/1),final parameter(x=4,lambda=[2,1]/1,nu=[1,-1]/2),final parameter(x=3,lambda=[2,1]/1,nu=[0,0]/1),final parameter(x=2,lambda=[2,1]/1,nu=[0,0]/1),final parameter(x=1,lambda=[2,1]/1,nu=[0,0]/1),final parameter(x=0,lambda=[2,1]/1,nu=[0,0]/1)] atlas> void:for p in all_parameters_gamma (G,G.rho) do prints(p, " ", support(p), " ", tau(p)) od final parameter(x=10,lambda=[2,1]/1,nu=[2,1]/1) [0,1] [0,1] final parameter(x=10,lambda=[3,1]/1,nu=[2,1]/1) [0,1] [1] final parameter(x=10,lambda=[2,2]/1,nu=[2,1]/1) [0,1] [] final parameter(x=10,lambda=[3,2]/1,nu=[2,1]/1) [0,1] [0] final parameter(x=9,lambda=[2,1]/1,nu=[3,3]/2) [0,1] [1] final parameter(x=8,lambda=[2,1]/1,nu=[2,0]/1) [0,1] [0] final parameter(x=8,lambda=[3,1]/1,nu=[2,0]/1) [0,1] [0] final parameter(x=7,lambda=[2,1]/1,nu=[2,0]/1) [0,1] [0] final parameter(x=7,lambda=[3,1]/1,nu=[2,0]/1) [0,1] [0] final parameter(x=6,lambda=[2,1]/1,nu=[0,1]/1) [1] [1] final parameter(x=6,lambda=[2,2]/1,nu=[0,1]/1) [1] [] final parameter(x=5,lambda=[2,1]/1,nu=[0,1]/1) [1] [1] final parameter(x=5,lambda=[2,2]/1,nu=[0,1]/1) [1] [] final parameter(x=4,lambda=[2,1]/1,nu=[1,-1]/2) [0] [0] final parameter(x=3,lambda=[2,1]/1,nu=[0,0]/1) [] [0] final parameter(x=2,lambda=[2,1]/1,nu=[0,0]/1) [] [0] final parameter(x=1,lambda=[2,1]/1,nu=[0,0]/1) [] [] final parameter(x=0,lambda=[2,1]/1,nu=[0,0]/1) [] [] atlas> set G=Sp(6,R) Variable G: RealForm (overriding previous instance, which had type RealForm) atlas> void:for p@i in all_parameters_gamma (G,G.rho) do prints(i, " ", p, " ", support(p), " ", tau(p)) od 0 final parameter(x=44,lambda=[3,2,1]/1,nu=[3,2,1]/1) [0,1,2] [0,1,2] 1 final parameter(x=44,lambda=[4,2,1]/1,nu=[3,2,1]/1) [0,1,2] [1,2] 2 final parameter(x=44,lambda=[3,3,1]/1,nu=[3,2,1]/1) [0,1,2] [2] 3 final parameter(x=44,lambda=[4,3,1]/1,nu=[3,2,1]/1) [0,1,2] [0,2] 4 final parameter(x=44,lambda=[3,2,2]/1,nu=[3,2,1]/1) [0,1,2] [0] 5 final parameter(x=44,lambda=[4,2,2]/1,nu=[3,2,1]/1) [0,1,2] [] 6 final parameter(x=44,lambda=[3,3,2]/1,nu=[3,2,1]/1) [0,1,2] [1] 7 final parameter(x=44,lambda=[4,3,2]/1,nu=[3,2,1]/1) [0,1,2] [0,1] 8 final parameter(x=43,lambda=[3,2,1]/1,nu=[5,5,2]/2) [0,1,2] [1,2] 9 final parameter(x=43,lambda=[3,2,2]/1,nu=[5,5,2]/2) [0,1,2] [1] 10 final parameter(x=42,lambda=[3,2,1]/1,nu=[6,3,3]/2) [0,1,2] [0,2] 11 final parameter(x=42,lambda=[4,2,1]/1,nu=[6,3,3]/2) [0,1,2] [0,2] 12 final parameter(x=41,lambda=[3,2,1]/1,nu=[3,2,0]/1) [0,1,2] [0,1] 13 final parameter(x=41,lambda=[4,2,1]/1,nu=[3,2,0]/1) [0,1,2] [1] 14 final parameter(x=41,lambda=[3,3,1]/1,nu=[3,2,0]/1) [0,1,2] [1] 15 final parameter(x=41,lambda=[4,3,1]/1,nu=[3,2,0]/1) [0,1,2] [0,1] 16 final parameter(x=40,lambda=[3,2,1]/1,nu=[3,2,0]/1) [0,1,2] [0,1] 17 final parameter(x=40,lambda=[4,2,1]/1,nu=[3,2,0]/1) [0,1,2] [1] 18 final parameter(x=40,lambda=[3,3,1]/1,nu=[3,2,0]/1) [0,1,2] [1] 19 final parameter(x=40,lambda=[4,3,1]/1,nu=[3,2,0]/1) [0,1,2] [0,1] 20 final parameter(x=39,lambda=[3,2,1]/1,nu=[5,5,0]/2) [0,1,2] [1] 21 final parameter(x=38,lambda=[3,2,1]/1,nu=[5,5,0]/2) [0,1,2] [1] 22 final parameter(x=37,lambda=[3,2,1]/1,nu=[2,2,2]/1) [0,1,2] [2] 23 final parameter(x=37,lambda=[3,3,1]/1,nu=[2,2,2]/1) [0,1,2] [2] 24 final parameter(x=36,lambda=[3,2,1]/1,nu=[3,0,1]/1) [0,1,2] [0,2] 25 final parameter(x=36,lambda=[4,2,1]/1,nu=[3,0,1]/1) [0,1,2] [0,2] 26 final parameter(x=36,lambda=[3,2,2]/1,nu=[3,0,1]/1) [0,1,2] [0] 27 final parameter(x=36,lambda=[4,2,2]/1,nu=[3,0,1]/1) [0,1,2] [0] 28 final parameter(x=35,lambda=[3,2,1]/1,nu=[3,0,1]/1) [0,1,2] [0,2] 29 final parameter(x=35,lambda=[4,2,1]/1,nu=[3,0,1]/1) [0,1,2] [0,2] 30 final parameter(x=35,lambda=[3,2,2]/1,nu=[3,0,1]/1) [0,1,2] [0] 31 final parameter(x=35,lambda=[4,2,2]/1,nu=[3,0,1]/1) [0,1,2] [0] 32 final parameter(x=34,lambda=[3,2,1]/1,nu=[6,1,-1]/2) [0,1,2] [0,1] 33 final parameter(x=34,lambda=[4,2,1]/1,nu=[6,1,-1]/2) [0,1,2] [0,1] 34 final parameter(x=31,lambda=[3,2,1]/1,nu=[3,0,0]/1) [0,1,2] [0,1] 35 final parameter(x=31,lambda=[4,2,1]/1,nu=[3,0,0]/1) [0,1,2] [0,1] 36 final parameter(x=30,lambda=[3,2,1]/1,nu=[3,0,0]/1) [0,1,2] [0,1] 37 final parameter(x=30,lambda=[4,2,1]/1,nu=[3,0,0]/1) [0,1,2] [0,1] 38 final parameter(x=29,lambda=[3,2,1]/1,nu=[3,0,0]/1) [0,1,2] [0] 39 final parameter(x=29,lambda=[4,2,1]/1,nu=[3,0,0]/1) [0,1,2] [0] 40 final parameter(x=28,lambda=[3,2,1]/1,nu=[3,0,0]/1) [0,1,2] [0] 41 final parameter(x=28,lambda=[4,2,1]/1,nu=[3,0,0]/1) [0,1,2] [0] 42 final parameter(x=33,lambda=[3,2,1]/1,nu=[2,0,2]/1) [0,1,2] [0,2] 43 final parameter(x=32,lambda=[3,2,1]/1,nu=[2,0,2]/1) [0,1,2] [0,2] 44 final parameter(x=27,lambda=[3,2,1]/1,nu=[0,2,1]/1) [1,2] [1,2] 45 final parameter(x=27,lambda=[3,3,1]/1,nu=[0,2,1]/1) [1,2] [2] 46 final parameter(x=27,lambda=[3,2,2]/1,nu=[0,2,1]/1) [1,2] [] 47 final parameter(x=27,lambda=[3,3,2]/1,nu=[0,2,1]/1) [1,2] [1] 48 final parameter(x=26,lambda=[3,2,1]/1,nu=[0,2,1]/1) [1,2] [1,2] 49 final parameter(x=26,lambda=[3,3,1]/1,nu=[0,2,1]/1) [1,2] [2] 50 final parameter(x=26,lambda=[3,2,2]/1,nu=[0,2,1]/1) [1,2] [] 51 final parameter(x=26,lambda=[3,3,2]/1,nu=[0,2,1]/1) [1,2] [1] 52 final parameter(x=25,lambda=[3,2,1]/1,nu=[1,2,-1]/1) [0,1,2] [1] 53 final parameter(x=25,lambda=[3,3,1]/1,nu=[1,2,-1]/1) [0,1,2] [1] 54 final parameter(x=24,lambda=[3,2,1]/1,nu=[0,3,3]/2) [1,2] [2] 55 final parameter(x=23,lambda=[3,2,1]/1,nu=[0,3,3]/2) [1,2] [2] 56 final parameter(x=22,lambda=[3,2,1]/1,nu=[0,2,0]/1) [1,2] [1] 57 final parameter(x=22,lambda=[3,3,1]/1,nu=[0,2,0]/1) [1,2] [1] 58 final parameter(x=21,lambda=[3,2,1]/1,nu=[0,2,0]/1) [1,2] [1] 59 final parameter(x=21,lambda=[3,3,1]/1,nu=[0,2,0]/1) [1,2] [1] 60 final parameter(x=20,lambda=[3,2,1]/1,nu=[0,2,0]/1) [1,2] [1] 61 final parameter(x=20,lambda=[3,3,1]/1,nu=[0,2,0]/1) [1,2] [1] 62 final parameter(x=19,lambda=[3,2,1]/1,nu=[0,2,0]/1) [1,2] [1] 63 final parameter(x=19,lambda=[3,3,1]/1,nu=[0,2,0]/1) [1,2] [1] 64 final parameter(x=18,lambda=[3,2,1]/1,nu=[1,0,-1]/1) [0,1] [0,1] 65 final parameter(x=17,lambda=[3,2,1]/1,nu=[1,0,-1]/1) [0,1] [0,1] 66 final parameter(x=16,lambda=[3,2,1]/1,nu=[1,-1,2]/2) [0,2] [0,2] 67 final parameter(x=16,lambda=[3,2,2]/1,nu=[1,-1,2]/2) [0,2] [0] 68 final parameter(x=15,lambda=[3,2,1]/1,nu=[0,0,1]/1) [2] [0,2] 69 final parameter(x=15,lambda=[3,2,2]/1,nu=[0,0,1]/1) [2] [0] 70 final parameter(x=14,lambda=[3,2,1]/1,nu=[0,0,1]/1) [2] [0,2] 71 final parameter(x=14,lambda=[3,2,2]/1,nu=[0,0,1]/1) [2] [0] 72 final parameter(x=13,lambda=[3,2,1]/1,nu=[0,0,1]/1) [2] [2] 73 final parameter(x=13,lambda=[3,2,2]/1,nu=[0,0,1]/1) [2] [] 74 final parameter(x=12,lambda=[3,2,1]/1,nu=[0,0,1]/1) [2] [2] 75 final parameter(x=12,lambda=[3,2,2]/1,nu=[0,0,1]/1) [2] [] 76 final parameter(x=11,lambda=[3,2,1]/1,nu=[0,1,-1]/2) [1] [1] 77 final parameter(x=10,lambda=[3,2,1]/1,nu=[0,1,-1]/2) [1] [1] 78 final parameter(x=9,lambda=[3,2,1]/1,nu=[1,-1,0]/2) [0] [0] 79 final parameter(x=8,lambda=[3,2,1]/1,nu=[1,-1,0]/2) [0] [0] 80 final parameter(x=7,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] [0,1] 81 final parameter(x=6,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] [0] 82 final parameter(x=5,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] [0,1] 83 final parameter(x=4,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] [] 84 final parameter(x=3,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] [1] 85 final parameter(x=2,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] [0] 86 final parameter(x=1,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] [1] 87 final parameter(x=0,lambda=[3,2,1]/1,nu=[0,0,0]/1) [] [] atlas> set all=all_parameters_gamma (G,G.rho) Variable all: [Param] (overriding previous instance, which had type [Param]) atlas> set p=all[48] Variable p: Param atlas> p Value: final parameter(x=26,lambda=[3,2,1]/1,nu=[0,2,1]/1) atlas> set d=cuspidal_data (p) Variable d: (KGPElt,Param) atlas> d Value: (([2],KGB element #40),final parameter(x=0,lambda=[1,1,3]/1,nu=[2,1,0]/1)) atlas> set (y,q)=cuspidal_data (p) Variable y: KGPElt Variable q: Param atlas> y.Levi Value: disconnected split real group with Lie algebra 'sl(2,R).gl(1,R).gl(1,R)' atlas> q Value: final parameter(x=0,lambda=[1,1,3]/1,nu=[2,1,0]/1) atlas> theta_stable_data (p) Value: (([1,2],KGB element #26),final parameter(x=10,lambda=[0,2,1]/1,nu=[0,2,1]/1)) atlas> set (z,t)=theta_stable_data (p) Variable z: KGPElt Variable t: Param atlas> z.Levi Value: connected quasisplit real group with Lie algebra 'sp(4,R).u(1)' atlas> t Value: final parameter(x=10,lambda=[0,2,1]/1,nu=[0,2,1]/1) atlas> theta_induce_irreducible(t,G) Value: 1*parameter(x=26,lambda=[3,2,1]/1,nu=[0,2,1]/1) [15] atlas> set (z,t)=theta_stable_data (all[48]) Variable z: KGPElt (overriding previous instance, which had type KGPElt) Variable t: Param (overriding previous instance, which had type Param) atlas> theta_stable_data (all[48]) {The last four (standard) reps in "all" are cohomologically induced from four different principal series on the same theta-stable parabolic:} atlas> theta_stable_data (all[48]) Value: (([1,2],KGB element #26),final parameter(x=10,lambda=[0,2,1]/1,nu=[0,2,1]/1)) atlas> theta_stable_data (all[49]) Value: (([1,2],KGB element #26),final parameter(x=10,lambda=[0,3,1]/1,nu=[0,2,1]/1)) atlas> theta_stable_data (all[50]) Value: (([1,2],KGB element #26),final parameter(x=10,lambda=[0,2,2]/1,nu=[0,2,1]/1)) atlas> theta_stable_data (all[51]) Value: (([1,2],KGB element #26),final parameter(x=10,lambda=[0,3,2]/1,nu=[0,2,1]/1)) {The Langlands quotient of the first of these four principal series one-dimensional, as atlas will tell you:} atlas> set (z,t)=theta_stable_data (all[48]) Variable z: KGPElt (overriding previous instance, which had type KGPElt) Variable t: Param (overriding previous instance, which had type Param) atlas> dimension(t) Value: 1 {But the other three are not:} atlas> set (z,t)=theta_stable_data (all[49]) Variable z: KGPElt (overriding previous instance, which had type KGPElt) Variable t: Param (overriding previous instance, which had type Param) atlas> dimension(t) Runtime error: representation is infinite dimensional Evaluation aborted. atlas> set (z,t)=theta_stable_data (all[50]) Variable z: KGPElt (overriding previous instance, which had type KGPElt) Variable t: Param (overriding previous instance, which had type Param) atlas> dimension(t) Runtime error: representation is infinite dimensional Evaluation aborted. atlas> set (z,t)=theta_stable_data (all[51]) Variable z: KGPElt (overriding previous instance, which had type KGPElt) Variable t: Param (overriding previous instance, which had type Param) atlas> dimension(t) Runtime error: representation is infinite dimensional Evaluation aborted. {The function "test_support" tests the conjecture that in each cell there is either an element with proper support, or an element whose dual support is proper.} atlas> test_support(all_parameters_gamma (Sp(4,R),Sp(4,R).rho)) Value: [[([final parameter(x=0,lambda=[2,1]/1,nu=[0,0]/1)],[final parameter(x=0,lambda=[2,1]/1,nu=[0,0]/1)]),([final parameter(x=1,lambda=[2,1]/1,nu=[0,0]/1)],[final parameter(x=1,lambda=[2,1]/1,nu=[0,0]/1)]),([final parameter(x=2,lambda=[2,1]/1,nu=[0,0]/1),final parameter(x=5,lambda=[2,1]/1,nu=[0,1]/1),final parameter(x=7,lambda=[2,1]/1,nu=[2,0]/1)],[final parameter(x=2,lambda=[2,1]/1,nu=[0,0]/1),final parameter(x=5,lambda=[2,1]/1,nu=[0,1]/1),final parameter(x=7,lambda=[2,1]/1,nu=[2,0]/1)]),([final parameter(x=3,lambda=[2,1]/1,nu=[0,0]/1),final parameter(x=6,lambda=[2,1]/1,nu=[0,1]/1),final parameter(x=8,lambda=[2,1]/1,nu=[2,0]/1)],[final parameter(x=3,lambda=[2,1]/1,nu=[0,0]/1),final parameter(x=6,lambda=[2,1]/1,nu=[0,1]/1),final parameter(x=8,lambda=[2,1]/1,nu=[2,0]/1)]),([final parameter(x=4,lambda=[2,1]/1,nu=[1,-1]/2),final parameter(x=9,lambda=[2,1]/1,nu=[3,3]/2),final parameter(x=10,lambda=[3,2]/1,nu=[2,1]/1)],[final parameter(x=4,lambda=[2,1]/1,nu=[1,-1]/2),final parameter(x=9,lambda=[2,1]/1,nu=[3,3]/2),final parameter(x=10,lambda=[3,2]/1,nu=[2,1]/1)]),([final parameter(x=10,lambda=[2,1]/1,nu=[2,1]/1)],[final parameter(x=10,lambda=[2,1]/1,nu=[2,1]/1)])],[([final parameter(x=5,lambda=[2,2]/1,nu=[0,1]/1)],[final parameter(x=5,lambda=[2,2]/1,nu=[0,1]/1)]),([final parameter(x=6,lambda=[2,2]/1,nu=[0,1]/1)],[final parameter(x=6,lambda=[2,2]/1,nu=[0,1]/1)]),([final parameter(x=7,lambda=[3,1]/1,nu=[2,0]/1),final parameter(x=8,lambda=[3,1]/1,nu=[2,0]/1),final parameter(x=10,lambda=[3,1]/1,nu=[2,1]/1)],[final parameter(x=7,lambda=[3,1]/1,nu=[2,0]/1),final parameter(x=8,lambda=[3,1]/1,nu=[2,0]/1),final parameter(x=10,lambda=[3,1]/1,nu=[2,1]/1)])],[([final parameter(x=10,lambda=[2,2]/1,nu=[2,1]/1)],[final parameter(x=10,lambda=[2,2]/1,nu=[2,1]/1)])]] {The answers are hidden in there! The function test_support_long offers some explanations...} atlas> test_support_long(all_parameters_gamma (Sp(4,R),Sp(4,R).rho)) #params: 18 #blocks: 3 block #0 #cells: 6 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [1] [0] 1 1 1 0/0 [0] [1] [0] 2 3 3 0/2 [0,1,2] [1,1,0] [0,0,1] 3 3 3 0/2 [0,1,2] [1,1,0] [0,0,1] 4 3 3 1/3 [1,2,3] [1,0,0] [0,1,1] 5 1 1 3/3 [3] [0] [1] block #1 #cells: 3 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [1] [0] 1 1 1 0/0 [0] [1] [0] 2 3 3 1/2 [1,1,2] [0,0,0] [1,1,1] block #2 #cells: 1 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [0] [1] Value: true atlas> test_support_long(all_parameters_gamma (Sp(6,R),Sp(6,R).rho)) #params: 88 #blocks: 4 block #0 #cells: 16 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [1] [0] 1 1 1 0/0 [0] [1] [0] 2 5 5 0/3 [0,1,1,2,3] [1,1,1,1,0] [0,0,0,0,1] 3 5 5 0/4 [0,1,2,3,4] [1,1,1,1,0] [0,0,0,0,1] 4 5 5 0/3 [0,1,1,2,3] [1,1,1,1,0] [0,0,0,0,1] 5 3 3 0/2 [0,1,2] [1,1,1] [0,0,0] 6 5 5 0/4 [0,1,2,3,4] [1,1,1,1,0] [0,0,0,0,1] 7 3 3 0/2 [0,1,2] [1,1,1] [0,0,0] 8* 3 2 2/4 [2,4] [1,0,0] [0,0,1] 9* 3 2 2/4 [2,4] [1,0,0] [0,0,1] 10* 3 2 2/4 [2,4] [1,0,0] [0,0,1] 11 3 3 4/6 [4,5,6] [0,0,0] [1,1,1] 12 4 4 3/5 [3,3,4,5] [1,0,0,0] [0,1,1,1] 13 4 4 3/5 [3,3,4,5] [1,0,0,0] [0,1,1,1] 14 4 4 5/6 [5,5,5,6] [0,0,0,0] [1,1,1,1] 15 1 1 6/6 [6] [0] [1] block #1 #cells: 8 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [1] [0] 1 1 1 0/0 [0] [1] [0] 2 5 5 0/2 [0,1,1,2,2] [1,1,1,1,0] [0,0,0,0,1] 3 5 5 0/2 [0,1,1,2,2] [1,1,1,1,0] [0,0,0,0,1] 4* 5 4 1/5 [1,3,4,5] [1,0,0,0,0] [0,0,1,1,1] 5 3 3 2/4 [2,3,4] [0,0,0] [1,1,1] 6 3 3 2/4 [2,3,4] [0,0,0] [1,1,1] 7 4 4 3/5 [3,4,5,5] [0,0,0,0] [1,1,1,1] block #2 #cells: 3 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [1] [0] 1 1 1 0/0 [0] [1] [0] 2 5 5 1/3 [1,1,2,2,3] [0,0,0,0,0] [1,1,1,1,1] block #3 #cells: 1 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [0] [1] Value: true atlas> test_support_long(all_parameters_gamma (Sp(8,R),Sp(8,R).rho)) #params: 460 #blocks: 5 block #0 #cells: 35 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [1] [0] 1 1 1 0/0 [0] [1] [0] 2 7 7 0/5 [0,1,1,2,3,4,5] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 3 7 7 0/4 [0,0,1,1,2,3,4] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 4 8 8 0/4 [0,1,1,2,2,3,3,4] [1,1,1,1,1,1,1,1] [0,0,0,0,0,0,0,0] 5 7 7 0/5 [0,1,1,2,3,4,5] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 6* 8 5 2/6 [2,3,3,4,6] [1,1,1,1,0,0,0,0] [0,0,0,0,0,0,0,1] 7* 8 7 0/4 [0,1,1,2,2,2,3] [1,1,1,1,1,1,1,0] [0,0,0,0,0,0,0,0] 8 7 7 0/4 [0,0,1,1,2,3,4] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 9* 8 7 0/4 [0,1,1,2,2,2,3] [1,1,1,1,1,1,1,0] [0,0,0,0,0,0,0,0] 10 8 8 0/4 [0,1,1,2,2,3,3,4] [1,1,1,1,1,1,1,1] [0,0,0,0,0,0,0,0] 11 8 8 0/4 [0,1,2,2,3,3,4,4] [1,1,1,1,1,1,1,1] [0,0,0,0,0,0,0,0] 12 8 8 4/8 [4,4,5,5,6,6,7,8] [1,0,0,1,1,0,0,0] [0,1,1,0,0,1,1,1] 13 10 10 0/6 [0,1,2,3,3,4,4,5,5,6] [1,1,1,1,1,1,0,1,0,0] [0,0,0,0,0,0,1,0,1,1] 14 8 8 0/4 [0,1,2,2,3,3,4,4] [1,1,1,1,1,1,1,1] [0,0,0,0,0,0,0,0] 15 8 8 4/8 [4,4,5,5,6,6,7,8] [1,0,0,1,1,0,0,0] [0,1,1,0,0,1,1,1] 16 10 10 0/6 [0,1,2,3,3,4,4,5,5,6] [1,1,1,1,1,1,0,1,0,0] [0,0,0,0,0,0,1,0,1,1] 17* 8 6 2/6 [2,2,3,3,4,6] [1,1,1,1,1,0,0,0] [0,0,0,0,0,0,0,1] 18* 8 6 2/6 [2,2,3,3,4,6] [1,1,1,1,1,0,0,0] [0,0,0,0,0,0,0,1] 19* 6 2 3/7 [3,7] [1,0,0,0,0,0] [0,0,0,0,0,1] 20* 6 2 3/7 [3,7] [1,0,0,0,0,0] [0,0,0,0,0,1] 21 9 9 3/7 [3,3,4,4,5,5,5,6,7] [1,1,1,0,0,1,0,0,0] [0,0,0,1,1,0,1,1,1] 22 9 9 3/7 [3,3,4,4,5,5,5,6,7] [1,1,1,0,0,1,0,0,0] [0,0,0,1,1,0,1,1,1] 23* 8 7 6/10 [6,7,7,8,8,9,10] [0,0,0,0,0,0,0,0] [0,1,1,1,1,1,1,1] 24 9 9 5/7 [5,5,5,5,6,6,6,7,7] [1,1,0,1,1,0,0,0,0] [0,0,1,0,0,1,1,1,1] 25* 10 7 3/9 [3,6,7,7,8,8,9] [1,0,0,0,0,0,0,0,0,0] [0,0,0,0,1,1,1,1,1,1] 26 9 9 5/7 [5,5,5,5,6,6,6,7,7] [1,1,0,1,1,0,0,0,0] [0,0,1,0,0,1,1,1,1] 27* 10 7 3/9 [3,6,7,7,8,8,9] [1,0,0,0,0,0,0,0,0,0] [0,0,0,0,1,1,1,1,1,1] 28* 8 6 4/8 [4,6,7,7,8,8] [1,0,0,0,0,0,0,0] [0,0,0,1,1,1,1,1] 29* 10 8 4/10 [4,7,7,8,8,9,9,10] [1,0,0,0,0,0,0,0,0,0] [0,0,0,1,1,1,1,1,1,1] 30 10 10 6/10 [6,6,7,7,8,8,9,9,9,10] [0,0,0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1,1,1] 31 5 5 6/9 [6,7,7,8,9] [1,0,0,0,0] [0,1,1,1,1] 32 5 5 6/9 [6,7,7,8,9] [1,0,0,0,0] [0,1,1,1,1] 33 5 5 8/10 [8,9,9,10,10] [0,0,0,0,0] [1,1,1,1,1] 34 1 1 10/10 [10] [0] [1] block #1 #cells: 20 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [1] [0] 1 1 1 0/0 [0] [1] [0] 2 7 7 0/3 [0,1,1,1,2,2,3] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 3 7 7 0/6 [0,1,2,3,4,5,6] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 4 7 7 0/3 [0,1,1,1,2,2,3] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 5 7 7 0/6 [0,1,2,3,4,5,6] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 6 8 8 0/4 [0,1,1,2,2,2,3,4] [1,1,1,1,1,1,1,1] [0,0,0,0,0,0,0,0] 7 8 8 0/4 [0,1,1,2,2,2,3,4] [1,1,1,1,1,1,1,1] [0,0,0,0,0,0,0,0] 8* 8 4 2/6 [2,2,3,6] [1,1,1,0,0,0,0,0] [0,0,0,0,0,0,0,1] 9* 8 3 2/6 [2,6,6] [1,0,0,0,0,0,0,0] [0,0,0,0,0,0,1,1] 10* 8 3 2/6 [2,6,6] [1,0,0,0,0,0,0,0] [0,0,0,0,0,0,1,1] 11 8 8 2/6 [2,3,3,4,4,4,5,6] [1,1,0,0,1,0,0,0] [0,0,1,1,0,1,1,1] 12 8 8 2/6 [2,3,3,4,4,4,5,6] [1,1,0,0,1,0,0,0] [0,0,1,1,0,1,1,1] 13 9 9 3/7 [3,3,4,4,5,5,5,6,7] [1,0,0,1,1,1,0,0,0] [0,1,1,0,0,0,1,1,1] 14 9 9 3/7 [3,3,4,4,5,5,5,6,7] [1,0,0,1,1,1,0,0,0] [0,1,1,0,0,0,1,1,1] 15 6 6 5/9 [5,6,7,7,8,9] [0,0,0,0,0,0] [1,1,1,1,1,1] 16 10 10 3/8 [3,4,5,5,6,6,6,7,7,8] [0,0,0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1,1,1] 17 10 10 3/8 [3,4,5,5,6,6,6,7,7,8] [0,0,0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1,1,1] 18 9 9 7/9 [7,7,7,7,7,8,8,8,9] [0,0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1,1] 19 5 5 8/9 [8,8,8,9,9] [0,0,0,0,0] [1,1,1,1,1] block #2 #cells: 8 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [1] [0] 1 1 1 0/0 [0] [1] [0] 2 7 7 0/3 [0,1,1,2,2,2,3] [1,1,1,1,1,0,1] [0,0,0,0,0,1,0] 3 7 7 0/3 [0,1,1,2,2,2,3] [1,1,1,1,1,0,1] [0,0,0,0,0,1,0] 4* 7 5 1/7 [1,4,5,6,7] [1,0,0,0,0,0,0] [0,0,0,1,1,1,1] 5 8 8 2/6 [2,3,3,4,4,4,5,6] [0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1] 6 8 8 2/6 [2,3,3,4,4,4,5,6] [0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1] 7 9 9 3/7 [3,4,5,5,6,6,7,7,7] [0,0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1,1] block #3 #cells: 3 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [1] [0] 1 1 1 0/0 [0] [1] [0] 2 7 7 1/4 [1,1,2,2,3,3,4] [0,0,0,0,0,0,0] [1,1,1,1,1,1,1] block #4 #cells: 1 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [0] [1] Value: true atlas> set G=Sp(8,R) Variable G: RealForm (overriding previous instance, which had type RealForm) atlas> set all=all_parameters_gamma (G,G.rho) Variable all: [Param] (overriding previous instance, which had type [Param]) {Now we want to break "all" into HC cells.} atlas> set cells=W_cells_of (all) Error during analysis of expression at :83:10-26 Type error: Subexpression all at :83:22-25 has wrong type: found [Param] while Param was needed. Error in 'set' command at :83:0-27: Expression analysis failed Command 'set cells' not executed, nothing defined. {This didn't work; "W_cells_of" takes a single parameter and returns the cells of the block of p.} {So we'll just get some of the cells: those in the block of the trivial.} atlas> set cells=W_cells_of(G.trivial) Variable cells: [WCell] atlas> show(cells) cell #0 vertices: [0] node tau links 0 [] [] cell #1 vertices: [5] node tau links 0 [] [] cell #2 vertices: [1,16,25,58,72,106,149] node tau links 0 [1] [(1,1),(2,1)] 1 [0] [(0,1)] 2 [2] [(0,1),(3,1)] 3 [3] [(2,1),(4,1)] 4 [2] [(3,1),(5,1)] 5 [1] [(4,1),(6,1)] 6 [0] [(5,1)] cell #3 vertices: [4,7,21,28,49,77,113] node tau links 0 [2] [(2,1),(3,1)] 1 [0] [(2,1)] 2 [1] [(0,1),(1,1)] 3 [3] [(0,1),(4,1)] 4 [2] [(3,1),(5,1)] 5 [1] [(4,1),(6,1)] 6 [0] [(5,1)] cell #4 vertices: [2,20,30,39,51,62,79,111] node tau links 0 [0,2] [(1,1),(2,1),(5,1)] 1 [1] [(0,1),(3,1)] 2 [0,3] [(0,1),(3,1),(4,1),(7,1)] 3 [1,3] [(1,1),(2,1),(5,1),(6,1)] 4 [0,2] [(2,1),(5,1),(6,1)] 5 [2] [(0,1),(3,1),(4,1),(7,1)] 6 [1] [(3,1),(4,1)] 7 [3] [(2,1),(5,1)] cell #5 vertices: [3,17,24,57,70,104,147] node tau links 0 [1] [(1,1),(2,1)] 1 [0] [(0,1)] 2 [2] [(0,1),(3,1)] 3 [3] [(2,1),(4,1)] 4 [2] [(3,1),(5,1)] 5 [1] [(4,1),(6,1)] 6 [0] [(5,1)] cell #6 vertices: [36,61,68,94,102,130,137,190] node tau links 0 [0,2] [(1,1),(2,1),(6,1)] 1 [1] [(0,1),(4,1)] 2 [0,3] [(0,1),(3,1),(4,1),(7,1)] 3 [0,2] [(2,1),(5,1),(6,1)] 4 [1,3] [(1,1),(2,1),(5,1),(6,1)] 5 [1] [(3,1),(4,1)] 6 [2] [(0,1),(3,1),(4,1),(7,1)] 7 [3] [(2,1),(6,1)] cell #7 vertices: [6,18,29,37,42,50,64,95] node tau links 0 [1,2] [(1,1),(2,1)] 1 [0,2] [(0,1),(3,1),(4,1)] 2 [1,3] [(0,1),(3,1),(5,1),(7,1)] 3 [0,3] [(1,1),(2,1),(6,1)] 4 [0,1] [(1,1)] 5 [2] [(2,1),(6,1)] 6 [0,2] [(3,1),(5,1),(7,1)] 7 [1] [(2,1),(6,1)] cell #8 vertices: [10,12,23,32,53,81,117] node tau links 0 [2] [(2,1),(3,1)] 1 [0] [(2,1)] 2 [1] [(0,1),(1,1)] 3 [3] [(0,1),(4,1)] 4 [2] [(3,1),(5,1)] 5 [1] [(4,1),(6,1)] 6 [0] [(5,1)] cell #9 vertices: [8,19,31,38,44,52,65,96] node tau links 0 [1,2] [(1,1),(2,1)] 1 [0,2] [(0,1),(3,1),(4,1)] 2 [1,3] [(0,1),(3,1),(5,1),(7,1)] 3 [0,3] [(1,1),(2,1),(6,1)] 4 [0,1] [(1,1)] 5 [2] [(2,1),(6,1)] 6 [0,2] [(3,1),(5,1),(7,1)] 7 [1] [(2,1),(6,1)] cell #10 vertices: [9,22,33,40,55,63,83,112] node tau links 0 [0,2] [(1,1),(2,1),(5,1)] 1 [1] [(0,1),(3,1)] 2 [0,3] [(0,1),(3,1),(4,1),(7,1)] 3 [1,3] [(1,1),(2,1),(5,1),(6,1)] 4 [0,2] [(2,1),(5,1),(6,1)] 5 [2] [(0,1),(3,1),(4,1),(7,1)] 6 [1] [(3,1),(4,1)] 7 [3] [(2,1),(5,1)] cell #11 vertices: [11,26,47,59,74,91,108,123] node tau links 0 [0,1] [(1,1)] 1 [0,2] [(0,1),(2,1),(3,1)] 2 [1,2] [(1,1),(5,1)] 3 [0,3] [(1,1),(4,1),(5,1)] 4 [0,2] [(3,1),(6,1),(7,1)] 5 [1,3] [(2,1),(3,1),(6,1),(7,1)] 6 [1] [(4,1),(5,1)] 7 [2] [(4,1),(5,1)] cell #12 vertices: [98,115,133,157,170,188,202,226] node tau links 0 [1,2] [(2,1),(3,1)] 1 [0,1] [(2,1)] 2 [0,2] [(0,1),(1,1),(5,1)] 3 [1,3] [(0,1),(4,1),(5,1),(7,1)] 4 [2] [(3,1),(6,1)] 5 [0,3] [(2,1),(3,1),(6,1)] 6 [0,2] [(4,1),(5,1),(7,1)] 7 [1] [(3,1),(6,1)] cell #13 vertices: [13,34,54,73,82,107,118,142,150,181] node tau links 0 [0,1,2] [(1,1),(7,1)] 1 [0,1,3] [(0,1),(2,1),(5,1)] 2 [0,2] [(1,1),(3,1),(4,1)] 3 [0,2,3] [(2,1),(5,1),(9,1)] 4 [1,2] [(2,1),(5,1),(6,1)] 5 [1,3] [(1,1),(3,1),(4,1),(7,1),(8,1)] 6 [0,1,2] [(4,1),(8,1)] 7 [1,2] [(0,1),(5,1),(9,1)] 8 [0,1,3] [(5,1),(6,1),(9,1)] 9 [0,2] [(3,1),(7,1),(8,1)] cell #14 vertices: [14,27,48,60,76,92,110,124] node tau links 0 [0,1] [(1,1)] 1 [0,2] [(0,1),(2,1),(3,1)] 2 [1,2] [(1,1),(5,1)] 3 [0,3] [(1,1),(4,1),(5,1)] 4 [0,2] [(3,1),(6,1),(7,1)] 5 [1,3] [(2,1),(3,1),(6,1),(7,1)] 6 [1] [(4,1),(5,1)] 7 [2] [(4,1),(5,1)] cell #15 vertices: [99,119,134,158,173,189,205,229] node tau links 0 [1,2] [(2,1),(3,1)] 1 [0,1] [(2,1)] 2 [0,2] [(0,1),(1,1),(5,1)] 3 [1,3] [(0,1),(4,1),(5,1),(7,1)] 4 [2] [(3,1),(6,1)] 5 [0,3] [(2,1),(3,1),(6,1)] 6 [0,2] [(4,1),(5,1),(7,1)] 7 [1] [(3,1),(6,1)] cell #16 vertices: [15,35,56,75,84,109,120,144,152,183] node tau links 0 [0,1,2] [(1,1),(7,1)] 1 [0,1,3] [(0,1),(2,1),(5,1)] 2 [0,2] [(1,1),(3,1),(4,1)] 3 [0,2,3] [(2,1),(5,1),(9,1)] 4 [1,2] [(2,1),(5,1),(6,1)] 5 [1,3] [(1,1),(3,1),(4,1),(7,1),(8,1)] 6 [0,1,2] [(4,1),(8,1)] 7 [1,2] [(0,1),(5,1),(9,1)] 8 [0,1,3] [(5,1),(6,1),(9,1)] 9 [0,2] [(3,1),(7,1),(8,1)] cell #17 vertices: [41,45,85,89,121,125,161,193] node tau links 0 [0,1] [(2,1)] 1 [1,2] [(2,1),(3,1)] 2 [0,2] [(0,1),(1,1),(5,1)] 3 [1,3] [(1,1),(4,1),(5,1),(7,1)] 4 [2] [(3,1),(6,1)] 5 [0,3] [(2,1),(3,1),(6,1)] 6 [0,2] [(4,1),(5,1),(7,1)] 7 [1] [(3,1),(6,1)] cell #18 vertices: [43,46,86,90,122,126,162,194] node tau links 0 [0,1] [(2,1)] 1 [1,2] [(2,1),(3,1)] 2 [0,2] [(0,1),(1,1),(5,1)] 3 [1,3] [(1,1),(4,1),(5,1),(7,1)] 4 [2] [(3,1),(6,1)] 5 [0,3] [(2,1),(3,1),(6,1)] 6 [0,2] [(4,1),(5,1),(7,1)] 7 [1] [(3,1),(6,1)] cell #19 vertices: [66,100,135,155,186,216] node tau links 0 [0,1,3] [(1,1),(4,1)] 1 [0,2] [(0,1),(2,1),(3,1),(5,1)] 2 [1,2] [(1,1),(4,1)] 3 [0,3] [(1,1),(4,1)] 4 [1,3] [(0,1),(2,1),(3,1),(5,1)] 5 [2] [(1,1),(4,1)] cell #20 vertices: [67,101,136,156,187,217] node tau links 0 [0,1,3] [(1,1),(4,1)] 1 [0,2] [(0,1),(2,1),(3,1),(5,1)] 2 [1,2] [(1,1),(4,1)] 3 [0,3] [(1,1),(4,1)] 4 [1,3] [(0,1),(2,1),(3,1),(5,1)] 5 [2] [(1,1),(4,1)] cell #21 vertices: [69,80,103,116,132,138,146,177,207] node tau links 0 [2,3] [(2,1)] 1 [1,2] [(2,1),(3,1)] 2 [1,3] [(0,1),(1,1),(5,1),(6,1)] 3 [0,2] [(1,1),(4,1),(6,1)] 4 [0,1] [(3,1)] 5 [1,2] [(2,1),(7,1)] 6 [0,3] [(2,1),(3,1),(7,1)] 7 [0,2] [(5,1),(6,1),(8,1)] 8 [0,1] [(7,1)] cell #22 vertices: [71,78,105,114,131,140,148,179,209] node tau links 0 [2,3] [(2,1)] 1 [1,2] [(2,1),(3,1)] 2 [1,3] [(0,1),(1,1),(5,1),(6,1)] 3 [0,2] [(1,1),(4,1),(6,1)] 4 [0,1] [(3,1)] 5 [1,2] [(2,1),(7,1)] 6 [0,3] [(2,1),(3,1),(7,1)] 7 [0,2] [(5,1),(6,1),(8,1)] 8 [0,1] [(7,1)] cell #23 vertices: [166,168,198,200,232,234,249,255] node tau links 0 [1,2] [(2,1),(3,1)] 1 [0,1] [(2,1)] 2 [0,2] [(0,1),(1,1),(4,1)] 3 [1,3] [(0,1),(4,1),(5,1),(7,1)] 4 [0,3] [(2,1),(3,1),(6,1)] 5 [2] [(3,1),(6,1)] 6 [0,2] [(4,1),(5,1),(7,1)] 7 [1] [(3,1),(6,1)] cell #24 vertices: [139,143,151,159,171,178,182,203,208] node tau links 0 [1,2] [(4,1),(5,1)] 1 [1,2] [(4,1),(6,1)] 2 [0,1] [(6,1)] 3 [2,3] [(4,1)] 4 [1,3] [(0,1),(1,1),(3,1),(7,1)] 5 [0,2] [(0,1),(7,1),(8,1)] 6 [0,2] [(1,1),(2,1),(7,1)] 7 [0,3] [(4,1),(5,1),(6,1)] 8 [0,1] [(5,1)] cell #25 vertices: [87,127,163,191,195,212,218,227,237,242] node tau links 0 [0,1,2] [(1,1),(8,1)] 1 [0,1,3] [(0,1),(2,1),(6,1)] 2 [0,2] [(1,1),(3,1),(4,1)] 3 [0,2,3] [(2,1),(6,1),(9,1)] 4 [1,2] [(2,1),(5,1),(6,1)] 5 [0,1,2] [(4,1),(7,1)] 6 [1,3] [(1,1),(3,1),(4,1),(7,1),(8,1)] 7 [0,1,3] [(5,1),(6,1),(9,1)] 8 [1,2] [(0,1),(6,1),(9,1)] 9 [0,2] [(3,1),(7,1),(8,1)] cell #26 vertices: [141,145,153,160,174,180,184,206,210] node tau links 0 [1,2] [(4,1),(5,1)] 1 [1,2] [(4,1),(6,1)] 2 [0,1] [(6,1)] 3 [2,3] [(4,1)] 4 [1,3] [(0,1),(1,1),(3,1),(7,1)] 5 [0,2] [(0,1),(7,1),(8,1)] 6 [0,2] [(1,1),(2,1),(7,1)] 7 [0,3] [(4,1),(5,1),(6,1)] 8 [0,1] [(5,1)] cell #27 vertices: [88,128,164,192,196,214,219,230,238,245] node tau links 0 [0,1,2] [(1,1),(8,1)] 1 [0,1,3] [(0,1),(2,1),(6,1)] 2 [0,2] [(1,1),(3,1),(4,1)] 3 [0,2,3] [(2,1),(6,1),(9,1)] 4 [1,2] [(2,1),(5,1),(6,1)] 5 [0,1,2] [(4,1),(7,1)] 6 [1,3] [(1,1),(3,1),(4,1),(7,1),(8,1)] 7 [0,1,3] [(5,1),(6,1),(9,1)] 8 [1,2] [(0,1),(6,1),(9,1)] 9 [0,2] [(3,1),(7,1),(8,1)] cell #28 vertices: [93,129,165,167,197,199,231,233] node tau links 0 [0,2,3] [(1,1),(4,1)] 1 [1,3] [(0,1),(2,1),(3,1)] 2 [1,2] [(1,1),(4,1),(5,1)] 3 [0,1,3] [(1,1),(4,1)] 4 [0,2] [(0,1),(2,1),(3,1),(6,1)] 5 [1,3] [(2,1),(6,1),(7,1)] 6 [0,3] [(4,1),(5,1)] 7 [2,3] [(5,1)] cell #29 vertices: [97,154,185,215,222,223,239,246,251,253] node tau links 0 [0,1,2] [(1,1),(8,1)] 1 [0,1,3] [(0,1),(2,1),(6,1)] 2 [0,2] [(1,1),(3,1),(4,1)] 3 [1,2] [(2,1),(5,1),(6,1)] 4 [0,2,3] [(2,1),(6,1),(9,1)] 5 [0,1,2] [(3,1),(7,1)] 6 [1,3] [(1,1),(3,1),(4,1),(7,1),(8,1)] 7 [0,1,3] [(5,1),(6,1),(9,1)] 8 [1,2] [(0,1),(6,1),(9,1)] 9 [0,2] [(4,1),(7,1),(8,1)] cell #30 vertices: [175,176,220,221,235,236,241,244,248,254] node tau links 0 [0,1,2] [(2,1),(7,1)] 1 [0,1,2] [(3,1),(6,1)] 2 [0,1,3] [(0,1),(4,1),(9,1)] 3 [0,1,3] [(1,1),(5,1),(9,1)] 4 [0,2] [(2,1),(6,1),(8,1)] 5 [0,2] [(3,1),(7,1),(8,1)] 6 [1,2] [(1,1),(4,1),(9,1)] 7 [1,2] [(0,1),(5,1),(9,1)] 8 [0,2,3] [(4,1),(5,1),(9,1)] 9 [1,3] [(2,1),(3,1),(6,1),(7,1),(8,1)] cell #31 vertices: [169,201,211,225,240] node tau links 0 [1,2,3] [(1,1)] 1 [0,2,3] [(0,1),(3,1)] 2 [0,1,2] [(3,1)] 3 [0,1,3] [(1,1),(2,1),(4,1)] 4 [0,1,2] [(3,1)] cell #32 vertices: [172,204,213,228,243] node tau links 0 [1,2,3] [(1,1)] 1 [0,2,3] [(0,1),(3,1)] 2 [0,1,2] [(3,1)] 3 [0,1,3] [(1,1),(2,1),(4,1)] 4 [0,1,2] [(3,1)] cell #33 vertices: [224,247,250,256,257] node tau links 0 [0,1,2] [(1,1)] 1 [0,1,3] [(0,1),(3,1),(4,1)] 2 [1,2,3] [(3,1)] 3 [0,2,3] [(1,1),(2,1)] 4 [0,1,2] [(1,1)] cell #34 vertices: [252] node tau links 0 [0,1,2,3] [] atlas> set cell=cells[9] Variable cell: WCell atlas> #cell Value: 8 atlas> cell Value: ([8,19,31,38,44,52,65,96],(simply connected root datum of Lie type 'C4',[([1,2],[(1,1),(2,1)]),([0,2],[(0,1),(3,1),(4,1)]),([1,3],[(0,1),(3,1),(5,1),(7,1)]),([0,3],[(1,1),(2,1),(6,1)]),([0,1],[(1,1)]),([2],[(2,1),(6,1)]),([0,2],[(3,1),(5,1),(7,1)]),([1],[(2,1),(6,1)])]),[[[(0,1),(1,1)],[(1,-1)],[(2,1),(3,1)],[(3,-1)],[(4,-1)],[(5,1),(6,1)],[(6,-1)],[(7,1),(6,1)]],[[(0,-1)],[(1,1),(0,1),(4,1)],[(2,-1)],[(3,1),(2,1)],[(4,-1)],[(5,1),(2,1)],[(6,1),(7,1)],[(7,-1)]],[[(0,-1)],[(1,-1)],[(2,1),(0,1),(5,1)],[(3,1),(1,1),(6,1)],[(4,1),(1,1)],[(5,-1)],[(6,-1)],[(7,1),(6,1)]],[[(0,1),(2,1)],[(1,1),(3,1)],[(2,-1)],[(3,-1)],[(4,1)],[(5,1),(2,1)],[(6,1),(3,1)],[(7,1),(2,1)]]]) atlas> test_support_long (parameters(cell)) Error in expression parameters(cell) at :90:19-35 Failed to match 'parameters' with argument type WCell Expression analysis failed Evaluation aborted. atlas> whattype parameters? Overloaded instances of 'parameters' ([Param],WCell)->[Param] ([Param],[WCell])->[Param] [([Param],[WCell])]->[Param] [(int,int,Param)]->[Param] ([([Param],[WCell])],[(int,int,Param)])->[Param] [([([Param],[WCell])],[(int,int,Param)])]->[Param] ([int],[Param])->[int] ([*],[Param])->[int] {Each Wcell records (only) the numbers of the block elements in the block from which it was constructed. THERE IS NO WAY TO RECOVER THE PARAMETERS THAT MADE A WCell FROM THE WCELL! The function "parameters" expects to be handed (B,C), with B the list of parameters in a block, and C a cell constructed from B. In this case it returns the list of parameters in C. IF INSTEAD YOU DO parameters(L,C) WITH L A LONGER LIST OF MORE PARAMETERS, THE ANSWER WILL BE NONSENSE. Here is an example. atlas> set G=Sp(4,R) Variable G: RealForm atlas> set B=block_of(G.trivial) Variable B: [Param] atlas> set cells=W_cells_of(G.trivial) Variable cells: [WCell] atlas> show(cells[3]) vertices: [3,6,8] node tau links 0 [0] [(1,1)] 1 [1] [(0,1),(2,1)] 2 [0] [(1,1)] atlas> parameters(B,cells[3]) Value: [final parameter(x=3,lambda=[2,1]/1,nu=[0,0]/1),final parameter(x=6,lambda=[2,1]/1,nu=[0,1]/1),final parameter(x=8,lambda=[2,1]/1,nu=[2,0]/1)] {This is the right answer: these are the three parameters of which cells[3] is comprised, namely elements 3, 6, and 8 of the block B.} atlas> parameters(all_parameters_gamma(G,G.rho),cells[3]) Value: [final parameter(x=10,lambda=[3,2]/1,nu=[2,1]/1),final parameter(x=8,lambda=[3,1]/1,nu=[2,0]/1),final parameter(x=7,lambda=[3,1]/1,nu=[2,0]/1)] {This is nonsense: it's elements 3, 6, and 8 of the all_parameters list; none of them is in cells[3].} atlas> test_support_long (parameters(all,cell)) #params: 8 #blocks: 3 block #0 #cells: 8 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [1] [0] 1 1 1 0/0 [0] [1] [0] 2 7 7 0/3 [0,1,1,2,2,2,3] [1,1,1,1,1,0,1] [0,0,0,0,0,1,0] 3 7 7 0/3 [0,1,1,2,2,2,3] [1,1,1,1,1,0,1] [0,0,0,0,0,1,0] 4* 7 5 1/7 [1,4,5,6,7] [1,0,0,0,0,0,0] [0,0,0,1,1,1,1] 5 8 8 2/6 [2,3,3,4,4,4,5,6] [0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1] 6 8 8 2/6 [2,3,3,4,4,4,5,6] [0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1] 7 9 9 3/7 [3,4,5,5,6,6,7,7,7] [0,0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1,1] block #1 #cells: 35 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [1] [0] 1 1 1 0/0 [0] [1] [0] 2 7 7 0/5 [0,1,1,2,3,4,5] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 3 7 7 0/4 [0,0,1,1,2,3,4] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 4 8 8 0/4 [0,1,1,2,2,3,3,4] [1,1,1,1,1,1,1,1] [0,0,0,0,0,0,0,0] 5 7 7 0/5 [0,1,1,2,3,4,5] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 6* 8 5 2/6 [2,3,3,4,6] [1,1,1,1,0,0,0,0] [0,0,0,0,0,0,0,1] 7* 8 7 0/4 [0,1,1,2,2,2,3] [1,1,1,1,1,1,1,0] [0,0,0,0,0,0,0,0] 8 7 7 0/4 [0,0,1,1,2,3,4] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 9* 8 7 0/4 [0,1,1,2,2,2,3] [1,1,1,1,1,1,1,0] [0,0,0,0,0,0,0,0] 10 8 8 0/4 [0,1,1,2,2,3,3,4] [1,1,1,1,1,1,1,1] [0,0,0,0,0,0,0,0] 11 8 8 0/4 [0,1,2,2,3,3,4,4] [1,1,1,1,1,1,1,1] [0,0,0,0,0,0,0,0] 12 8 8 4/8 [4,4,5,5,6,6,7,8] [1,0,0,1,1,0,0,0] [0,1,1,0,0,1,1,1] 13 10 10 0/6 [0,1,2,3,3,4,4,5,5,6] [1,1,1,1,1,1,0,1,0,0] [0,0,0,0,0,0,1,0,1,1] 14 8 8 0/4 [0,1,2,2,3,3,4,4] [1,1,1,1,1,1,1,1] [0,0,0,0,0,0,0,0] 15 8 8 4/8 [4,4,5,5,6,6,7,8] [1,0,0,1,1,0,0,0] [0,1,1,0,0,1,1,1] 16 10 10 0/6 [0,1,2,3,3,4,4,5,5,6] [1,1,1,1,1,1,0,1,0,0] [0,0,0,0,0,0,1,0,1,1] 17* 8 6 2/6 [2,2,3,3,4,6] [1,1,1,1,1,0,0,0] [0,0,0,0,0,0,0,1] 18* 8 6 2/6 [2,2,3,3,4,6] [1,1,1,1,1,0,0,0] [0,0,0,0,0,0,0,1] 19* 6 2 3/7 [3,7] [1,0,0,0,0,0] [0,0,0,0,0,1] 20* 6 2 3/7 [3,7] [1,0,0,0,0,0] [0,0,0,0,0,1] 21 9 9 3/7 [3,3,4,4,5,5,5,6,7] [1,1,1,0,0,1,0,0,0] [0,0,0,1,1,0,1,1,1] 22 9 9 3/7 [3,3,4,4,5,5,5,6,7] [1,1,1,0,0,1,0,0,0] [0,0,0,1,1,0,1,1,1] 23* 8 7 6/10 [6,7,7,8,8,9,10] [0,0,0,0,0,0,0,0] [0,1,1,1,1,1,1,1] 24 9 9 5/7 [5,5,5,5,6,6,6,7,7] [1,1,0,1,1,0,0,0,0] [0,0,1,0,0,1,1,1,1] 25* 10 7 3/9 [3,6,7,7,8,8,9] [1,0,0,0,0,0,0,0,0,0] [0,0,0,0,1,1,1,1,1,1] 26 9 9 5/7 [5,5,5,5,6,6,6,7,7] [1,1,0,1,1,0,0,0,0] [0,0,1,0,0,1,1,1,1] 27* 10 7 3/9 [3,6,7,7,8,8,9] [1,0,0,0,0,0,0,0,0,0] [0,0,0,0,1,1,1,1,1,1] 28* 8 6 4/8 [4,6,7,7,8,8] [1,0,0,0,0,0,0,0] [0,0,0,1,1,1,1,1] 29* 10 8 4/10 [4,7,7,8,8,9,9,10] [1,0,0,0,0,0,0,0,0,0] [0,0,0,1,1,1,1,1,1,1] 30 10 10 6/10 [6,6,7,7,8,8,9,9,9,10] [0,0,0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1,1,1] 31 5 5 6/9 [6,7,7,8,9] [1,0,0,0,0] [0,1,1,1,1] 32 5 5 6/9 [6,7,7,8,9] [1,0,0,0,0] [0,1,1,1,1] 33 5 5 8/10 [8,9,9,10,10] [0,0,0,0,0] [1,1,1,1,1] 34 1 1 10/10 [10] [0] [1] block #2 #cells: 20 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [1] [0] 1 1 1 0/0 [0] [1] [0] 2 7 7 0/3 [0,1,1,1,2,2,3] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 3 7 7 0/6 [0,1,2,3,4,5,6] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 4 7 7 0/3 [0,1,1,1,2,2,3] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 5 7 7 0/6 [0,1,2,3,4,5,6] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 6 8 8 0/4 [0,1,1,2,2,2,3,4] [1,1,1,1,1,1,1,1] [0,0,0,0,0,0,0,0] 7 8 8 0/4 [0,1,1,2,2,2,3,4] [1,1,1,1,1,1,1,1] [0,0,0,0,0,0,0,0] 8* 8 4 2/6 [2,2,3,6] [1,1,1,0,0,0,0,0] [0,0,0,0,0,0,0,1] 9* 8 3 2/6 [2,6,6] [1,0,0,0,0,0,0,0] [0,0,0,0,0,0,1,1] 10* 8 3 2/6 [2,6,6] [1,0,0,0,0,0,0,0] [0,0,0,0,0,0,1,1] 11 8 8 2/6 [2,3,3,4,4,4,5,6] [1,1,0,0,1,0,0,0] [0,0,1,1,0,1,1,1] 12 8 8 2/6 [2,3,3,4,4,4,5,6] [1,1,0,0,1,0,0,0] [0,0,1,1,0,1,1,1] 13 9 9 3/7 [3,3,4,4,5,5,5,6,7] [1,0,0,1,1,1,0,0,0] [0,1,1,0,0,0,1,1,1] 14 9 9 3/7 [3,3,4,4,5,5,5,6,7] [1,0,0,1,1,1,0,0,0] [0,1,1,0,0,0,1,1,1] 15 6 6 5/9 [5,6,7,7,8,9] [0,0,0,0,0,0] [1,1,1,1,1,1] 16 10 10 3/8 [3,4,5,5,6,6,6,7,7,8] [0,0,0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1,1,1] 17 10 10 3/8 [3,4,5,5,6,6,6,7,7,8] [0,0,0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1,1,1] 18 9 9 7/9 [7,7,7,7,7,8,8,8,9] [0,0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1,1] 19 5 5 8/9 [8,8,8,9,9] [0,0,0,0,0] [1,1,1,1,1] Value: true atlas> set list=parameters(all,cell) Variable list: [Param] (overriding previous instance, which had type [RealForm]) atlas> #list Value: 8 atlas> for p in list do prints(p) od final parameter(x=200,lambda=[4,3,2,2]/1,nu=[4,3,2,1]/1) final parameter(x=199,lambda=[4,3,3,2]/1,nu=[7,7,4,2]/2) final parameter(x=196,lambda=[5,4,2,1]/1,nu=[4,3,2,0]/1) final parameter(x=195,lambda=[4,4,2,1]/1,nu=[4,3,2,0]/1) final parameter(x=194,lambda=[4,3,2,1]/1,nu=[7,7,3,3]/2) final parameter(x=190,lambda=[5,3,2,1]/1,nu=[8,5,5,0]/2) final parameter(x=187,lambda=[4,3,2,2]/1,nu=[4,3,0,1]/1) final parameter(x=176,lambda=[4,4,2,1]/1,nu=[4,3,0,0]/1) Value: [(),(),(),(),(),(),(),()] atlas> for p in list do prints(p, " ", p.length) od final parameter(x=200,lambda=[4,3,2,2]/1,nu=[4,3,2,1]/1) 7 final parameter(x=199,lambda=[4,3,3,2]/1,nu=[7,7,4,2]/2) 9 final parameter(x=196,lambda=[5,4,2,1]/1,nu=[4,3,2,0]/1) 9 final parameter(x=195,lambda=[4,4,2,1]/1,nu=[4,3,2,0]/1) 6 final parameter(x=194,lambda=[4,3,2,1]/1,nu=[7,7,3,3]/2) 8 final parameter(x=190,lambda=[5,3,2,1]/1,nu=[8,5,5,0]/2) 7 final parameter(x=187,lambda=[4,3,2,2]/1,nu=[4,3,0,1]/1) 7 final parameter(x=176,lambda=[4,4,2,1]/1,nu=[4,3,0,0]/1) 4 Value: [(),(),(),(),(),(),(),()] atlas> set G=SL(4,C) Variable G: RealForm (overriding previous instance, which had type RealForm) atlas> test_support_long (all_parameters_gamma (G,G.rho)) #params: 24 #blocks: 1 block #0 #cells: 5 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [1] [0] 1 9 9 1/3 [1,1,1,2,2,2,2,3,3] [1,1,1,1,1,1,1,0,0] [0,0,0,0,0,0,0,1,1] 2* 4 2 2/4 [2,4] [1,0,0,0] [0,0,0,1] 3 9 9 3/5 [3,3,4,4,4,4,5,5,5] [1,1,0,0,0,0,0,0,0] [0,0,1,1,1,1,1,1,1] 4 1 1 6/6 [6] [0] [1] Value: true atlas> set G=SL(6,C) Variable G: RealForm (overriding previous instance, which had type RealForm) atlas> test_support_long (all_parameters_gamma (G,G.rho)) #params: 720 #blocks: 1 block #0 #cells: 11 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [1] [0] 1 25 25 1/5 [1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,5,5] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0] [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1] 2* 81 61 2/8 [2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,8,8] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0,0,0] [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1] 3* 100 94 3/9 [3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0] [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1] 4* 25 8 3/9 [3,4,4,4,4,5,5,9] [1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1] 5* 256 140 4/11 [4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,1,0,0,0,1,1,0,1,1,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0,1,1,0,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] 6* 100 94 6/12 [6,6,6,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12] [1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,1,1,1,1,1,0,1,1,0,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] 7* 25 8 6/12 [6,10,10,11,11,11,11,12] [1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,1,1,1,1] 8* 81 61 7/13 [7,7,9,9,9,9,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13] [1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] [0,0,0,0,0,0,0,0,1,0,0,1,0,1,0,1,0,0,0,1,0,0,1,0,1,0,1,1,0,0,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] 9 25 25 10/14 [10,10,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,13,14,14,14,14,14] [1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] [0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] 10 1 1 15/15 [15] [0] [1] Value: true atlas> set G=SL(5,C) Variable G: RealForm (overriding previous instance, which had type RealForm) atlas> test_support_long (all_parameters_gamma (G,G.rho)) #params: 120 #blocks: 1 block #0 #cells: 7 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [1] [0] 1 16 16 1/4 [1,1,1,1,2,2,2,2,2,2,3,3,3,3,4,4] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0] [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1] 2* 25 15 2/6 [2,2,2,3,3,3,3,3,3,3,3,4,4,6,6] [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1] 3* 36 34 3/7 [3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7] [1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0] [0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,0,1,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1] 4* 25 15 4/8 [4,4,6,6,7,7,7,7,7,7,7,7,8,8,8] [1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] [0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1] 5 16 16 6/9 [6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9] [1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0] [0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1] 6 1 1 10/10 [10] [0] [1] Value: true atlas> test_support_long(all_parameters_gamma (Sp(8,R),Sp(8,R).rho)) #params: 460 #blocks: 5 block #0 #cells: 35 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [1] [0] 1 1 1 0/0 [0] [1] [0] 2 7 7 0/5 [0,1,1,2,3,4,5] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 3 7 7 0/4 [0,0,1,1,2,3,4] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 4 8 8 0/4 [0,1,1,2,2,3,3,4] [1,1,1,1,1,1,1,1] [0,0,0,0,0,0,0,0] 5 7 7 0/5 [0,1,1,2,3,4,5] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 6* 8 5 2/6 [2,3,3,4,6] [1,1,1,1,0,0,0,0] [0,0,0,0,0,0,0,1] 7* 8 7 0/4 [0,1,1,2,2,2,3] [1,1,1,1,1,1,1,0] [0,0,0,0,0,0,0,0] 8 7 7 0/4 [0,0,1,1,2,3,4] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 9* 8 7 0/4 [0,1,1,2,2,2,3] [1,1,1,1,1,1,1,0] [0,0,0,0,0,0,0,0] 10 8 8 0/4 [0,1,1,2,2,3,3,4] [1,1,1,1,1,1,1,1] [0,0,0,0,0,0,0,0] 11 8 8 0/4 [0,1,2,2,3,3,4,4] [1,1,1,1,1,1,1,1] [0,0,0,0,0,0,0,0] 12 8 8 4/8 [4,4,5,5,6,6,7,8] [1,0,0,1,1,0,0,0] [0,1,1,0,0,1,1,1] 13 10 10 0/6 [0,1,2,3,3,4,4,5,5,6] [1,1,1,1,1,1,0,1,0,0] [0,0,0,0,0,0,1,0,1,1] 14 8 8 0/4 [0,1,2,2,3,3,4,4] [1,1,1,1,1,1,1,1] [0,0,0,0,0,0,0,0] 15 8 8 4/8 [4,4,5,5,6,6,7,8] [1,0,0,1,1,0,0,0] [0,1,1,0,0,1,1,1] 16 10 10 0/6 [0,1,2,3,3,4,4,5,5,6] [1,1,1,1,1,1,0,1,0,0] [0,0,0,0,0,0,1,0,1,1] 17* 8 6 2/6 [2,2,3,3,4,6] [1,1,1,1,1,0,0,0] [0,0,0,0,0,0,0,1] 18* 8 6 2/6 [2,2,3,3,4,6] [1,1,1,1,1,0,0,0] [0,0,0,0,0,0,0,1] 19* 6 2 3/7 [3,7] [1,0,0,0,0,0] [0,0,0,0,0,1] 20* 6 2 3/7 [3,7] [1,0,0,0,0,0] [0,0,0,0,0,1] 21 9 9 3/7 [3,3,4,4,5,5,5,6,7] [1,1,1,0,0,1,0,0,0] [0,0,0,1,1,0,1,1,1] 22 9 9 3/7 [3,3,4,4,5,5,5,6,7] [1,1,1,0,0,1,0,0,0] [0,0,0,1,1,0,1,1,1] 23* 8 7 6/10 [6,7,7,8,8,9,10] [0,0,0,0,0,0,0,0] [0,1,1,1,1,1,1,1] 24 9 9 5/7 [5,5,5,5,6,6,6,7,7] [1,1,0,1,1,0,0,0,0] [0,0,1,0,0,1,1,1,1] 25* 10 7 3/9 [3,6,7,7,8,8,9] [1,0,0,0,0,0,0,0,0,0] [0,0,0,0,1,1,1,1,1,1] 26 9 9 5/7 [5,5,5,5,6,6,6,7,7] [1,1,0,1,1,0,0,0,0] [0,0,1,0,0,1,1,1,1] 27* 10 7 3/9 [3,6,7,7,8,8,9] [1,0,0,0,0,0,0,0,0,0] [0,0,0,0,1,1,1,1,1,1] 28* 8 6 4/8 [4,6,7,7,8,8] [1,0,0,0,0,0,0,0] [0,0,0,1,1,1,1,1] 29* 10 8 4/10 [4,7,7,8,8,9,9,10] [1,0,0,0,0,0,0,0,0,0] [0,0,0,1,1,1,1,1,1,1] 30 10 10 6/10 [6,6,7,7,8,8,9,9,9,10] [0,0,0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1,1,1] 31 5 5 6/9 [6,7,7,8,9] [1,0,0,0,0] [0,1,1,1,1] 32 5 5 6/9 [6,7,7,8,9] [1,0,0,0,0] [0,1,1,1,1] 33 5 5 8/10 [8,9,9,10,10] [0,0,0,0,0] [1,1,1,1,1] 34 1 1 10/10 [10] [0] [1] block #1 #cells: 20 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [1] [0] 1 1 1 0/0 [0] [1] [0] 2 7 7 0/3 [0,1,1,1,2,2,3] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 3 7 7 0/6 [0,1,2,3,4,5,6] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 4 7 7 0/3 [0,1,1,1,2,2,3] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 5 7 7 0/6 [0,1,2,3,4,5,6] [1,1,1,1,1,1,0] [0,0,0,0,0,0,1] 6 8 8 0/4 [0,1,1,2,2,2,3,4] [1,1,1,1,1,1,1,1] [0,0,0,0,0,0,0,0] 7 8 8 0/4 [0,1,1,2,2,2,3,4] [1,1,1,1,1,1,1,1] [0,0,0,0,0,0,0,0] 8* 8 4 2/6 [2,2,3,6] [1,1,1,0,0,0,0,0] [0,0,0,0,0,0,0,1] 9* 8 3 2/6 [2,6,6] [1,0,0,0,0,0,0,0] [0,0,0,0,0,0,1,1] 10* 8 3 2/6 [2,6,6] [1,0,0,0,0,0,0,0] [0,0,0,0,0,0,1,1] 11 8 8 2/6 [2,3,3,4,4,4,5,6] [1,1,0,0,1,0,0,0] [0,0,1,1,0,1,1,1] 12 8 8 2/6 [2,3,3,4,4,4,5,6] [1,1,0,0,1,0,0,0] [0,0,1,1,0,1,1,1] 13 9 9 3/7 [3,3,4,4,5,5,5,6,7] [1,0,0,1,1,1,0,0,0] [0,1,1,0,0,0,1,1,1] 14 9 9 3/7 [3,3,4,4,5,5,5,6,7] [1,0,0,1,1,1,0,0,0] [0,1,1,0,0,0,1,1,1] 15 6 6 5/9 [5,6,7,7,8,9] [0,0,0,0,0,0] [1,1,1,1,1,1] 16 10 10 3/8 [3,4,5,5,6,6,6,7,7,8] [0,0,0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1,1,1] 17 10 10 3/8 [3,4,5,5,6,6,6,7,7,8] [0,0,0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1,1,1] 18 9 9 7/9 [7,7,7,7,7,8,8,8,9] [0,0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1,1] 19 5 5 8/9 [8,8,8,9,9] [0,0,0,0,0] [1,1,1,1,1] block #2 #cells: 8 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [1] [0] 1 1 1 0/0 [0] [1] [0] 2 7 7 0/3 [0,1,1,2,2,2,3] [1,1,1,1,1,0,1] [0,0,0,0,0,1,0] 3 7 7 0/3 [0,1,1,2,2,2,3] [1,1,1,1,1,0,1] [0,0,0,0,0,1,0] 4* 7 5 1/7 [1,4,5,6,7] [1,0,0,0,0,0,0] [0,0,0,1,1,1,1] 5 8 8 2/6 [2,3,3,4,4,4,5,6] [0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1] 6 8 8 2/6 [2,3,3,4,4,4,5,6] [0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1] 7 9 9 3/7 [3,4,5,5,6,6,7,7,7] [0,0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1,1] block #3 #cells: 3 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [1] [0] 1 1 1 0/0 [0] [1] [0] 2 7 7 1/4 [1,1,2,2,3,3,4] [0,0,0,0,0,0,0] [1,1,1,1,1,1,1] block #4 #cells: 1 i #cell #proper min/max lengths which which_dual 0 1 1 0/0 [0] [0] [1] Value: true atlas> test_support_long(all_parameters_gamma (Sp(3,1),Sp(3,1).rho)) #params: 16 #blocks: 1 block #0 #cells: 3 i #cell #proper min/max lengths which which_dual 0 8 8 0/3 [0,0,0,1,1,2,2,3] [1,1,1,1,1,1,1,1] [0,0,0,0,0,0,0,0] 1* 7 5 0/5 [0,1,2,3,4] [1,1,1,1,1,0,0] [0,0,0,0,0,0,0] 2 1 1 6/6 [6] [0] [1] Value: true atlas> test_support_long(all_parameters_gamma (Sp(3,2),Sp(3,2).rho)) #params: 130 #blocks: 1 block #0 #cells: 8 i #cell #proper min/max lengths which which_dual 0 10 10 0/3 [0,0,0,0,1,1,1,1,2,3] [1,1,1,1,1,1,1,1,1,1] [0,0,0,0,0,0,0,0,0,0] 1* 35 33 0/5 [0,0,0,0,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,5] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0] [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] 2* 15 12 0/6 [0,1,2,2,3,3,4,4,4,4,5,5] [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0] [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] 3* 30 20 0/8 [0,1,2,2,2,3,3,3,3,4,4,4,4,4,5,5,5,6,6,7] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] 4* 15 10 4/9 [4,4,5,5,6,6,7,8,8,9] [1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] [0,0,0,0,0,0,0,0,0,0,0,0,1,1,1] 5* 15 4 5/11 [5,6,10,11] [1,1,0,0,0,0,0,0,0,0,0,0,0,0,0] [0,0,0,0,0,0,0,0,0,0,0,0,1,0,1] 6* 9 7 6/11 [6,8,8,9,10,10,11] [1,0,1,0,0,0,0,0,0] [0,0,0,1,1,0,1,1,1] 7 1 1 12/12 [12] [0] [1] Value: true atlas> RootDatum) Defined sp_product: (int->RootDatum) Added definition [2] of sp_product: (int,[ratvec]->RootDatum) Added definition [3] of sp_product: (int,[vec]->RootDatum) Defined all_vectors: (int->[vec]) Defined sp_products: (int->[RealForm]) Defined sp_products_long: (int->[([vec],RealForm)]) Defined sp_orbits: (int->[(RealForm,ComplexNilpotent)]) Defined sp_character_table: (int->CharacterTable) Defined sp_springer_table_dual: (int->CharacterTable,[ComplexNilpotent],(ComplexNilpotent->ComplexNilpotent),(ComplexNilpotent->ComplexNilpotent),(ComplexNilpotent->int)) Defined sp_test: (int->[void]) Defined show_groups: ([([vec],RealForm)]->[void]) Added definition [2] of show_groups: (int->[void]) Completely read file 'vogan_cell_question.at'. atlas> set groups=sp_products(3) [ 0, 0, 0 ] [ 0, 0, 0 ] [ 0, 0, 0 ] [ 0, 0, 1 ] [ 0, 0, 0 ] [ 0, 1, 0 ] [ 0, 0, 0 ] [ 0, 1, 1 ] [ 0, 0, 0 ] [ 1, 0, 0 ] [ 0, 0, 0 ] [ 1, 0, 1 ] [ 0, 0, 0 ] [ 1, 1, 0 ] [ 0, 0, 0 ] [ 1, 1, 1 ] [ 0, 0, 1 ] [ 0, 0, 0 ] [ 0, 0, 1 ] [ 0, 0, 1 ] [ 0, 0, 1 ] [ 0, 1, 0 ] [ 0, 0, 1 ] [ 0, 1, 1 ] [ 0, 0, 1 ] [ 1, 0, 0 ] [ 0, 0, 1 ] [ 1, 0, 1 ] [ 0, 0, 1 ] [ 1, 1, 0 ] [ 0, 0, 1 ] [ 1, 1, 1 ] [ 0, 1, 0 ] [ 0, 0, 0 ] [ 0, 1, 0 ] [ 0, 0, 1 ] [ 0, 1, 0 ] [ 0, 1, 0 ] [ 0, 1, 0 ] [ 0, 1, 1 ] [ 0, 1, 0 ] [ 1, 0, 0 ] [ 0, 1, 0 ] [ 1, 0, 1 ] [ 0, 1, 0 ] [ 1, 1, 0 ] [ 0, 1, 0 ] [ 1, 1, 1 ] [ 0, 1, 1 ] [ 0, 0, 0 ] [ 0, 1, 1 ] [ 0, 0, 1 ] [ 0, 1, 1 ] [ 0, 1, 0 ] [ 0, 1, 1 ] [ 0, 1, 1 ] [ 0, 1, 1 ] [ 1, 0, 0 ] [ 0, 1, 1 ] [ 1, 0, 1 ] [ 0, 1, 1 ] [ 1, 1, 0 ] [ 0, 1, 1 ] [ 1, 1, 1 ] [ 1, 0, 0 ] [ 0, 0, 0 ] [ 1, 0, 0 ] [ 0, 0, 1 ] [ 1, 0, 0 ] [ 0, 1, 0 ] [ 1, 0, 0 ] [ 0, 1, 1 ] [ 1, 0, 0 ] [ 1, 0, 0 ] [ 1, 0, 0 ] [ 1, 0, 1 ] [ 1, 0, 0 ] [ 1, 1, 0 ] [ 1, 0, 0 ] [ 1, 1, 1 ] [ 1, 0, 1 ] [ 0, 0, 0 ] [ 1, 0, 1 ] [ 0, 0, 1 ] [ 1, 0, 1 ] [ 0, 1, 0 ] [ 1, 0, 1 ] [ 0, 1, 1 ] [ 1, 0, 1 ] [ 1, 0, 0 ] [ 1, 0, 1 ] [ 1, 0, 1 ] [ 1, 0, 1 ] [ 1, 1, 0 ] [ 1, 0, 1 ] [ 1, 1, 1 ] [ 1, 1, 0 ] [ 0, 0, 0 ] [ 1, 1, 0 ] [ 0, 0, 1 ] [ 1, 1, 0 ] [ 0, 1, 0 ] [ 1, 1, 0 ] [ 0, 1, 1 ] [ 1, 1, 0 ] [ 1, 0, 0 ] [ 1, 1, 0 ] [ 1, 0, 1 ] [ 1, 1, 0 ] [ 1, 1, 0 ] [ 1, 1, 0 ] [ 1, 1, 1 ] [ 1, 1, 1 ] [ 0, 0, 0 ] [ 1, 1, 1 ] [ 0, 0, 1 ] [ 1, 1, 1 ] [ 0, 1, 0 ] [ 1, 1, 1 ] [ 0, 1, 1 ] [ 1, 1, 1 ] [ 1, 0, 0 ] [ 1, 1, 1 ] [ 1, 0, 1 ] [ 1, 1, 1 ] [ 1, 1, 0 ] [ 1, 1, 1 ] [ 1, 1, 1 ] Variable groups: [RealForm] (overriding previous instance, which had type [RealForm]) atlas> for G in groups do prints(G, " ", Z.center) od Error during analysis of expression at :110:0-47 Undefined identifier 'Z' Expression analysis failed Evaluation aborted. atlas> for G in groups do prints(G, " ", G.center) od disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [] connected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, -1, 0, 0, 0, 0 ]/2,[ 0, 0, 0, -1, 0, 0 ]/2,[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2,[ 0, 0, 0, -1, 0, 0 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, -1, 0, 0 ]/2,[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, -1, 0, 0 ]/2,[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, -1, 0, 0 ]/2,[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, -1, 0, 0 ]/2,[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, -1, 0, 0 ]/2,[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, -1, 0, 0 ]/2,[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2,[ 0, 0, 0, -1, 0, 0 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, -1, 0, 0 ]/2,[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, -1, 0, 0 ]/2,[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, -1, 0, 0 ]/2,[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, -1, 0, 0 ]/2,[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, -1, 0, 0 ]/2,[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, -1, 0, 0 ]/2,[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2,[ 0, 0, 0, -1, 0, 0 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, -2, 0, 1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, -2, 0, 1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, -1, 0, 0 ]/2,[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, -1, 0, 0 ]/2,[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, -1, 0, 0 ]/2,[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, -1, 0, 0 ]/2,[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, -1, 0, 0 ]/2,[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, -1, 0, 0 ]/2,[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] disconnected split real group with Lie algebra 'sp(4,R).sp(4,R).sp(4,R)' [[ 0, 0, 0, 0, 0, -1 ]/2] Value: [(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),()] atlas>