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jda@Leonidas:~/atlasSoftware/master/atlasofliegroups/atlas-scripts$ ../atlas all
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> 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> 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> 
atlas>  set rd=simply_connected(D4)
Variable rd: RootDatum (overriding previous instance, which had type RootDatum)
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> form_names (inner_class (rd,"u"))
Value: ["so(7,1)","so(5,3)"]
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 |