This is 'atlas' (version 1.0.6, axis language version 0.9.5), the Atlas of Lie Groups and Representations interpreter, compiled on Jul 10 2017 at 11:13:00. http://www.liegroups.org/ atlas> atlas> set rd=simply_connected(A4) Variable rd: RootDatum atlas> rd Value: simply connected root datum of Lie type 'A4' atlas> set ic=inner_class (rd,"c") Variable ic: InnerClass atlas> real_form real_form real_forms atlas> real_form real_form real_forms atlas> form_n form_name form_names form_number atlas> form_names (ic) Value: ["su(5)","su(4,1)","su(3,2)"] atlas> rd:=simply_connected(A4) Value: simply connected root datum of Lie type 'A4' atlas> atlas> rd Value: simply connected root datum of Lie type 'A4' atlas> set ic_split=inner_class (rd,"s") Variable ic_split: InnerClass atlas> form_n form_name form_names form_number atlas> form_names (ic_split) Value: ["sl(5,R)"] atlas> atlas> atlas> atlas> atlas> atlas> inner_class (rd,"s") Value: Complex reductive group of type A4, with involution defining inner class of type 's', with 1 real form and 3 dual real forms atlas> atlas> atlas> atlas> atlas> atlas> atlas> form_names (inner_class (rd,"s")) Value: ["sl(5,R)"] atlas> form_names (inner_class (rd,"c")) Value: ["su(5)","su(4,1)","su(3,2)"] atlas> form_names (inner_class (rd,s)) Error in expression inner_class(rd,s) at :25:12-30 Failed to match 'inner_class' with argument type (RootDatum,Split) Expression analysis failed atlas> atlas> atlas> atlas> set rd=simply_connected(D4) Variable rd: RootDatum (overriding previous instance, which had type RootDatum) atlas> atlas> atlas> atlas> atlas> form_names (inner_class (rd,"c")) Value: ["so(8)","so(6,2)","so*(8)[0,1]","so*(8)[1,0]","so(4,4)"] atlas> form_names (inner_class (rd,"s") ( > ) Value: ["so(8)","so(6,2)","so*(8)[0,1]","so*(8)[1,0]","so(4,4)"] atlas> atlas> atlas> atlas> form_names (inner_class (rd,"u")) Value: ["so(7,1)","so(5,3)"] atlas> rd=simply_connected("C2C2") Error in expression =(rd,simply_connected("C2C2")) at :41:0-27 Failed to match '=' with argument type (RootDatum,RootDatum) Expression analysis failed atlas> rd:=simply_connected("C2C2") Value: simply connected root datum of Lie type 'C2.C2' atlas> rd Value: simply connected root datum of Lie type 'C2.C2' atlas> set ic=inner_class (rd,"C") Variable ic: InnerClass (overriding previous instance, which had type InnerClass) atlas> form_names (ic) Value: ["sp(4,C)"] atlas> rd:=simply_connected("A3.B4.C5.D6.E7.F4") Value: simply connected root datum of Lie type 'A3.B4.C5.D6.E7.F4' atlas> rd:=simply_connected("A3.B4.C5.D6.E7.F4.F4") Runtime error: Total rank exceeds implementation limit 32 Evaluation aborted. atlas> rd:=simply_connected("A3.B4.C5.D6.F4.F4") Value: simply connected root datum of Lie type 'A3.B4.C5.D6.F4.F4' atlas> rd Value: simply connected root datum of Lie type 'A3.B4.C5.D6.F4.F4' atlas> set ic=inner_class (rd,"sccuC") Variable ic: InnerClass (overriding previous instance, which had type InnerClass) atlas> form_names (ic) Value: ["sl(2,H).so(9).sp(5).so(11,1).f4(C)","sl(2,H).so(8,1).sp(5).so(11,1).f4(C)","sl(2,H).so(9).sp(4,1).so(11,1).f4(C)","sl(4,R).so(9).sp(5).so(11,1).f4(C)","sl(2,H).so(7,2).sp(5).so(11,1).f4(C)","sl(2,H).so(8,1).sp(4,1).so(11,1).f4(C)","sl(2,H).so(9).sp(3,2).so(11,1).f4(C)","sl(2,H).so(9).sp(5).so(9,3).f4(C)","sl(2,H).so(6,3).sp(5).so(11,1).f4(C)","sl(4,R).so(8,1).sp(5).so(11,1).f4(C)","sl(4,R).so(9).sp(4,1).so(11,1).f4(C)","sl(2,H).so(7,2).sp(4,1).so(11,1).f4(C)","sl(2,H).so(8,1).sp(3,2).so(11,1).f4(C)","sl(2,H).so(8,1).sp(5).so(9,3).f4(C)","sl(2,H).so(9).sp(4,1).so(9,3).f4(C)","sl(4,R).so(7,2).sp(5).so(11,1).f4(C)","sl(2,H).so(5,4).sp(5).so(11,1).f4(C)","sl(2,H).so(6,3).sp(4,1).so(11,1).f4(C)","sl(4,R).so(8,1).sp(4,1).so(11,1).f4(C)","sl(4,R).so(9).sp(3,2).so(11,1).f4(C)","sl(2,H).so(7,2).sp(3,2).so(11,1).f4(C)","sl(4,R).so(9).sp(5).so(9,3).f4(C)","sl(2,H).so(7,2).sp(5).so(9,3).f4(C)","sl(2,H).so(8,1).sp(4,1).so(9,3).f4(C)","sl(2,H).so(9).sp(3,2).so(9,3).f4(C)","sl(2,H).so(9).sp(5).so(7,5).f4(C)","sl(4,R).so(6,3).sp(5).so(11,1).f4(C)","sl(4,R).so(7,2).sp(4,1).so(11,1).f4(C)","sl(2,H).so(5,4).sp(4,1).so(11,1).f4(C)","sl(2,H).so(6,3).sp(3,2).so(11,1).f4(C)","sl(4,R).so(8,1).sp(3,2).so(11,1).f4(C)","sl(2,H).so(9).sp(10,R).so(11,1).f4(C)","sl(2,H).so(6,3).sp(5).so(9,3).f4(C)","sl(4,R).so(8,1).sp(5).so(9,3).f4(C)","sl(4,R).so(9).sp(4,1).so(9,3).f4(C)","sl(2,H).so(7,2).sp(4,1).so(9,3).f4(C)","sl(2,H).so(8,1).sp(3,2).so(9,3).f4(C)","sl(2,H).so(8,1).sp(5).so(7,5).f4(C)","sl(2,H).so(9).sp(4,1).so(7,5).f4(C)","sl(4,R).so(5,4).sp(5).so(11,1).f4(C)","sl(4,R).so(6,3).sp(4,1).so(11,1).f4(C)","sl(4,R).so(7,2).sp(3,2).so(11,1).f4(C)","sl(2,H).so(5,4).sp(3,2).so(11,1).f4(C)","sl(2,H).so(8,1).sp(10,R).so(11,1).f4(C)","sl(4,R).so(7,2).sp(5).so(9,3).f4(C)","sl(2,H).so(5,4).sp(5).so(9,3).f4(C)","sl(2,H).so(6,3).sp(4,1).so(9,3).f4(C)","sl(4,R).so(8,1).sp(4,1).so(9,3).f4(C)","sl(4,R).so(9).sp(3,2).so(9,3).f4(C)","sl(2,H).so(7,2).sp(3,2).so(9,3).f4(C)","sl(4,R).so(9).sp(5).so(7,5).f4(C)","sl(2,H).so(7,2).sp(5).so(7,5).f4(C)","sl(2,H).so(8,1).sp(4,1).so(7,5).f4(C)","sl(2,H).so(9).sp(3,2).so(7,5).f4(C)","sl(4,R).so(5,4).sp(4,1).so(11,1).f4(C)","sl(4,R).so(6,3).sp(3,2).so(11,1).f4(C)","sl(4,R).so(9).sp(10,R).so(11,1).f4(C)","sl(2,H).so(7,2).sp(10,R).so(11,1).f4(C)","sl(4,R).so(6,3).sp(5).so(9,3).f4(C)","sl(4,R).so(7,2).sp(4,1).so(9,3).f4(C)","sl(2,H).so(5,4).sp(4,1).so(9,3).f4(C)","sl(2,H).so(6,3).sp(3,2).so(9,3).f4(C)","sl(4,R).so(8,1).sp(3,2).so(9,3).f4(C)","sl(2,H).so(9).sp(10,R).so(9,3).f4(C)","sl(2,H).so(6,3).sp(5).so(7,5).f4(C)","sl(4,R).so(8,1).sp(5).so(7,5).f4(C)","sl(4,R).so(9).sp(4,1).so(7,5).f4(C)","sl(2,H).so(7,2).sp(4,1).so(7,5).f4(C)","sl(2,H).so(8,1).sp(3,2).so(7,5).f4(C)","sl(4,R).so(5,4).sp(3,2).so(11,1).f4(C)","sl(2,H).so(6,3).sp(10,R).so(11,1).f4(C)","sl(4,R).so(8,1).sp(10,R).so(11,1).f4(C)","sl(4,R).so(5,4).sp(5).so(9,3).f4(C)","sl(4,R).so(6,3).sp(4,1).so(9,3).f4(C)","sl(4,R).so(7,2).sp(3,2).so(9,3).f4(C)","sl(2,H).so(5,4).sp(3,2).so(9,3).f4(C)","sl(2,H).so(8,1).sp(10,R).so(9,3).f4(C)","sl(4,R).so(7,2).sp(5).so(7,5).f4(C)","sl(2,H).so(5,4).sp(5).so(7,5).f4(C)","sl(2,H).so(6,3).sp(4,1).so(7,5).f4(C)","sl(4,R).so(8,1).sp(4,1).so(7,5).f4(C)","sl(4,R).so(9).sp(3,2).so(7,5).f4(C)","sl(2,H).so(7,2).sp(3,2).so(7,5).f4(C)","sl(4,R).so(7,2).sp(10,R).so(11,1).f4(C)","sl(2,H).so(5,4).sp(10,R).so(11,1).f4(C)","sl(4,R).so(5,4).sp(4,1).so(9,3).f4(C)","sl(4,R).so(6,3).sp(3,2).so(9,3).f4(C)","sl(4,R).so(9).sp(10,R).so(9,3).f4(C)","sl(2,H).so(7,2).sp(10,R).so(9,3).f4(C)","sl(4,R).so(6,3).sp(5).so(7,5).f4(C)","sl(4,R).so(7,2).sp(4,1).so(7,5).f4(C)","sl(2,H).so(5,4).sp(4,1).so(7,5).f4(C)","sl(2,H).so(6,3).sp(3,2).so(7,5).f4(C)","sl(4,R).so(8,1).sp(3,2).so(7,5).f4(C)","sl(2,H).so(9).sp(10,R).so(7,5).f4(C)","sl(4,R).so(6,3).sp(10,R).so(11,1).f4(C)","sl(4,R).so(5,4).sp(3,2).so(9,3).f4(C)","sl(2,H).so(6,3).sp(10,R).so(9,3).f4(C)","sl(4,R).so(8,1).sp(10,R).so(9,3).f4(C)","sl(4,R).so(5,4).sp(5).so(7,5).f4(C)","sl(4,R).so(6,3).sp(4,1).so(7,5).f4(C)","sl(4,R).so(7,2).sp(3,2).so(7,5).f4(C)","sl(2,H).so(5,4).sp(3,2).so(7,5).f4(C)","sl(2,H).so(8,1).sp(10,R).so(7,5).f4(C)","sl(4,R).so(5,4).sp(10,R).so(11,1).f4(C)","sl(4,R).so(7,2).sp(10,R).so(9,3).f4(C)","sl(2,H).so(5,4).sp(10,R).so(9,3).f4(C)","sl(4,R).so(5,4).sp(4,1).so(7,5).f4(C)","sl(4,R).so(6,3).sp(3,2).so(7,5).f4(C)","sl(4,R).so(9).sp(10,R).so(7,5).f4(C)","sl(2,H).so(7,2).sp(10,R).so(7,5).f4(C)","sl(4,R).so(6,3).sp(10,R).so(9,3).f4(C)","sl(4,R).so(5,4).sp(3,2).so(7,5).f4(C)","sl(2,H).so(6,3).sp(10,R).so(7,5).f4(C)","sl(4,R).so(8,1).sp(10,R).so(7,5).f4(C)","sl(4,R).so(5,4).sp(10,R).so(9,3).f4(C)","sl(4,R).so(7,2).sp(10,R).so(7,5).f4(C)","sl(2,H).so(5,4).sp(10,R).so(7,5).f4(C)","sl(4,R).so(6,3).sp(10,R).so(7,5).f4(C)","sl(4,R).so(5,4).sp(10,R).so(7,5).f4(C)"] atlas> for a in form_names (ic) do prints(a) od sl(2,H).so(9).sp(5).so(11,1).f4(C) sl(2,H).so(8,1).sp(5).so(11,1).f4(C) sl(2,H).so(9).sp(4,1).so(11,1).f4(C) sl(4,R).so(9).sp(5).so(11,1).f4(C) sl(2,H).so(7,2).sp(5).so(11,1).f4(C) sl(2,H).so(8,1).sp(4,1).so(11,1).f4(C) sl(2,H).so(9).sp(3,2).so(11,1).f4(C) sl(2,H).so(9).sp(5).so(9,3).f4(C) sl(2,H).so(6,3).sp(5).so(11,1).f4(C) sl(4,R).so(8,1).sp(5).so(11,1).f4(C) sl(4,R).so(9).sp(4,1).so(11,1).f4(C) sl(2,H).so(7,2).sp(4,1).so(11,1).f4(C) sl(2,H).so(8,1).sp(3,2).so(11,1).f4(C) sl(2,H).so(8,1).sp(5).so(9,3).f4(C) sl(2,H).so(9).sp(4,1).so(9,3).f4(C) sl(4,R).so(7,2).sp(5).so(11,1).f4(C) sl(2,H).so(5,4).sp(5).so(11,1).f4(C) sl(2,H).so(6,3).sp(4,1).so(11,1).f4(C) sl(4,R).so(8,1).sp(4,1).so(11,1).f4(C) sl(4,R).so(9).sp(3,2).so(11,1).f4(C) sl(2,H).so(7,2).sp(3,2).so(11,1).f4(C) sl(4,R).so(9).sp(5).so(9,3).f4(C) sl(2,H).so(7,2).sp(5).so(9,3).f4(C) sl(2,H).so(8,1).sp(4,1).so(9,3).f4(C) sl(2,H).so(9).sp(3,2).so(9,3).f4(C) sl(2,H).so(9).sp(5).so(7,5).f4(C) sl(4,R).so(6,3).sp(5).so(11,1).f4(C) sl(4,R).so(7,2).sp(4,1).so(11,1).f4(C) sl(2,H).so(5,4).sp(4,1).so(11,1).f4(C) sl(2,H).so(6,3).sp(3,2).so(11,1).f4(C) sl(4,R).so(8,1).sp(3,2).so(11,1).f4(C) sl(2,H).so(9).sp(10,R).so(11,1).f4(C) sl(2,H).so(6,3).sp(5).so(9,3).f4(C) sl(4,R).so(8,1).sp(5).so(9,3).f4(C) sl(4,R).so(9).sp(4,1).so(9,3).f4(C) sl(2,H).so(7,2).sp(4,1).so(9,3).f4(C) sl(2,H).so(8,1).sp(3,2).so(9,3).f4(C) sl(2,H).so(8,1).sp(5).so(7,5).f4(C) sl(2,H).so(9).sp(4,1).so(7,5).f4(C) sl(4,R).so(5,4).sp(5).so(11,1).f4(C) sl(4,R).so(6,3).sp(4,1).so(11,1).f4(C) sl(4,R).so(7,2).sp(3,2).so(11,1).f4(C) sl(2,H).so(5,4).sp(3,2).so(11,1).f4(C) sl(2,H).so(8,1).sp(10,R).so(11,1).f4(C) sl(4,R).so(7,2).sp(5).so(9,3).f4(C) sl(2,H).so(5,4).sp(5).so(9,3).f4(C) sl(2,H).so(6,3).sp(4,1).so(9,3).f4(C) sl(4,R).so(8,1).sp(4,1).so(9,3).f4(C) sl(4,R).so(9).sp(3,2).so(9,3).f4(C) sl(2,H).so(7,2).sp(3,2).so(9,3).f4(C) sl(4,R).so(9).sp(5).so(7,5).f4(C) sl(2,H).so(7,2).sp(5).so(7,5).f4(C) sl(2,H).so(8,1).sp(4,1).so(7,5).f4(C) sl(2,H).so(9).sp(3,2).so(7,5).f4(C) sl(4,R).so(5,4).sp(4,1).so(11,1).f4(C) sl(4,R).so(6,3).sp(3,2).so(11,1).f4(C) sl(4,R).so(9).sp(10,R).so(11,1).f4(C) sl(2,H).so(7,2).sp(10,R).so(11,1).f4(C) sl(4,R).so(6,3).sp(5).so(9,3).f4(C) sl(4,R).so(7,2).sp(4,1).so(9,3).f4(C) sl(2,H).so(5,4).sp(4,1).so(9,3).f4(C) sl(2,H).so(6,3).sp(3,2).so(9,3).f4(C) sl(4,R).so(8,1).sp(3,2).so(9,3).f4(C) sl(2,H).so(9).sp(10,R).so(9,3).f4(C) sl(2,H).so(6,3).sp(5).so(7,5).f4(C) sl(4,R).so(8,1).sp(5).so(7,5).f4(C) sl(4,R).so(9).sp(4,1).so(7,5).f4(C) sl(2,H).so(7,2).sp(4,1).so(7,5).f4(C) sl(2,H).so(8,1).sp(3,2).so(7,5).f4(C) sl(4,R).so(5,4).sp(3,2).so(11,1).f4(C) sl(2,H).so(6,3).sp(10,R).so(11,1).f4(C) sl(4,R).so(8,1).sp(10,R).so(11,1).f4(C) sl(4,R).so(5,4).sp(5).so(9,3).f4(C) sl(4,R).so(6,3).sp(4,1).so(9,3).f4(C) sl(4,R).so(7,2).sp(3,2).so(9,3).f4(C) sl(2,H).so(5,4).sp(3,2).so(9,3).f4(C) sl(2,H).so(8,1).sp(10,R).so(9,3).f4(C) sl(4,R).so(7,2).sp(5).so(7,5).f4(C) sl(2,H).so(5,4).sp(5).so(7,5).f4(C) sl(2,H).so(6,3).sp(4,1).so(7,5).f4(C) sl(4,R).so(8,1).sp(4,1).so(7,5).f4(C) sl(4,R).so(9).sp(3,2).so(7,5).f4(C) sl(2,H).so(7,2).sp(3,2).so(7,5).f4(C) sl(4,R).so(7,2).sp(10,R).so(11,1).f4(C) sl(2,H).so(5,4).sp(10,R).so(11,1).f4(C) sl(4,R).so(5,4).sp(4,1).so(9,3).f4(C) sl(4,R).so(6,3).sp(3,2).so(9,3).f4(C) sl(4,R).so(9).sp(10,R).so(9,3).f4(C) sl(2,H).so(7,2).sp(10,R).so(9,3).f4(C) sl(4,R).so(6,3).sp(5).so(7,5).f4(C) sl(4,R).so(7,2).sp(4,1).so(7,5).f4(C) sl(2,H).so(5,4).sp(4,1).so(7,5).f4(C) sl(2,H).so(6,3).sp(3,2).so(7,5).f4(C) sl(4,R).so(8,1).sp(3,2).so(7,5).f4(C) sl(2,H).so(9).sp(10,R).so(7,5).f4(C) sl(4,R).so(6,3).sp(10,R).so(11,1).f4(C) sl(4,R).so(5,4).sp(3,2).so(9,3).f4(C) sl(2,H).so(6,3).sp(10,R).so(9,3).f4(C) sl(4,R).so(8,1).sp(10,R).so(9,3).f4(C) sl(4,R).so(5,4).sp(5).so(7,5).f4(C) sl(4,R).so(6,3).sp(4,1).so(7,5).f4(C) sl(4,R).so(7,2).sp(3,2).so(7,5).f4(C) sl(2,H).so(5,4).sp(3,2).so(7,5).f4(C) sl(2,H).so(8,1).sp(10,R).so(7,5).f4(C) sl(4,R).so(5,4).sp(10,R).so(11,1).f4(C) sl(4,R).so(7,2).sp(10,R).so(9,3).f4(C) sl(2,H).so(5,4).sp(10,R).so(9,3).f4(C) sl(4,R).so(5,4).sp(4,1).so(7,5).f4(C) sl(4,R).so(6,3).sp(3,2).so(7,5).f4(C) sl(4,R).so(9).sp(10,R).so(7,5).f4(C) sl(2,H).so(7,2).sp(10,R).so(7,5).f4(C) sl(4,R).so(6,3).sp(10,R).so(9,3).f4(C) sl(4,R).so(5,4).sp(3,2).so(7,5).f4(C) sl(2,H).so(6,3).sp(10,R).so(7,5).f4(C) sl(4,R).so(8,1).sp(10,R).so(7,5).f4(C) sl(4,R).so(5,4).sp(10,R).so(9,3).f4(C) sl(4,R).so(7,2).sp(10,R).so(7,5).f4(C) sl(2,H).so(5,4).sp(10,R).so(7,5).f4(C) sl(4,R).so(6,3).sp(10,R).so(7,5).f4(C) sl(4,R).so(5,4).sp(10,R).so(7,5).f4(C) Value: [(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),()] atlas> #$ Value: 120 atlas> rd:=simply_connected("A3.T1") Value: simply connected root datum of Lie type 'A3.T1' atlas> atlas> atlas> atlas> atlas> atlas> inner_class (rd,"ss") Value: Complex reductive group of type A3.T1, with involution defining inner class of type 'ss', with 2 real forms and 3 dual real forms atlas> form_names ($) Value: ["sl(2,H).gl(1,R)","sl(4,R).gl(1,R)"] atlas> simple_roots (rd) Value: | 2, -1, 0 | | -1, 2, -1 | | 0, -1, 2 | | 0, 0, 0 | atlas> atlas> atlas> atlas> atlas> atlas> set delta=distinguished_involution (ic) Variable delta: mat atlas> atlas> atlas> atlas> simply_connected("C2C2") Value: simply connected root datum of Lie type 'C2.C2' atlas> simply_connected("C2.C2") Value: simply connected root datum of Lie type 'C2.C2' atlas> atlas> atlas> atlas> atlas> simply_connected("C2..C2") Value: simply connected root datum of Lie type 'C2.C2' atlas> simply_connected("C2........C2") Value: simply connected root datum of Lie type 'C2.C2' atlas> simply_connected("C2........C2.") Value: simply connected root datum of Lie type 'C2.C2' atlas> atlas> atlas> atlas> ic Value: Complex reductive group of type A3.B4.C5.D6.F4.F4, with involution defining inner class of type 'sccuC', with 120 real forms and 216 dual real forms atlas> rd:=simply_connected(A4) Value: simply connected root datum of Lie type 'A4' atlas> set G=GL(4,R) Variable G: RealForm atlas> distinguished_involution (G) Value: | 0, 0, 0, -1 | | 0, 0, -1, 0 | | 0, -1, 0, 0 | | -1, 0, 0, 0 | atlas> simple_roots (G) Value: | 1, 0, 0 | | -1, 1, 0 | | 0, -1, 1 | | 0, 0, -1 | atlas> set delta=distinguished_involution (G) Variable delta: mat (overriding previous instance, which had type mat) atlas> delta*simple_roots (G) Value: | 0, 0, 1 | | 0, 1, -1 | | 1, -1, 0 | | -1, 0, 0 | atlas> atlas> atlas> atlas> rd:=simply_connected(A4) Value: simply connected root datum of Lie type 'A4' atlas> ic=inner_class (rd,"s") Value: false atlas> ic:=inner_class (rd,"s") 'Value: Complex reductive group of type A4, with involution defining inner class of type 's', with 1 real form and 3 dual real forms atlas> delta:=distinguished_involution (ic) Value: | 0, 0, 0, 1 | | 0, 0, 1, 0 | | 0, 1, 0, 0 | | 1, 0, 0, 0 | atlas> simple_roots (rd) Value: | 2, -1, 0, 0 | | -1, 2, -1, 0 | | 0, -1, 2, -1 | | 0, 0, -1, 2 | atlas> delta*simple_roots (rd) Value: | 0, 0, -1, 2 | | 0, -1, 2, -1 | | -1, 2, -1, 0 | | 2, -1, 0, 0 | atlas> rd:=simply_connected("A3.D4.C5.D6.F4.F4") Value: simply connected root datum of Lie type 'A3.D4.C5.D6.F4.F4'