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[marc@Pleiona ~/atlas/atlas-scripts]$ atlas
This is 'atlas' (version 1.0.6, axis language version 0.9.5),
the Atlas of Lie Groups and Representations interpreter,
compiled on Jul 8 2017 at 20:08:14. http://www.liegroups.org/
atlas> 345/23
Value: 15/1
atlas> 345\23
Value: 15
atlas> 347\23
Value: 15
atlas> 347%23
Value: 2
atlas> 347 \% 23
Value: (15,2)
atlas> 0-4
Value: -4
atlas> 1/6
Value: 1/6
atlas> /6
Value: 1/6
atlas> 6^-1
Runtime error:
Negative power of integer
(in call at <standard input>:9:0-4 of ^@(int,int), built-in)
Evaluation aborted.
atlas> whattype ^ ?
Overloaded instances of '^'
(int,int)->int
(rat,int)->rat
vec->mat
mat->mat
(int,[vec])->mat
(bool,bool)->bool
(mat,vec)->mat
(vec,mat)->mat
(mat,mat)->mat
(mat,int)->mat
Split->int
(Split,int)->Split
((RootDatum,[int]),int)->(RootDatum,[int])
(vec,int)->vec
(mat,string,int)->(mat,string,int)
((mat,string,int),int)->(mat,string,int)
[ratvec]->(mat,string,int)
((RootDatum,ratvec,mat),int)->(RootDatum,ratvec,mat)
(([rat],string),int)->([rat],string)
(([rat],(int,[int])),int)->([rat],(int,[int]))
atlas> (6/1)^-1
^C\
Terminated
[marc@Pleiona ~/atlas/atlas-scripts]$ \
>
[marc@Pleiona ~/atlas/atlas-scripts]$ atlas
This is 'atlas' (version 1.0.6, axis language version 0.9.5),
the Atlas of Lie Groups and Representations interpreter,
compiled on Jul 8 2017 at 20:08:14. http://www.liegroups.org/
atlas> [2,4,45,76,-879]
Value: [2,4,45,76,-879]
atlas> whattype $ ?
^
syntax error, unexpected '?', expecting '\n'
atlas> whattype $
type: [int]
atlas> vec: $
Value: [ 2, 4, 45, 76, -879 ]
atlas> set v=$
Variable v: vec
atlas> v+v
Value: [ 4, 8, 90, 152, -1758 ]
atlas> v*3
Value: [ 6, 12, 135, 228, -2637 ]
atlas> v*v
Value: 780462
atlas> v/4
Value: [ 2, 4, 45, 76, -879 ]/4
atlas> whattype $
type: ratvec
atlas> $ + v/5
Value: [ 18, 36, 405, 684, -7911 ]/20
atlas> whattype rho ?
Overloaded instances of 'rho'
RootDatum->ratvec
(RootDatum,ratvec)->ratvec
(InnerClass,mat,ratvec,vec,mat,ratvec,vec,mat,vec,vec)->ratvec
int->[rat]
Block->ratvec
atlas> 345/23
Value: 15/1
atlas> 346/23
Value: 346/23
atlas> floor($)
Value: 15
atlas> (346/23)\1
Value: 15
atlas> (-346/23)\1
Value: -16
atlas> v/8 + v/5
Value: [ 26, 52, 585, 988, -11427 ]/40
atlas> $\1
Value: [ 0, 1, 14, 24, -286 ]
atlas> v/8 + v/5
Value: [ 26, 52, 585, 988, -11427 ]/40
atlas> floor($)
Value: [ 0, 1, 14, 24, -286 ]
atlas> v/8 + v/5
Value: [ 26, 52, 585, 988, -11427 ]/40
atlas> [rat]: $
Value: [13/20,13/10,117/8,247/10,-11427/40]
atlas> 2^234/3^231
Value: 27606985387162255149739023449108101809804435888681546220650096895197184/164062694609488086547539746812648575659318856476507740436897453222447961474036515706307096943652603236842951947
atlas> ratvec:[$]
Integer value to big for conversion
Evaluation aborted.
atlas> set A = [1,2,3|4,5,6|3,3,2]
Variable A: mat
atlas> det(A)
Value: 3
atlas> inverse(A)
Runtime error:
Matrix not invertible over the integers
(in call at /home/marc/atlas/atlas-scripts/basic.at:320:23-71 of error@string, built-in)
[inv=
| -8, 5, -3 |
| 10, -7, 6 |
| -3, 3, -3 |
, d=3]
[M=
| 1, 2, 3 |
| 4, 5, 6 |
| 3, 3, 2 |
]
(in call at <standard input>:28:0-10 of inverse@mat, defined at /home/marc/atlas/atlas-scripts/basic.at:318:4--320:74)
Evaluation aborted.
atlas> invert(A)
Value: (
| -8, 5, -3 |
| 10, -7, 6 |
| -3, 3, -3 |
,3)
atlas> let (n,d)=$ in n/d
Value: (
| -8, 5, -3 |
| 10, -7, 6 |
| -3, 3, -3 |
,"/",3)
atlas> whattype $
type: (mat,string,int)
atlas> whattype - ?
Overloaded instances of '-'
(int,int)->int
int->int
(rat,int)->rat
(rat,rat)->rat
rat->rat
vec->vec
(vec,vec)->vec
(ratvec,ratvec)->ratvec
ratvec->ratvec
(mat,int)->mat
(int,mat)->mat
(mat,mat)->mat
(Split,Split)->Split
Split->Split
(ParamPol,Param)->ParamPol
(ParamPol,ParamPol)->ParamPol
mat->mat
ParamPol->ParamPol
(ParamPol,(Split,Param))->ParamPol
[[vec]]->[[vec]]
([[vec]],[[vec]])->[[vec]]
([[vec]],vec)->[[vec]]
((mat,string,int),(mat,string,int))->(mat,string,int)
(mat,string,int)->(mat,int,void)
([ratvec],(mat,string,int))->(mat,string,int)
((mat,string,int),[ratvec])->(mat,string,int)
([ratvec],mat)->(mat,string,int)
(mat,[ratvec])->(mat,string,int)
((ParamPol,ParamPol,ParamPol),(ParamPol,ParamPol,ParamPol))->(ParamPol,ParamPol,ParamPol)
(Param,string)->(ParamPol,string)
(ParamPol,string)->(ParamPol,string)
((Param,string),(Param,string))->(ParamPol,string)
((Param,string),(ParamPol,string))->(ParamPol,string)
((ParamPol,string),(ParamPol,string))->(ParamPol,string)
([rat],string)->([rat],string)
(([rat],string),([rat],string))->([rat],string)
(([rat],(int,[int])),([rat],(int,[int])))->([rat],(int,[int]))
([rat],(int,[int]))->([rat],(int,[int]))
atlas> invert(A)
Value: (
| -8, 5, -3 |
| 10, -7, 6 |
| -3, 3, -3 |
,3)
atlas> let (n,d)=$ in n/d
Value: (
| -8, 5, -3 |
| 10, -7, 6 |
| -3, 3, -3 |
,"/",3)
atlas> - $
Value: (
| 8, -5, 3 |
| -10, 7, -6 |
| 3, -3, 3 |
,3,())
atlas> $ +4
Error in expression +($,4) at <standard input>:36:0-4
Failed to match '+' with argument type ((mat,int,void),int)
Expression analysis failed
atlas> A
Value:
| 1, 2, 3 |
| 4, 5, 6 |
| 3, 3, 2 |
atlas> A-2
Value:
| -1, 2, 3 |
| 4, 3, 6 |
| 3, 3, 0 |
atlas> (A-2)*(a*3)
Error during analysis of expression at <standard input>:39:1-10
Undefined identifier 'a'
Expression analysis failed
atlas> (A-2)*(A*3)
Error in expression *(A,3) at <standard input>:40:7-10
Failed to match '*' with argument type (mat,int)
Expression analysis failed
atlas> (A-2)*(A+3)
Value:
| 13, 23, 24 |
| 46, 50, 60 |
| 24, 30, 27 |
atlas> id_mat(2)
Value:
| 1, 0 |
| 0, 1 |
atlas> id_mat(3)
Value:
| 1, 0, 0 |
| 0, 1, 0 |
| 0, 0, 1 |
atlas> $*4
Error in expression *($,4) at <standard input>:44:0-3
Failed to match '*' with argument type (mat,int)
Expression analysis failed
atlas> 4*$
Value:
| 4, 0, 0 |
| 0, 4, 0 |
| 0, 0, 4 |
atlas> invert(4)
Error during analysis of expression at <standard input>:46:0-9
Type error:
Subexpression 4 at <standard input>:46:7-8
has wrong type: found int while mat was needed.
Expression analysis failed
atlas> invert($)
Value: (
| 1, 0, 0 |
| 0, 1, 0 |
| 0, 0, 1 |
,4)
atlas> A
Value:
| 1, 2, 3 |
| 4, 5, 6 |
| 3, 3, 2 |
atlas> char_poly(A)
Value: [ -3, -18, -8, 1 ]
atlas> v
Value: [ 2, 4, 45, 76, -879 ]
atlas> v[2] := 3
Value: 3
atlas> v
Value: [ 2, 4, 3, 76, -879 ]
atlas> forget v
Identifier 'v' forgotten
atlas> v
Error during analysis of expression at <standard input>:54:0-1
Undefined identifier 'v'
Expression analysis failed
atlas> set M = 2* id_mat(5)
Variable M: mat
atlas> M
Value:
| 2, 0, 0, 0, 0 |
| 0, 2, 0, 0, 0 |
| 0, 0, 2, 0, 0 |
| 0, 0, 0, 2, 0 |
| 0, 0, 0, 0, 2 |
atlas> M[2,4]
Value: 0
atlas> M[2,4] := 1
Value: 1
atlas> M
Value:
| 2, 0, 0, 0, 0 |
| 0, 2, 0, 0, 0 |
| 0, 0, 2, 0, 1 |
| 0, 0, 0, 2, 0 |
| 0, 0, 0, 0, 2 |
atlas> M[1,3] = 1
Value: false
atlas> M[1,3] = 1; M
Error in expression =(M[1,3],1) at <standard input>:61:0-10
Use op equality operator '=' in void context; did you mean ':=' instead?
If you really want the result of '=' to be voided, use a cast to bool.
Expression analysis failed
atlas> M[1,3] := 3; M
Value:
| 2, 0, 0, 0, 0 |
| 0, 2, 0, 3, 0 |
| 0, 0, 2, 0, 1 |
| 0, 0, 0, 2, 0 |
| 0, 0, 0, 0, 2 |
atlas> set v = vec: [4,2,-5,4]
Variable v: vec
atlas> v
Value: [ 4, 2, -5, 4 ]
atlas> mat: [v]
Value:
| 4 |
| 2 |
| -5 |
| 4 |
atlas> mat: [v,2*v]
Value:
| 4, 8 |
| 2, 4 |
| -5, -10 |
| 4, 8 |
atlas> [v,2*v]
Value: [[ 4, 2, -5, 4 ],[ 8, 4, -10, 8 ]]
atlas> mat: $
Value:
| 4, 8 |
| 2, 4 |
| -5, -10 |
| 4, 8 |
atlas> mat: v
Error during analysis of expression at <standard input>:69:0-6
Type error:
Subexpression v at <standard input>:69:5-6
has wrong type: found vec while mat was needed.
Expression analysis failed
atlas> mat: [v]
Value:
| 4 |
| 2 |
| -5 |
| 4 |
atlas> mat: ^[v]
Value:
| 4, 2, -5, 4 |
atlas> ^[v]
Value:
| 4, 2, -5, 4 |
atlas> ^[v,3*v]
Value:
| 4, 2, -5, 4 |
| 12, 6, -15, 12 |
atlas> [ 2,65,3 | 6,32,5 ]
Value:
| 2, 65, 3 |
| 6, 32, 5 |
atlas> ["helo", "there" ]
Value: ["helo","there"]
atlas> ["hello", "there" ]
Value: ["hello","there"]
atlas> ["hello", "the" ]
Value: ["hello","the"]
atlas> mat: $
Error during analysis of expression at <standard input>:78:0-6
Type error:
Subexpression $ at <standard input>:78:5-6
has wrong type: found [string] while mat was needed.
Expression analysis failed
atlas> ["hello",4]
Error in expression ["hello",4] at <standard input>:79:0-11
No common type found between components of list expression: { string, int }
Expression analysis failed
atlas> [2,3/4,0]
Value: [2/1,3/4,0/1]
atlas> set list= $
Variable list: [rat]
atlas> list[1]:=/5
Value: 1/5
atlas> list
Value: [2/1,1/5,0/1]
atlas> list # 55
Error in expression #(list,55) at <standard input>:84:0-9
Failed to match '#' with argument type ([rat],int)
Expression analysis failed
atlas> list # 55/1
Error in expression #(list,55) at <standard input>:85:0-9
Failed to match '#' with argument type ([rat],int)
Expression analysis failed
atlas> list # (55/1)
Value: [2/1,1/5,0/1,55/1]
atlas> set L = [1]
Variable L: [int]
atlas> for :5 do L:=L # sum(l) od; L
Error during analysis of expression at <standard input>:88:0-29
Undefined identifier 'l'
Expression analysis failed
atlas> for :5 do L:=L # sum(L) od; L
Value: [1,1,2,4,8,16]
atlas> $ ## $
Value: [1,1,2,4,8,16,1,1,2,4,8,16]
atlas> #5
Value: [0,1,2,3,4]
atlas> for i:5 do #i od
Value: [[],[0],[0,1],[0,1,2],[0,1,2,3]]
atlas> ## $
Value: [0,0,1,0,1,2,0,1,2,3]
atlas> whattype gcd ?
Overloaded instances of 'gcd'
(int,int)->int
[int]->int
mat->int
atlas> for i:30 do if gcd(i,30)=1 then i fi od
Value: [(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),()]
atlas> for i:30 do if gcd(i,30)=1 then [i] else [] fi od
Value: [[],[1],[],[],[],[],[],[7],[],[],[],[11],[],[13],[],[],[],[17],[],[19],[],[],[],[23],[],[],[],[],[],[29]]
atlas> ## for i:30 do if gcd(i,30)=1 then [i] else [] fi od
Value: [1,7,11,13,17,19,23,29]
atlas> list:=[]
Value: []
atlas> whattype list ?
Overloaded instances of 'list'
((int->bool),int)->[int]
atlas> whattype list
type: [rat]
atlas> set list = []
Variable list: [*] (overriding previous instance, which had type [rat])
atlas> list := list # [1]
Value: [[1]]
atlas> whattype list ?
Overloaded instances of 'list'
((int->bool),int)->[int]
atlas> whattype list
type: [[int]]
atlas> list := list # 3
Error in expression #(list,3) at <standard input>:105:8-16
Failed to match '#' with argument type ([[int]],int)
Expression analysis failed
atlas> set list = []
Variable list: [*] (overriding previous instance, which had type [[int]])
atlas> list # [1]
Value: [[1]]
atlas> list # 1
Value: [1]
atlas> whattype $
type: [int]
atlas> whattype list
type: [*]
atlas> list := list # 3
Value: [3]
atlas> list :=[]
Value: []
atlas> whattype list
type: [int]
atlas>
Display all 1432 possibilities? (y or n)
atlas> gcd([3,2,5])
Value: 1
atlas> ## for i:30 do if gcd([i,30])=1 then [i] else [] fi od
Value: [1,7,11,13,17,19,23,29]
atlas> $ [1:5]
Value: [7,11,13,17]
atlas> ## for i:30 do if gcd([i,30])=1 then [i] else [] fi od
Value: [1,7,11,13,17,19,23,29]
atlas> v := $
Value: [ 1, 7, 11, 13, 17, 19, 23, 29 ]
atlas> v [1:5]
Value: [ 7, 11, 13, 17 ]
atlas> "atlas workshop"[1:5]
Value: "tlas"
atlas> set str="atlas workshop"
Variable str: string
atlas> "atlas workshop"[1:#str]
Value: "tlas workshop"
atlas> "atlas workshop"[1:#str-1]
Value: "tlas worksho"
atlas> "atlas workshop"[1:1]
Value: ""
atlas> "atlas workshop"[1:-1]
Value: ""
atlas> "atlas workshop"[1:-2]
Value: ""
atlas> "atlas workshop"[1:1~]
Value: "tlas worksho"
atlas> "atlas workshop"[1:0~]
Value: "tlas workshop"
atlas> "atlas workshop"[1: ]
Value: "tlas workshop"
atlas> "atlas workshop"[~3: ]
Error during analysis of expression at <standard input>:130:0-22
Undefined identifier '~'
Expression analysis failed
atlas> "atlas workshop"[3~: ]
Value: "hop"
atlas> "atlas workshop"[3: ]
Value: "as workshop"
atlas> "atlas workshop"~[3: ]
Value: "skrow salta"
atlas> "atlas workshop"~[3~: ]
Value: "lta"
atlas> "atlas workshop"~[ : ]
Value: "pohskrow salta"
atlas> v
Value: [ 1, 7, 11, 13, 17, 19, 23, 29 ]
atlas> v~
~ > [:]
^
syntax error, unexpected ':', expecting ']'
atlas> v~[:]
Value: [ 29, 23, 19, 17, 13, 11, 7, 1 ]
atlas> v[:~1]
Error during analysis of expression at <standard input>:140:0-6
Undefined identifier '~'
Expression analysis failed
atlas> v[:1~]
Value: [ 1, 7, 11, 13, 17, 19, 23 ]
atlas> v[1:]
Value: [ 7, 11, 13, 17, 19, 23, 29 ]
atlas> id_mat(5)
Value:
| 1, 0, 0, 0, 0 |
| 0, 1, 0, 0, 0 |
| 0, 0, 1, 0, 0 |
| 0, 0, 0, 1, 0 |
| 0, 0, 0, 0, 1 |
atlas> id_mat(5)~[:]
Value:
| 0, 0, 0, 0, 1 |
| 0, 0, 0, 1, 0 |
| 0, 0, 1, 0, 0 |
| 0, 1, 0, 0, 0 |
| 1, 0, 0, 0, 0 |
atlas> id_mat(5)(:1~]
^
syntax error, unexpected ':', expecting ')'
atlas> id_mat(5)[:1~]
Value:
| 1, 0, 0, 0 |
| 0, 1, 0, 0 |
| 0, 0, 1, 0 |
| 0, 0, 0, 1 |
| 0, 0, 0, 0 |
atlas> M
Value:
| 2, 0, 0, 0, 0 |
| 0, 2, 0, 3, 0 |
| 0, 0, 2, 0, 1 |
| 0, 0, 0, 2, 0 |
| 0, 0, 0, 0, 2 |
atlas> M[2,3]
Value: 0
atlas> M[2]
Value: [ 0, 0, 2, 0, 0 ]
atlas> M[3]
Value: [ 0, 3, 0, 2, 0 ]
atlas> set arr = for i:10 do #i od
Variable arr: [[int]]
atlas> M:=[[1,2]]
Value:
| 1 |
| 2 |
atlas> M:=[[1,2],5,6]]
^
syntax error, unexpected ']', expecting '\n'
atlas> M:=[[1,2],[5,6]]
Value:
| 1, 5 |
| 2, 6 |
atlas> M:=[[1,2,4],[5,6]]
Runtime error:
Vector sizes differ in conversion to matrix
Evaluation aborted.
atlas> M:=[[1,2,4],[5,6,8]]
Value:
| 1, 5 |
| 2, 6 |
| 4, 8 |
atlas> M:=2*id_mat(5)
Value:
| 2, 0, 0, 0, 0 |
| 0, 2, 0, 0, 0 |
| 0, 0, 2, 0, 0 |
| 0, 0, 0, 2, 0 |
| 0, 0, 0, 0, 2 |
atlas> M[2,4] := 1
Value: 1
atlas> M[1,3] := 3; M
Value:
| 2, 0, 0, 0, 0 |
| 0, 2, 0, 3, 0 |
| 0, 0, 2, 0, 1 |
| 0, 0, 0, 2, 0 |
| 0, 0, 0, 0, 2 |
atlas> invert(M)
Value: (
| 2, 0, 0, 0, 0 |
| 0, 2, 0, -3, 0 |
| 0, 0, 2, 0, -1 |
| 0, 0, 0, 2, 0 |
| 0, 0, 0, 0, 2 |
,4)
atlas> inv_fact(M)
Value: [ 1, 1, 2, 4, 4 ]
atlas> diagonal([2,5,4,6])
Value:
| 2, 0, 0, 0 |
| 0, 5, 0, 0 |
| 0, 0, 4, 0 |
| 0, 0, 0, 6 |
atlas> set alpha=vec: [1,-1,0], beta=vec:[0,1,-1])
^
syntax error, unexpected ')', expecting '\n' or ','
atlas> set alpha=vec: [1,-1,0], beta=vec:[0,1,-1]
Variable alpha: vec
Variable beta: vec
atlas> set simple_roots=mat:[alpha,beta]
Variable simple_roots: mat
atlas> simple_roots
Value:
| 1, 0 |
| -1, 1 |
| 0, -1 |
atlas> set simple_coroots=simple_roots
Variable simple_coroots: mat
atlas> root_data(simple_roots , simple_coroots )
Error during analysis of expression at <standard input>:168:0-41
Undefined identifier 'root_data'
Expression analysis failed
atlas> root_datum(simple_roots , simple_coroots )
Value: simply connected adjoint root datum of Lie type 'A2.T1'
atlas> set rd=$
Variable rd: RootDatum
atlas> roots(rd)
Value:
| -1, 0, -1, 1, 0, 1 |
| 0, -1, 1, -1, 1, 0 |
| 1, 1, 0, 0, -1, -1 |
atlas> root([0],rs)
Error during analysis of expression at <standard input>:172:0-12
Undefined identifier 'rs'
Expression analysis failed
atlas> root([0],rd)
Error in expression root([0],rd) at <standard input>:173:0-12
Failed to match 'root' with argument type ([int],RootDatum)
Expression analysis failed
atlas> root(rd,[0])
Runtime error:
Illegal root index 3
(in call at /home/marc/atlas/atlas-scripts/basic.at:635:44-77 of root@(RootDatum,int), built-in)
[rd=simply connected adjoint root datum of Lie type 'A2.T1', alpha_v=[ 0 ]]
(in call at <standard input>:174:0-12 of root@(RootDatum,vec), defined at /home/marc/atlas/atlas-scripts/basic.at:635:4-77)
Evaluation aborted.
atlas> root(rd,0)
Value: [ 1, -1, 0 ]
atlas> root(rd,1)
Value: [ 0, 1, -1 ]
atlas> root(rd,2)
Value: [ 1, 0, -1 ]
atlas> root(rd,3)
Runtime error:
Illegal root index 3
(in call at <standard input>:178:0-10 of root@(RootDatum,int), built-in)
Evaluation aborted.
atlas> root(rd,-1)
Value: [ -1, 1, 0 ]
atlas> root(rd,-3)
Value: [ -1, 0, 1 ]
atlas> root(rd,-4)
Runtime error:
Illegal root index -4
(in call at <standard input>:181:0-11 of root@(RootDatum,int), built-in)
Evaluation aborted.
atlas> posroots(rd)
Value:
| 1, 0, 1 |
| -1, 1, 0 |
| 0, -1, -1 |
atlas> roots(rd)
Value:
| -1, 0, -1, 1, 0, 1 |
| 0, -1, 1, -1, 1, 0 |
| 1, 1, 0, 0, -1, -1 |
atlas> rd:=root_data([[2]],[[1]])
Error during analysis of expression at <standard input>:184:0-26
Undefined identifier 'root_data'
Expression analysis failed
atlas> rd:=root_datum([[2]],[[1]])
Value: simply connected root datum of Lie type 'A1'
atlas> set ic := inner_class(rd,[[1]])
Error during analysis of expression at <standard input>:186:0-31
Undefined identifier 'ic' in assignment ic:=inner_class(rd,[[1]])
Expression analysis failed
atlas> set ic = inner_class(rd,[[1]])
Variable ic: InnerClass
atlas> ic
Value: Complex reductive group of type A1, with involution defining
inner class of type 'c', with 2 real forms and 2 dual real forms
atlas> form_names(ic)
Value: ["su(2)","sl(2,R)"]
atlas> set sl2r = real_form(ic,1)
Variable sl2r: RealForm
atlas> sl2r
Value: connected split real group with Lie algebra 'sl(2,R)'
atlas> print_KGB(sl2r)
kgbsize: 3
Base grading: [1].
0: 0 [n] 1 2 (0)#0 e
1: 0 [n] 0 2 (1)#0 e
2: 1 [r] 2 * (0)#1 1^e
atlas> print_X(ic)
\exp(i\pi\check\rho) = \exp(2i\pi([1]/4))
0: 0 [n] 1 4 [0]/1 0 e
1: 0 [n] 0 4 [1]/2 0 e
2: 0 [c] 2 * [1]/4 0 e
3: 0 [c] 3 * [3]/4 0 e
4: 1 [r] 4 * [0]/1 1 1^e
atlas> quit