Archived web site of the Workshop on the Atlas of Lie Groups and Representations, Salt Lake City, July 10–21, 2017. All Atlas workshops
Computer input/output: adams_7.19.out
Back
jda@Leonidas:~/atlasSoftware/master/atlasofliegroups$
jda@Leonidas:~/atlasSoftware/master/atlasofliegroups$
jda@Leonidas:~/atlasSoftware/master/atlasofliegroups$ cd atlas-scripts/
jda@Leonidas:~/atlasSoftware/master/atlasofliegroups/atlas-scripts$ ../atlas all
This is 'atlas' (version 1.0.7, axis language version 0.9.6),
the Atlas of Lie Groups and Representations interpreter,
compiled on Jul 17 2017 at 20:01:50. http://www.liegroups.org/
atlas> set G=SL(2,R)
Variable G: RealForm
atlas> set B=block_of (trivial(G))
Variable B: [Param]
atlas> set p=trivial(G)
Variable p: Param
atlas> print_block(p)
Parameter defines element 2 of the following block:
0: 0 [i1] 1 (2,*) *(x=0,lam_rho= [0], nu= [0]/1) e
1: 0 [i1] 0 (2,*) *(x=1,lam_rho= [0], nu= [0]/1) e
2: 1 [r1] 2 (0,1) *(x=2,lam_rho= [0], nu= [1]/1) 1^e
atlas>
atlas>
atlas>
atlas>
atlas> whattype coherent_std ?
Overloaded instances of 'coherent_std'
(Param,int)->ParamPol
(Param,[int])->ParamPol
(ParamPol,int)->ParamPol
(ParamPol,[int])->ParamPol
((RootDatum,[int]),Param)->ParamPol
((RootDatum,[int]),ParamPol)->ParamPol
atlas> set ds=B[0]
Variable ds: Param
atlas> ds
Value: final parameter(x=0,lambda=[1]/1,nu=[0]/1)
atlas> coherent_std(ds,0)
Value:
1*parameter(x=2,lambda=[1]/1,nu=[1]/1) [0]
-1*parameter(x=1,lambda=[1]/1,nu=[0]/1) [1]
atlas> set ds2=B[1]
Variable ds2: Param
atlas> coherent_std(ds2,0)
Value:
1*parameter(x=2,lambda=[1]/1,nu=[1]/1) [0]
-1*parameter(x=0,lambda=[1]/1,nu=[0]/1) [1]
atlas>
atlas>
atlas>
atlas> coherent_irr (ds,0)
Value:
1*parameter(x=2,lambda=[1]/1,nu=[1]/1) [0]
1*parameter(x=0,lambda=[1]/1,nu=[0]/1) [1]
atlas> coherent_irr (B[2],0)
Value:
-1*parameter(x=2,lambda=[1]/1,nu=[1]/1) [0]
atlas> G
Value: connected split real group with Lie algebra 'sl(2,R)'
atlas>
atlas>
atlas> B:=block_of (trivial(G))
Value: [final parameter(x=0,lambda=[1]/1,nu=[0]/1),final parameter(x=1,lambda=[1]/1,nu=[0]/1),final parameter(x=2,lambda=[1]/1,nu=[1]/1)]
atlas> whattype B
type: [Param]
atlas>
atlas>
atlas> set Gd=dual_quasisplit_form (G)
Variable Gd: RealForm
atlas> Gd
Value: disconnected split real group with Lie algebra 'sl(2,R)'
atlas> set B2=block(G,Gd)
Variable B2: Block (overriding previous instance, which had type string)
atlas> whattype B2
type: Block
atlas> print_W_cells (B2)
// Cells and their vertices.
#0={0}
#1={1}
#2={2}
// Induced graph on cells.
#0:.
#1:.
#2:->#0,#1.
// Individual cells.
// cell #0:
0[0]: {}
// cell #1:
0[1]: {}
// cell #2:
0[2]: {1}
atlas> set G=Sp(4,R)
Variable G: RealForm (overriding previous instance, which had type RealForm)
atlas> set Gd=dual_quasisplit_form (G)
Variable Gd: RealForm (overriding previous instance, which had type RealForm)
atlas> print_block(trivial(G))
Parameter defines element 10 of the following block:
0: 0 [i1,i1] 1 2 ( 4, *) ( 5, *) *(x= 0,lam_rho= [0,0], nu= [0,0]/1) e
1: 0 [i1,i1] 0 3 ( 4, *) ( 6, *) *(x= 1,lam_rho= [0,0], nu= [0,0]/1) e
2: 0 [ic,i1] 2 0 ( *, *) ( 5, *) *(x= 2,lam_rho= [0,0], nu= [0,0]/1) e
3: 0 [ic,i1] 3 1 ( *, *) ( 6, *) *(x= 3,lam_rho= [0,0], nu= [0,0]/1) e
4: 1 [r1,C+] 4 9 ( 0, 1) ( *, *) *(x= 4,lam_rho= [0,0], nu= [1,-1]/2) 1^e
5: 1 [C+,r1] 7 5 ( *, *) ( 0, 2) *(x= 5,lam_rho= [0,0], nu= [0,1]/1) 2^e
6: 1 [C+,r1] 8 6 ( *, *) ( 1, 3) *(x= 6,lam_rho= [0,0], nu= [0,1]/1) 2^e
7: 2 [C-,i1] 5 8 ( *, *) (10, *) *(x= 7,lam_rho= [0,0], nu= [2,0]/1) 1x2^e
8: 2 [C-,i1] 6 7 ( *, *) (10, *) *(x= 8,lam_rho= [0,0], nu= [2,0]/1) 1x2^e
9: 2 [i2,C-] 9 4 (10,11) ( *, *) *(x= 9,lam_rho= [0,0], nu= [3,3]/2) 2x1^e
10: 3 [r2,r1] 11 10 ( 9, *) ( 7, 8) *(x=10,lam_rho= [0,0], nu= [2,1]/1) 1^2x1^e
11: 3 [r2,rn] 10 11 ( 9, *) ( *, *) *(x=10,lam_rho= [1,1], nu= [2,1]/1) 1^2x1^e
atlas> print_W_cells (block(G,Gd))
// Cells and their vertices.
#0={0}
#1={1}
#2={2,5,7}
#3={3,6,8}
#4={4,9,11}
#5={10}
// Induced graph on cells.
#0:.
#1:.
#2:->#0.
#3:->#1.
#4:->#0,#1.
#5:->#2,#3,#4.
// Individual cells.
// cell #0:
0[0]: {}
// cell #1:
0[1]: {}
// cell #2:
0[2]: {1} --> 1
1[5]: {2} --> 0,2
2[7]: {1} --> 1
// cell #3:
0[3]: {1} --> 1
1[6]: {2} --> 0,2
2[8]: {1} --> 1
// cell #4:
0[4]: {1} --> 1
1[9]: {2} --> 0,2
2[11]: {1} --> 1
// cell #5:
0[10]: {1,2}
atlas> set W= generate_W (G)
Variable W: [(RootDatum,[int])]
atlas>
atlas>
atlas>
atlas> set W= generate_W (G)
Variable W: [(RootDatum,[int])] (overriding previous instance, which had type [(RootDatum,[int])])
atlas> print_W_cells (block(G,Gd))
// Cells and their vertices.
#0={0}
#1={1}
#2={2,5,7}
#3={3,6,8}
#4={4,9,11}
#5={10}
// Induced graph on cells.
#0:.
#1:.
#2:->#0.
#3:->#1.
#4:->#0,#1.
#5:->#2,#3,#4.
// Individual cells.
// cell #0:
0[0]: {}
// cell #1:
0[1]: {}
// cell #2:
0[2]: {1} --> 1
1[5]: {2} --> 0,2
2[7]: {1} --> 1
// cell #3:
0[3]: {1} --> 1
1[6]: {2} --> 0,2
2[8]: {1} --> 1
// cell #4:
0[4]: {1} --> 1
1[9]: {2} --> 0,2
2[11]: {1} --> 1
// cell #5:
0[10]: {1,2}
atlas> set p=B[6]
index 6 out of range (0<= . <3) in subscription B[6]
Command 'set p' interrupted, nothing defined.
atlas> set B=block_of (trivial(G))
Variable B: [Param] (overriding previous instance, which had type [Param])
atlas> set p=B[6]
Variable p: Param (overriding previous instance, which had type Param)
atlas> coherent_irr (p,0)
Value:
1*parameter(x=8,lambda=[2,1]/1,nu=[2,0]/1) [3]
1*parameter(x=6,lambda=[2,1]/1,nu=[0,1]/1) [6]
1*parameter(x=3,lambda=[2,1]/1,nu=[0,0]/1) [7]
atlas> coherent_irr (p,1)
Value:
-1*parameter(x=6,lambda=[2,1]/1,nu=[0,1]/1) [6]
atlas> set cells=W_cells (B)
Error during analysis of expression at <standard input>:47:11-22
Type error:
Subexpression B at <standard input>:47:20-21
has wrong type: found [Param] while Block was needed.
Expression analysis failed
Command 'set cells' not executed, nothing defined.
atlas> set B2=block(G,Gd)
Variable B2: Block (overriding previous instance, which had type Block)
atlas> set cells=W_cells (B2)
Variable cells: [([int],[([int],[(int,int)])])]
atlas> set (a,b)=cells
Type [([int],[([int],[(int,int)])])] of right hand side does not match required pattern (*,*)
Command 'set (a,b)' not executed, nothing defined.
atlas> set (a,b,c)=cells
Type [([int],[([int],[(int,int)])])] of right hand side does not match required pattern (*,*,*)
Command 'set (a,b,c)' not executed, nothing defined.
atlas> whattype cells
type: [([int],[([int],[(int,int)])])]
atlas> cells[0]
Value: ([0],[([],[])])
atlas> cells[2]
Value: ([2,5,7],[([0],[(1,1)]),([1],[(0,1),(2,1)]),([0],[(1,1)])])
atlas> cells[1]
Value: ([1],[([],[])])
atlas> for a in cells do prints(a)
G > od
[0][([],[])]
[1][([],[])]
[2,5,7][([0],[(1,1)]),([1],[(0,1),(2,1)]),([0],[(1,1)])]
[3,6,8][([0],[(1,1)]),([1],[(0,1),(2,1)]),([0],[(1,1)])]
[4,9,11][([0],[(1,1)]),([1],[(0,1),(2,1)]),([0],[(1,1)])]
[10][([0,1],[])]
Value: [(),(),(),(),(),()]
atlas>
atlas>
atlas>
atlas> zg
Error during analysis of expression at <standard input>:61:0-2
Undefined identifier 'zg'
Expression analysis failed
atlas>
atlas>
atlas> set cell=cells[3][0]
Error in expression cells[3][0] at <standard input>:64:9-20
Cannot subscript value of type ([int],[([int],[(int,int)])]) with index of type int
Expression analysis failed
Command 'set cell' not executed, nothing defined.
atlas> cells[3]
Value: ([3,6,8],[([0],[(1,1)]),([1],[(0,1),(2,1)]),([0],[(1,1)])])
atlas> set (cell,,)=cells[3]
Type ([int],[([int],[(int,int)])]) of right hand side does not match required pattern (*,*,*)
Command 'set (cell,,)' not executed, nothing defined.
atlas> set (cell,)=cells[3]
Variable cell: [int]
atlas> cell
Value: [3,6,8]
atlas> <W_cells.at
Starting to read from file 'W_cells.at'.
Defined find_mate: ([(int,int)],int->int)
Added definition [3] of matrix: (([int],[([int],[(int,int)])]),int->mat)
Completely read file 'W_cells.at'.
atlas> set cell=cells[2]
Variable cell: ([int],[([int],[(int,int)])]) (overriding previous instance, which had type [int])
atlas> cell
Value: ([2,5,7],[([0],[(1,1)]),([1],[(0,1),(2,1)]),([0],[(1,1)])])
atlas> matrix(cell,0)
taus=[[0],[1],[0]]
arrows=[[(1,1)],[(0,1),(2,1)],[(1,1)]]
Value:
| -1, 1, 0 |
| 0, 1, 0 |
| 0, 1, -1 |
atlas> matrix(cell,1)
taus=[[0],[1],[0]]
arrows=[[(1,1)],[(0,1),(2,1)],[(1,1)]]
Value:
| 1, 0, 0 |
| 1, -1, 1 |
| 0, 0, 1 |
atlas>
atlas>
atlas>
atlas>
atlas>
atlas>
atlas>
atlas> print_W_cells (B2)
// Cells and their vertices.
#0={0}
#1={1}
#2={2,5,7}
#3={3,6,8}
#4={4,9,11}
#5={10}
// Induced graph on cells.
#0:.
#1:.
#2:->#0.
#3:->#1.
#4:->#0,#1.
#5:->#2,#3,#4.
// Individual cells.
// cell #0:
0[0]: {}
// cell #1:
0[1]: {}
// cell #2:
0[2]: {1} --> 1
1[5]: {2} --> 0,2
2[7]: {1} --> 1
// cell #3:
0[3]: {1} --> 1
1[6]: {2} --> 0,2
2[8]: {1} --> 1
// cell #4:
0[4]: {1} --> 1
1[9]: {2} --> 0,2
2[11]: {1} --> 1
// cell #5:
0[10]: {1,2}
atlas> set cells=W_cells (B2)
Variable cells: [([int],[([int],[(int,int)])])] (overriding previous instance, which had type [([int],[([int],[(int,int)])])])
atlas>
atlas>
atlas> for cell in cells do prints(cell)
G >
G >
G > od
[0][([],[])]
[1][([],[])]
[2,5,7][([0],[(1,1)]),([1],[(0,1),(2,1)]),([0],[(1,1)])]
[3,6,8][([0],[(1,1)]),([1],[(0,1),(2,1)]),([0],[(1,1)])]
[4,9,11][([0],[(1,1)]),([1],[(0,1),(2,1)]),([0],[(1,1)])]
[10][([0,1],[])]
Value: [(),(),(),(),(),()]
atlas>
atlas>
atlas>
atlas>
atlas> set cell=cells[2]
Variable cell: ([int],[([int],[(int,int)])]) (overriding previous instance, which had type ([int],[([int],[(int,int)])]))
atlas> whattype matrix ?
Overloaded instances of 'matrix'
((int,int),(int,int->int))->mat
((int,int),(int,int->rat))->(mat,string,int)
(([int],[([int],[(int,int)])]),int)->mat
atlas> matrix(cell,0)
taus=[[0],[1],[0]]
arrows=[[(1,1)],[(0,1),(2,1)],[(1,1)]]
Value:
| -1, 1, 0 |
| 0, 1, 0 |
| 0, 1, -1 |
atlas>
atlas>
atlas>
atlas>
atlas> matrix(cell,1)
taus=[[0],[1],[0]]
arrows=[[(1,1)],[(0,1),(2,1)],[(1,1)]]
Value:
| 1, 0, 0 |
| 1, -1, 1 |
| 0, 0, 1 |
atlas> set s0=matrix(cell,0)
taus=[[0],[1],[0]]
arrows=[[(1,1)],[(0,1),(2,1)],[(1,1)]]
Variable s0: mat
atlas> set s1=matrix(cell,1)
taus=[[0],[1],[0]]
arrows=[[(1,1)],[(0,1),(2,1)],[(1,1)]]
Variable s1: mat
atlas> s0^2
Value:
| 1, 0, 0 |
| 0, 1, 0 |
| 0, 0, 1 |
atlas> s1^2
Value:
| 1, 0, 0 |
| 0, 1, 0 |
| 0, 0, 1 |
atlas> s0*s1*s0*s1=s1*s0*s1*s0
Value: true
atlas>