atlas> test_s(0,-1,1,1/4) v coordinates p unitary in FPP ind -1/1 [1/2,0/1] (x=8,[3,0],[1,0]/2) true true -3/4 [3/8,0/1] (x=8,[3,0],[3,0]/8) true true -1/2 [1/4,0/1] (x=8,[3,0],[1,0]/4) true true -1/4 [1/8,0/1] (x=8,[3,0],[1,0]/8) true true 0/1 [0/1,0/1] (x=0,[0,0],[0,0]) true true 2T1 1/4 [1/8,0/1] (x=8,[3,0],[1,0]/8) true true 1/2 [1/4,0/1] (x=8,[3,0],[1,0]/4) true true 3/4 [3/8,0/1] (x=8,[3,0],[3,0]/8) true true atlas> <[(KType,int)]) Redefined certificate: (Param->[(KType,int)]) Completely read file 'certificate.at'. atlas> set p=p_s(0,3) Variable p: [Param] atlas> set p=p_s(0,3)[0] Variable p: Param (overriding previous instance, which had type [Param]) atlas> is_unitary(p) Value: false atlas> certificate (p) hermitian indefinite Value: [(final K-type K_type(x=3, lambda=[-1,1]/1),3),(final K-type K_type(x=4, lambda=[1,0]/1),5),(final K-type K_type(x=0, lambda=[1,0]/1),6),(final K-type K_type(x=2, lambda=[1,0]/1),6)] atlas> set h=hermitian_form_irreducible(p) Variable h: KTypePol (overriding previous instance, which had type (vec,int)) atlas> h Value: (1+0s)* K_type(x=0, lambda=[0,0]/1) [0] (-1+1s)* K_type(x=3, lambda=[-1,1]/1) [3] (1-1s)* K_type(x=4, lambda=[1,0]/1) [5] (-1+1s)* K_type(x=0, lambda=[1,0]/1) [6] (-1+1s)* K_type(x=2, lambda=[1,0]/1) [6] atlas> print_branch_std_long (h,20) m x lambda hw dim height 1 0 [ 0, 0 ]/1 KGB element #0[ -1, 1 ] 3 0 s 3 [ -1, 1 ]/1 KGB element #0[ 1, 0 ] 4 3 1 4 [ 1, 0 ]/1 KGB element #0[ -2, 2 ] 5 5 1+s 0 [ 1, 0 ]/1 KGB element #0[ 0, 1 ] 8 6 s 2 [ 1, 0 ]/1 KGB element #0[ 3, -1 ] 3 6 2s 3 [ 0, 1 ]/1 KGB element #0[ 2, 0 ] 9 9 2+s 0 [ 0, 1 ]/1 KGB element #0[ -1, 2 ] 12 10 1+s 1 [ 0, 1 ]/1 KGB element #0[ -3, 3 ] 7 10 1+3s 0 [ 2, 0 ]/1 KGB element #0[ 1, 1 ] 15 12 2s 2 [ 2, 0 ]/1 KGB element #0[ 4, -1 ] 8 12 4s 3 [ 1, 1 ]/1 KGB element #0[ 3, 0 ] 16 15 2+2s 4 [ 1, 1 ]/1 KGB element #0[ -2, 3 ] 16 15 2+3s 0 [ 1, 1 ]/1 KGB element #0[ 0, 2 ] 21 16 1+s 1 [ 1, 1 ]/1 KGB element #0[ -4, 4 ] 9 16 s 2 [ 1, 1 ]/1 KGB element #0[ 6, -2 ] 5 16 1+5s 0 [ 3, 0 ]/1 KGB element #0[ 2, 1 ] 24 18 4s 2 [ 3, 0 ]/1 KGB element #0[ 5, -1 ] 15 18 3+4s 0 [ 0, 2 ]/1 KGB element #0[ -1, 3 ] 27 20 2+3s 1 [ 0, 2 ]/1 KGB element #0[ -3, 4 ] 20 20 atlas> < make_s(0,-1,1,1/4) Value: [final parameter(x=8,lambda=[3,0]/1,nu=[1,0]/2),final parameter(x=8,lambda=[3,0]/1,nu=[3,0]/8),final parameter(x=8,lambda=[3,0]/1,nu=[1,0]/4),final parameter(x=8,lambda=[3,0]/1,nu=[1,0]/8),final parameter(x=0,lambda=[0,0]/1,nu=[0,0]/1),final parameter(x=8,lambda=[3,0]/1,nu=[1,0]/8),final parameter(x=8,lambda=[3,0]/1,nu=[1,0]/4),final parameter(x=8,lambda=[3,0]/1,nu=[3,0]/8)] atlas> atlas> atlas> atlas> atlas> M Value: | 1, 1 | | 0, 1 | | -1, -2 | atlas> for a in G.simple_roots do prints(a, " ", M*a) od [ 2, -1 ] [ 1, -1, 0 ] [ -3, 2 ] [ -1, 2, -1 ] Value: [(),()] atlas> for a in G.posroots do prints(a, " ", M*a) od [ 2, -1 ] [ 1, -1, 0 ] [ -3, 2 ] [ -1, 2, -1 ] [ 3, -1 ] [ 2, -1, -1 ] [ 0, 1 ] [ 1, 1, -2 ] [ -1, 1 ] [ 0, 1, -1 ] [ 1, 0 ] [ 1, 0, -1 ] Value: [(),(),(),(),(),()] atlas> atlas> atlas> atlas> atlas> atlas> atlas> atlas> atlas> p_s (0,1) Value: [final parameter(x=8,lambda=[3,0]/1,nu=[1,0]/2)] atlas> p_s(0,1) Value: [final parameter(x=8,lambda=[3,0]/1,nu=[1,0]/2)] atlas> atlas> atlas> atlas> atlas> set p=p_s(0,1)[0] Variable p: Param atlas> p Value: final parameter(x=8,lambda=[3,0]/1,nu=[1,0]/2) atlas> p.infinitesimal_character Value: [ 1, 0 ]/2 atlas> M*p.infinitesimal_character Value: [ 1, 0, -1 ]/2 atlas> atlas> atlas> p_s(1,0) Value: [final parameter(x=4,lambda=[1,0]/1,nu=[0,0]/1)] atlas> p_s(1,0)[0].is_unitary Value: true atlas> p_s(1,0)[1/2].is_unitary Error in expression p_s(1,0)[/(1,2)] at :32:0-13 Cannot subscript value of type [Param] with index of type rat Expression analysis failed Evaluation aborted. atlas> p_s(1,1/2)[0].is_unitary Value: true atlas> p_s(1,10/11)[0].is_unitary Value: true atlas> p_s(1,12/11)[0].is_unitary Value: false atlas> test_s(1,-2,2,1/4) v coordinates p unitary in FPP ind -2/1 [1/2,1/2] (x=5,[-1,2],[-1,1]) false true -7/4 [5/8,3/8] (x=5,[-1,2],[-7,7]/8) false true -3/2 [3/4,1/4] (x=5,[-1,2],[-3,3]/4) false true -5/4 [7/8,1/8] (x=5,[-1,2],[-5,5]/8) false true -1/1 [1/1,0/1] (x=4,[1,0],[2,-1]/2) true true A1+T1 -3/4 [3/4,1/8] (x=4,[1,0],[6,-3]/8) true true A1+T1 -1/2 [1/2,1/4] (x=4,[1,0],[2,-1]/4) true true A1+T1 -1/4 [1/4,3/8] (x=4,[1,0],[2,-1]/8) true true A1+T1 0/1 [0/1,1/2] (x=4,[1,0],[0,0]) true true A1+T1 1/4 [1/4,3/8] (x=4,[1,0],[2,-1]/8) true true A1+T1 1/2 [1/2,1/4] (x=4,[1,0],[2,-1]/4) true true A1+T1 3/4 [3/4,1/8] (x=4,[1,0],[6,-3]/8) true true A1+T1 1/1 [1/1,0/1] (x=4,[1,0],[2,-1]/2) true true A1+T1 5/4 [7/8,1/8] (x=5,[-1,2],[-5,5]/8) false true 3/2 [3/4,1/4] (x=5,[-1,2],[-3,3]/4) false true 7/4 [5/8,3/8] (x=5,[-1,2],[-7,7]/8) false true atlas> set p=p_s(0,1/4)[0] Variable p: Param (overriding previous instance, which had type Param) atlas> p Value: final parameter(x=8,lambda=[3,0]/1,nu=[1,0]/8) atlas> p.infinitesimal_character Value: [ 1, 0 ]/8 atlas> M*p.infinitesimal_character Value: [ 1, 0, -1 ]/8 atlas> set p=p_s(0,0)[0] Variable p: Param (overriding previous instance, which had type Param) atlas> p Value: final parameter(x=0,lambda=[0,0]/1,nu=[0,0]/1) atlas> p.infinitesimal_character Value: [ 0, 0 ]/1 atlas> atlas> atlas> atlas> p.infinitesimal_character Value: [ 0, 0 ]/1 atlas> p Value: final parameter(x=0,lambda=[0,0]/1,nu=[0,0]/1) atlas> p.is_unitary Value: true atlas> print_branch_irr_long (p,20) m x lambda hw dim height 1 0 [ 0, 0 ]/1 KGB element #0[ -1, 1 ] 3 0 1 3 [ -1, 1 ]/1 KGB element #0[ 1, 0 ] 4 3 1 4 [ 1, 0 ]/1 KGB element #0[ -2, 2 ] 5 5 2 0 [ 1, 0 ]/1 KGB element #0[ 0, 1 ] 8 6 1 2 [ 1, 0 ]/1 KGB element #0[ 3, -1 ] 3 6 2 3 [ 0, 1 ]/1 KGB element #0[ 2, 0 ] 9 9 3 0 [ 0, 1 ]/1 KGB element #0[ -1, 2 ] 12 10 2 1 [ 0, 1 ]/1 KGB element #0[ -3, 3 ] 7 10 4 0 [ 2, 0 ]/1 KGB element #0[ 1, 1 ] 15 12 2 2 [ 2, 0 ]/1 KGB element #0[ 4, -1 ] 8 12 4 3 [ 1, 1 ]/1 KGB element #0[ 3, 0 ] 16 15 4 4 [ 1, 1 ]/1 KGB element #0[ -2, 3 ] 16 15 5 0 [ 1, 1 ]/1 KGB element #0[ 0, 2 ] 21 16 2 1 [ 1, 1 ]/1 KGB element #0[ -4, 4 ] 9 16 1 2 [ 1, 1 ]/1 KGB element #0[ 6, -2 ] 5 16 6 0 [ 3, 0 ]/1 KGB element #0[ 2, 1 ] 24 18 4 2 [ 3, 0 ]/1 KGB element #0[ 5, -1 ] 15 18 7 0 [ 0, 2 ]/1 KGB element #0[ -1, 3 ] 27 20 5 1 [ 0, 2 ]/1 KGB element #0[ -3, 4 ] 20 20 atlas> set h=hermitian_form_irreducible(p) Variable h: KTypePol (overriding previous instance, which had type (vec,int)) atlas> h Value: 1* K_type(x=0, lambda=[0,0]/1) [0] atlas> print_branch_std_long (h,20) m x lambda hw dim height 1 0 [ 0, 0 ]/1 KGB element #0[ -1, 1 ] 3 0 1 3 [ -1, 1 ]/1 KGB element #0[ 1, 0 ] 4 3 1 4 [ 1, 0 ]/1 KGB element #0[ -2, 2 ] 5 5 2 0 [ 1, 0 ]/1 KGB element #0[ 0, 1 ] 8 6 1 2 [ 1, 0 ]/1 KGB element #0[ 3, -1 ] 3 6 2 3 [ 0, 1 ]/1 KGB element #0[ 2, 0 ] 9 9 3 0 [ 0, 1 ]/1 KGB element #0[ -1, 2 ] 12 10 2 1 [ 0, 1 ]/1 KGB element #0[ -3, 3 ] 7 10 4 0 [ 2, 0 ]/1 KGB element #0[ 1, 1 ] 15 12 2 2 [ 2, 0 ]/1 KGB element #0[ 4, -1 ] 8 12 4 3 [ 1, 1 ]/1 KGB element #0[ 3, 0 ] 16 15 4 4 [ 1, 1 ]/1 KGB element #0[ -2, 3 ] 16 15 5 0 [ 1, 1 ]/1 KGB element #0[ 0, 2 ] 21 16 2 1 [ 1, 1 ]/1 KGB element #0[ -4, 4 ] 9 16 1 2 [ 1, 1 ]/1 KGB element #0[ 6, -2 ] 5 16 6 0 [ 3, 0 ]/1 KGB element #0[ 2, 1 ] 24 18 4 2 [ 3, 0 ]/1 KGB element #0[ 5, -1 ] 15 18 7 0 [ 0, 2 ]/1 KGB element #0[ -1, 3 ] 27 20 5 1 [ 0, 2 ]/1 KGB element #0[ -3, 4 ] 20 20 atlas> set p=p_s(0,1/4)[0] Variable p: Param (overriding previous instance, which had type Param) atlas> p Value: final parameter(x=8,lambda=[3,0]/1,nu=[1,0]/8) atlas> p.is_unitary Value: true atlas> set h=hermitian_form_irreducible(p) Variable h: KTypePol (overriding previous instance, which had type KTypePol) atlas> h Value: 1* K_type(x=0, lambda=[0,0]/1) [0] atlas> set p=p_s(0,9/10)[0] Variable p: Param (overriding previous instance, which had type Param) atlas> p.is_unitary Value: true atlas> set h=hermitian_form_irreducible(p) Variable h: KTypePol (overriding previous instance, which had type KTypePol) atlas> h Value: 1* K_type(x=0, lambda=[0,0]/1) [0] atlas> set p=p_s(0,11/10)[0] Variable p: Param (overriding previous instance, which had type Param) atlas> is_unitary(p) Value: true atlas> set p=p_s(1,1/4)[0] Variable p: Param (overriding previous instance, which had type Param) atlas> is_unitary(p) Value: true atlas> hermitian_form_irreducible(p) Value: 1* K_type(x=4, lambda=[1,0]/1) [5] atlas> set p=p_s(1,9/10)[0] Variable p: Param (overriding previous instance, which had type Param) atlas> is_unitary(p) Value: true atlas> hermitian_form_irreducible(p) Value: 1* K_type(x=4, lambda=[1,0]/1) [5] atlas> set p=p_s(1,11/10)[0] Variable p: Param (overriding previous instance, which had type Param) atlas> is_unitary(p) Value: false atlas> set h=hermitian_form_irreducible(p) Variable h: KTypePol (overriding previous instance, which had type KTypePol) atlas> h Value: (1+0s)* K_type(x=4, lambda=[1,0]/1) [5] (-1+1s)* K_type(x=0, lambda=[1,0]/1) [6] atlas> print_branch_irr_long (h,20) Error in expression print_branch_irr_long(h,20) at :75:0-28 Failed to match 'print_branch_irr_long' with argument type (KTypePol,int) Expression analysis failed Evaluation aborted. atlas> print_branch_std (h,20) (1+0s)*(KGB element #0,[ -2, 2 ]) (0+1s)*(KGB element #0,[ 0, 1 ]) (0+1s)*(KGB element #0,[ 2, 0 ]) (1+1s)*(KGB element #0,[ -1, 2 ]) (0+1s)*(KGB element #0,[ -3, 3 ]) (0+2s)*(KGB element #0,[ 1, 1 ]) (0+1s)*(KGB element #0,[ 4, -1 ]) (0+2s)*(KGB element #0,[ 3, 0 ]) (1+2s)*(KGB element #0,[ -2, 3 ]) (1+3s)*(KGB element #0,[ 0, 2 ]) (1+1s)*(KGB element #0,[ -4, 4 ]) (0+1s)*(KGB element #0,[ 6, -2 ]) (0+4s)*(KGB element #0,[ 2, 1 ]) (0+2s)*(KGB element #0,[ 5, -1 ]) (1+4s)*(KGB element #0,[ -1, 3 ]) (1+3s)*(KGB element #0,[ -3, 4 ]) atlas> print_branch_std_long (h,20) m x lambda hw dim height 1 4 [ 1, 0 ]/1 KGB element #0[ -2, 2 ] 5 5 s 0 [ 1, 0 ]/1 KGB element #0[ 0, 1 ] 8 6 s 3 [ 0, 1 ]/1 KGB element #0[ 2, 0 ] 9 9 1+s 0 [ 0, 1 ]/1 KGB element #0[ -1, 2 ] 12 10 s 1 [ 0, 1 ]/1 KGB element #0[ -3, 3 ] 7 10 2s 0 [ 2, 0 ]/1 KGB element #0[ 1, 1 ] 15 12 s 2 [ 2, 0 ]/1 KGB element #0[ 4, -1 ] 8 12 2s 3 [ 1, 1 ]/1 KGB element #0[ 3, 0 ] 16 15 1+2s 4 [ 1, 1 ]/1 KGB element #0[ -2, 3 ] 16 15 1+3s 0 [ 1, 1 ]/1 KGB element #0[ 0, 2 ] 21 16 1+s 1 [ 1, 1 ]/1 KGB element #0[ -4, 4 ] 9 16 s 2 [ 1, 1 ]/1 KGB element #0[ 6, -2 ] 5 16 4s 0 [ 3, 0 ]/1 KGB element #0[ 2, 1 ] 24 18 2s 2 [ 3, 0 ]/1 KGB element #0[ 5, -1 ] 15 18 1+4s 0 [ 0, 2 ]/1 KGB element #0[ -1, 3 ] 27 20 1+3s 1 [ 0, 2 ]/1 KGB element #0[ -3, 4 ] 20 20 atlas> print_branch_irr_long (p,20) m x lambda hw dim height 1 4 [ 1, 0 ]/1 KGB element #0[ -2, 2 ] 5 5 1 0 [ 1, 0 ]/1 KGB element #0[ 0, 1 ] 8 6 1 3 [ 0, 1 ]/1 KGB element #0[ 2, 0 ] 9 9 2 0 [ 0, 1 ]/1 KGB element #0[ -1, 2 ] 12 10 1 1 [ 0, 1 ]/1 KGB element #0[ -3, 3 ] 7 10 2 0 [ 2, 0 ]/1 KGB element #0[ 1, 1 ] 15 12 1 2 [ 2, 0 ]/1 KGB element #0[ 4, -1 ] 8 12 2 3 [ 1, 1 ]/1 KGB element #0[ 3, 0 ] 16 15 3 4 [ 1, 1 ]/1 KGB element #0[ -2, 3 ] 16 15 4 0 [ 1, 1 ]/1 KGB element #0[ 0, 2 ] 21 16 2 1 [ 1, 1 ]/1 KGB element #0[ -4, 4 ] 9 16 1 2 [ 1, 1 ]/1 KGB element #0[ 6, -2 ] 5 16 4 0 [ 3, 0 ]/1 KGB element #0[ 2, 1 ] 24 18 2 2 [ 3, 0 ]/1 KGB element #0[ 5, -1 ] 15 18 5 0 [ 0, 2 ]/1 KGB element #0[ -1, 3 ] 27 20 4 1 [ 0, 2 ]/1 KGB element #0[ -3, 4 ] 20 20 atlas> set c=certificate (p) hermitian indefinite Variable c: [(KType,int)] (overriding previous instance, which had type (vec,int)) atlas> c Value: [(final K-type K_type(x=0, lambda=[1,0]/1),6)] atlas> set mu=LKT(p) Variable mu: KType atlas> atlas> atlas> mu Value: final K-type K_type(x=4, lambda=[1,0]/1) atlas> mu.highest_weight Value: ((),KGB element #0,[ -2, 2 ]) atlas> rho_0(KGB(G,0)) Error during analysis of expression at :86:0-15 Undefined identifier 'rho_0' Expression analysis failed Evaluation aborted. atlas> rho(KGB(G,0)) Error in expression rho(KGB(G,0)) at :87:0-13 Failed to match 'rho' with argument type KGBElt Expression analysis failed Evaluation aborted. atlas> rho_K(KGB(G,0)) Value: [ 1, 0 ]/1 atlas> set K_0(G) ^ syntax error, unexpected IDENT, expecting ')' atlas> set K=K_0(G) Variable K: RealForm atlas> K.simple_roots Value: | 3, -1 | | -1, 1 | atlas> fundamental_ fundamental_Cartan fundamental_group fundamental_weights fundamental_coweight fundamental_weight fundamental_weights_K_H fundamental_coweights fundamental_weight_coordinates atlas> whattype fundamental_weight_coordinates Type: Error during analysis of expression at :92:9-39 Undefined identifier 'fundamental_weight_coordinates' Expression analysis failed atlas> whattype fundamental_weight_coordinates ? Overloaded instances of 'fundamental_weight_coordinates' Param->vec KHighestWeight->vec atlas> mnuy Error during analysis of expression at :94:0-4 Undefined identifier 'mnuy' Expression analysis failed Evaluation aborted. atlas> nmuy Error during analysis of expression at :95:0-4 Undefined identifier 'nmuy' Expression analysis failed Evaluation aborted. atlas> ju\\\\\ \ \ > \ > \ > ? ^ syntax error, unexpected '?' atlas> mu Value: final K-type K_type(x=4, lambda=[1,0]/1) atlas> highest_weight(mu) Value: ((),KGB element #0,[ -2, 2 ]) atlas> fundamental_weight_coordinates(highest_weight(mu)) Value: [ 0, 4 ] atlas> atlas> atlas> atlas> atlas> atlas> atlas> atlas> atlas> atlas> set G=GL(2,R) Variable G: RealForm (overriding previous instance, which had type RealForm) atlas> atlas> atlas> set b=block_of (G.trivial) Variable b: [Param] (overriding previous instance, which had type (vec,int)) atlas> atlas> atlas> atlas> atlas> b Value: [final parameter(x=0,lambda=[1,-1]/2,nu=[0,0]/1),final parameter(x=1,lambda=[3,1]/2,nu=[1,-1]/2),final parameter(x=1,lambda=[1,-1]/2,nu=[1,-1]/2)] atlas> set data=for p in b do cuspidal_data (p) G > od Variable data: [(KGPElt,Param)] atlas> atlas> atlas> for (P,q) in data do prints(P, " ", P.Levi, " ", q) od ([0],KGB element #0) disconnected split real group with Lie algebra 'sl(2,R).gl(1,R)' final parameter(x=0,lambda=[1,-1]/2,nu=[0,0]/1) ([],KGB element #1) disconnected split real group with Lie algebra 'gl(1,R).gl(1,R)' final parameter(x=0,lambda=[1,1]/1,nu=[1,-1]/2) ([],KGB element #1) disconnected split real group with Lie algebra 'gl(1,R).gl(1,R)' final parameter(x=0,lambda=[0,0]/1,nu=[1,-1]/2) Value: [(),(),()] atlas> atlas> atlas> atlas> for (P,q) in data do prints(P, " ", P.Levi, " ", q) od ([0],KGB element #0) disconnected split real group with Lie algebra 'sl(2,R).gl(1,R)' final parameter(x=0,lambda=[1,-1]/2,nu=[0,0]/1) ([],KGB element #1) disconnected split real group with Lie algebra 'gl(1,R).gl(1,R)' final parameter(x=0,lambda=[1,1]/1,nu=[1,-1]/2) ([],KGB element #1) disconnected split real group with Lie algebra 'gl(1,R).gl(1,R)' final parameter(x=0,lambda=[0,0]/1,nu=[1,-1]/2) Value: [(),(),()] atlas> data[0] Value: (([0],KGB element #0),final parameter(x=0,lambda=[1,-1]/2,nu=[0,0]/1)) atlas> set P=data[0] Variable P: (KGPElt,Param) atlas> P Value: (([0],KGB element #0),final parameter(x=0,lambda=[1,-1]/2,nu=[0,0]/1)) atlas> set P=data[0][0] Error in expression data[0][0] at :134:6-16 Cannot subscript value of type (KGPElt,Param) with index of type int Error in 'set' command at :134:0-17: Expression analysis failed Command 'set P' not executed, nothing defined. atlas> P Value: (([0],KGB element #0),final parameter(x=0,lambda=[1,-1]/2,nu=[0,0]/1)) atlas> set d=data[0] Variable d: (KGPElt,Param) atlas> d Value: (([0],KGB element #0),final parameter(x=0,lambda=[1,-1]/2,nu=[0,0]/1)) atlas> set (P,q)=d Variable P: KGPElt (overriding previous instance, which had type (KGPElt,Param)) Variable q: Param atlas> P Value: ([0],KGB element #0) atlas> Levi(P) Value: disconnected split real group with Lie algebra 'sl(2,R).gl(1,R)' atlas> P Value: ([0],KGB element #0) atlas> for p in block do let (Q,) = cuspidal_data(p) in if P=Q then [p] else [] fi od.## Error during analysis of expression at :142:0-81 Undefined identifier 'block' Expression analysis failed Evaluation aborted. atlas> for p in b do let (Q,) = cuspidal_data(p) in if P=Q then [p] else [] fi od.## Value: [final parameter(x=0,lambda=[1,-1]/2,nu=[0,0]/1)] atlas> set d=data[1] Variable d: (KGPElt,Param) (overriding previous instance, which had type (KGPElt,Param)) atlas> set (P,q)=d Variable P: KGPElt (overriding previous instance, which had type KGPElt) Variable q: Param (overriding previous instance, which had type Param) atlas> for p in block do let (Q,) = cuspidal_data(p) in if P=Q then [p] else [] fi od.## Error during analysis of expression at :146:0-81 Undefined identifier 'block' Expression analysis failed Evaluation aborted. atlas> for p in b do let (Q,) = cuspidal_data(p) in if P=Q then [p] else [] fi od.## Value: [final parameter(x=1,lambda=[3,1]/2,nu=[1,-1]/2),final parameter(x=1,lambda=[1,-1]/2,nu=[1,-1]/2)] atlas> for p in b do let (Q,) = cuspidal_data(p) in if P=Q then [p] else [] fi od Value: [[],[final parameter(x=1,lambda=[3,1]/2,nu=[1,-1]/2)],[final parameter(x=1,lambda=[1,-1]/2,nu=[1,-1]/2)]] atlas> for p in b do let (Q,) = cuspidal_data(p) in if P=Q then [p] else [] fi od.## Value: [final parameter(x=1,lambda=[3,1]/2,nu=[1,-1]/2),final parameter(x=1,lambda=[1,-1]/2,nu=[1,-1]/2)] atlas> set induced=for p in b do let (Q,) = cuspidal_data(p) in if P=Q then [p] else [] fi od.## Variable induced: [Param] atlas> induced Value: [final parameter(x=1,lambda=[3,1]/2,nu=[1,-1]/2),final parameter(x=1,lambda=[1,-1]/2,nu=[1,-1]/2)] atlas> for p in b do if {condition} [p] else [] fi od.## ^^ syntax error, unexpected FI, expecting THEN atlas> let x=3 in x^2 Value: 9 atlas> set induced=for p in b do let (Q,) = cuspidal_data(p) in if P=Q then [p] else [] fi od.## Variable induced: [Param] (overriding previous instance, which had type [Param]) atlas> atlas> let a=1 in let b=2 in a+b Value: 3 atlas> b Value: [final parameter(x=0,lambda=[1,-1]/2,nu=[0,0]/1),final parameter(x=1,lambda=[3,1]/2,nu=[1,-1]/2),final parameter(x=1,lambda=[1,-1]/2,nu=[1,-1]/2)] atlas> for p in b do prints(p) od final parameter(x=0,lambda=[1,-1]/2,nu=[0,0]/1) final parameter(x=1,lambda=[3,1]/2,nu=[1,-1]/2) final parameter(x=1,lambda=[1,-1]/2,nu=[1,-1]/2) Value: [(),(),()] atlas> for p@i in b do prints(p) od final parameter(x=0,lambda=[1,-1]/2,nu=[0,0]/1) final parameter(x=1,lambda=[3,1]/2,nu=[1,-1]/2) final parameter(x=1,lambda=[1,-1]/2,nu=[1,-1]/2) Value: [(),(),()] atlas> for p@i in b do prints(i, " ", p) od 0 final parameter(x=0,lambda=[1,-1]/2,nu=[0,0]/1) 1 final parameter(x=1,lambda=[3,1]/2,nu=[1,-1]/2) 2 final parameter(x=1,lambda=[1,-1]/2,nu=[1,-1]/2) Value: [(),(),()] atlas> for i:5 do i G > od Value: [0,1,2,3,4] atlas> atlas> atlas> atlas> for i:#b do prints(i, " ", b[i]) od 0 final parameter(x=0,lambda=[1,-1]/2,nu=[0,0]/1) 1 final parameter(x=1,lambda=[3,1]/2,nu=[1,-1]/2) 2 final parameter(x=1,lambda=[1,-1]/2,nu=[1,-1]/2) Value: [(),(),()] atlas> set G=G2_s Variable G: RealForm (overriding previous instance, which had type RealForm) atlas> set gamma=[5/3,-1/3,-2/3] Variable gamma: [rat] atlas> <string) Redefined all_parameters_x_gamma: (KGBElt,ratvec->[Param]) Variable M: mat (overriding previous instance, which had type mat) Variable i_M: ratmat (overriding previous instance, which had type ratmat) Redefined g2_parameter: (KGBElt,ratvec,ratvec->Param) Variable cartans: [CartanClass] (overriding previous instance, which had type [CartanClass]) Variable H1: CartanClass (overriding previous instance, which had type CartanClass) Variable H2: CartanClass (overriding previous instance, which had type CartanClass) Variable H_s: CartanClass (overriding previous instance, which had type CartanClass) Variable H_l: CartanClass (overriding previous instance, which had type CartanClass) Redefined ps: (int,ratvec->Param) Redefined gamma_s: (rat,rat->ratvec) Variable x_s: KGBElt (overriding previous instance, which had type KGBElt) Redefined p_s: (rat,rat->[Param]) Redefined gamma_l: (rat,rat->ratvec) Variable x_l: KGBElt (overriding previous instance, which had type KGBElt) Redefined coords: (RootDatum,ratvec->[rat]) Redefined in_fpp: (ratvec->bool) Redefined in_fpp: (RootDatum,ratvec->bool) Redefined in_fpp: (Param->bool) Redefined p_l: (rat,rat->[Param]) Redefined test_s: (int,rat,rat,rat->) Redefined test_l: (int,rat,rat,rat->) Completely read file 'G2_unitary_dual.at'. atlas> set v=i_M(gamma) Error during analysis of expression at :170:6-16 Type error: Subexpression i_M at :170:6-9 has wrong type: found ratmat while (*->*) was needed. Error in 'set' command at :170:0-17: Expression analysis failed Command 'set v' not executed, nothing defined. atlas> set v=i_M*gamma Variable v: ratvec atlas> v Value: [ 18, -5 ]/9 atlas> for p in all_parameters_gamma (G,v) do prints(p) od final parameter(x=9,lambda=[1,1]/1,nu=[3,5]/9) final parameter(x=9,lambda=[2,1]/1,nu=[3,5]/9) final parameter(x=9,lambda=[1,2]/1,nu=[3,5]/9) final parameter(x=9,lambda=[2,2]/1,nu=[3,5]/9) final parameter(x=6,lambda=[2,0]/1,nu=[12,-4]/9) Value: [(),(),(),(),()] atlas> v Value: [ 18, -5 ]/9 atlas> parameter(KGB(G,9),G.rho,[0,0]) Value: final parameter(x=9,lambda=[1,1]/1,nu=[0,0]/1) atlas> parameter(KGB(G,9),G.rho+[1,0],[0,0]) Value: non-final parameter(x=9,lambda=[2,1]/1,nu=[0,0]/1) atlas> p=parameter(KGB(G,9),G.rho+[1,0],[0,0]) Value: false atlas> set p=parameter(KGB(G,9),G.rho+[1,0],[0,0]) Variable p: Param (overriding previous instance, which had type Param) atlas> p Value: non-final parameter(x=9,lambda=[2,1]/1,nu=[0,0]/1) atlas> set p_1=parameter(KGB(G,9),G.rho+[1,0],[2,1]) Variable p_1: Param atlas> p_1` ^ syntax error, unexpected $undefined, expecting '\n' atlas> p_1 Value: final parameter(x=9,lambda=[2,1]/1,nu=[2,1]/1) atlas> finalize(p) Value: 1*parameter(x=0,lambda=[0,0]/1,nu=[0,0]/1) [0] atlas> p Value: non-final parameter(x=9,lambda=[2,1]/1,nu=[0,0]/1) atlas> finalize(p) Value: 1*parameter(x=0,lambda=[0,0]/1,nu=[0,0]/1) [0]