atlas> set x=1 Identifier x: int (hiding previous one of type KGBElt) atlas> quit Bye. jda@Leonidas:~$ atlas This is 'atlas' (version 0.6, axis language version 0.9), the Atlas of Lie Groups and Representations interpreter, compiled on Feb 24 2016 at 20:51:51. http://www.liegroups.org/ atlas> atlas> atlas> atlas> set x=1 Identifier x: int atlas> x Value: 1 atlas> set x=2 Identifier x: int (hiding previous one of type int) atlas> x Value: 2 atlas> x:=3 Value: 3 atlas> atlas> atlas> atlas> atlas> atlas> atlas> y:=1 Error during analysis of expression at :15:0-4 Undefined identifier 'y' in assignment y:=1 Type check failed atlas> set y=1 Identifier y: int atlas> y:=2 Value: 2 atlas> set A=mat:[[2,1],[0,1]] Identifier A: mat atlas> A Value: | 2, 0 | | 1, 1 | atlas> A*[3,2] Value: [ 6, 5 ] atlas> inverse(A) Runtime error: Matrix not invertible over the integers (in call of error, built-in) (in call of inverse@mat, defined at /home/jda/atlasSoftware/atlasofliegroups/atlas-scripts/basic.at:254:4--256:74) Evaluation aborted. atlas> set B=rational_inverse(A) Identifier B: (mat,string,int) atlas> B Value: ( | 1, 0 | | -1, 2 | ,"/",2) atlas> whattype B type: (mat,string,int) atlas> show(B) 1/2 -1/2 0 1 atlas> B*A Value: ( | 1, 0 | | 0, 1 | ,"/",1) atlas> show(B*A) 1 0 0 1 atlas> set C=B*A Identifier C: (mat,string,int) atlas> C Value: ( | 1, 0 | | 0, 1 | ,"/",1) atlas> ratmat_as_mat (C) Value: | 1, 0 | | 0, 1 | atlas> B*[1/2,3/2] Value: [ 1, 5 ]/4 atlas> x:=2 Value: 2 atlas> x^3 Value: 8 atlas> x Value: 2 atlas> set y=x^3 Identifier y: int (hiding previous one of type int) atlas> y Value: 8 atlas> let a=2 in a^3 Value: 8 atlas> a Error during analysis of expression at :42:0-1 Undefined identifier 'a' Type check failed atlas> let a=2 in 3*a^2+4*a+1 Value: 21 atlas> set b=let a=2 in 3*a^2+4*a+1 Identifier b: int atlas> b Value: 21 atlas> let a=2 in let b=3 in a^b Value: 8 atlas> let a=2 in let b=3 in let c=4 in a*b*c Value: 24 atlas> let a=2 then b=3 then c=4 in a*b*c Value: 24 atlas> let a=2 L > in let b=3 L > in a^b Value: 8 atlas> let a=2 then b=3 then c=4 in a*b*c Value: 24 atlas> set d=let a=2 then b=3 then c=4 in a*b*c Identifier d: int atlas> d Value: 24 atlas> let a=2,b=3 in a^b Value: 8 atlas> x Value: 2 atlas> y Value: 8 atlas> x;y Value: 8 atlas> let x=2 in let y=3 in x^y;x+y Value: 5 atlas> prints("hello world") hello world atlas> set r=prints("hello world") hello world Identifier r: void atlas> r atlas> let x=2 in let y=3 in prints("x=",x,"y=",y);x^y x=2y=3 Value: 8 atlas> let x=2 in let y=3 in prints("x=",x);prints("y=",y);x^y x=2 y=3 Value: 8 atlas> set c=1 Identifier c: int atlas> c Value: 1 atlas> let c=3 in c*c Value: 9 atlas> c Value: 1 atlas> for i:4 do i G > od Value: [0,1,2,3] atlas> for i:4 do 2*i+1 od Value: [1,3,5,7] atlas> set v=[] Identifier v: [*] atlas> for i:4 do v#:=2*i+1 od Value: [[1],[1,3],[1,3,5],[1,3,5,7]] atlas> v Value: [1,3,5,7] atlas> set v=[] Identifier v: [*] (hiding previous one of type [int]) atlas> v Value: [] atlas> for i:4 do v#:=2*i+1 od;v Value: [1,3,5,7] atlas> set w=for i:4 do v#:=2*i+1 od;v Identifier w: [int] atlas> w Value: [1,3,5,7,1,3,5,7] atlas> set w=for i:4 do v#:=2*i+1 od;v Identifier w: [int] (hiding previous one of type [int]) atlas> w Value: [1,3,5,7,1,3,5,7,1,3,5,7] atlas> v:=[] Value: [] atlas> v Value: [] atlas> let a=for i:4 do v#:=2*i+1 od in v Value: [1,3,5,7] atlas> atlas> set G=Sp(4,R) Identifier G: RealForm atlas> whattype minimal_principal_series ? Overloaded instances of 'minimal_principal_series' (RealForm,ratvec,ratvec)->Param RealForm->Param atlas> minimal_principal_series(G,rho(G),rho(G)) Value: final parameter (x=10,lambda=[2,1]/1,nu=[2,1]/1) atlas> minimal_principal_series(G,rho(G),[0,0]) Value: final parameter (x=10,lambda=[2,1]/1,nu=[0,0]/1) atlas> all_p all_parameters all_parameters_KGB_gamma all_principal_series all_parameters_Cartan_gamma all_parameters_gamma atlas> whattype all_minimal_principal_series ? Overloaded instances of 'all_minimal_principal_series' (RealForm,ratvec)->[Param] atlas> set ps=all_minimal_principal_series (G,rho(G)) Identifier ps: [Param] atlas> for p in ps do prints(p) od final parameter (x=10,lambda=[2,1]/1,nu=[2,1]/1) final parameter (x=10,lambda=[3,1]/1,nu=[2,1]/1) final parameter (x=10,lambda=[2,2]/1,nu=[2,1]/1) final parameter (x=10,lambda=[3,2]/1,nu=[2,1]/1) Value: [(),(),(),()] atlas> set G=GL(2,R) Identifier G: RealForm (hiding previous one of type RealForm) atlas> set ps=all_minimal_principal_series (G,rho(G)) Identifier ps: [Param] (hiding previous one of type [Param]) atlas> #ps Value: 4 atlas> for p in ps do prints(p) od final parameter (x=1,lambda=[1,-1]/2,nu=[1,-1]/2) final parameter (x=1,lambda=[3,-1]/2,nu=[1,-1]/2) final parameter (x=1,lambda=[1,1]/2,nu=[1,-1]/2) final parameter (x=1,lambda=[3,1]/2,nu=[1,-1]/2) Value: [(),(),(),()] atlas> G:=U(2,2) Value: connected quasisplit real group with Lie algebra 'su(2,2).u(1)' atlas> set ps=all_minimal_principal_series (G,rho(G)) Identifier ps: [Param] (hiding previous one of type [Param]) atlas> #ps Value: 3 atlas> for p in ps do prints(p) od final parameter (x=12,lambda=[3,1,-1,-3]/2,nu=[1,-1,1,-1]/2) final parameter (x=17,lambda=[3,1,-1,-3]/2,nu=[1,1,-1,-1]/1) final parameter (x=20,lambda=[3,1,-1,-3]/2,nu=[3,1,-1,-3]/2) Value: [(),(),()] atlas> p:=ps[0] Error during analysis of expression at :109:0-8 Undefined identifier 'p' in assignment p:=ps[0] Type check failed atlas> set p=ps[0] Identifier p: Param atlas> set H=Cartan_class(p) Identifier H: CartanClass (hiding previous one of type string (constant)) atlas> print_Cartan_info (H) compact: 0, complex: 2, split: 0 canonical twisted involution: 2,1,3,2 twisted involution orbit size: 3; fiber size: 1; strong inv: 3 imaginary root system: empty real root system: A1.A1 complex factor: A1 atlas> whattype all_parameters_Cartan_gamma ? Overloaded instances of 'all_parameters_Cartan_gamma' (CartanClass,RealForm,ratvec)->[Param] atlas> set G=Sp(4,R) Identifier G: RealForm (hiding previous one of type RealForm) atlas> set H=Cartan_class(G,1) Identifier H: CartanClass (hiding previous one of type CartanClass) atlas> print_Cartan_info (H) compact: 0, complex: 1, split: 0 canonical twisted involution: 2,1,2 twisted involution orbit size: 2; fiber size: 1; strong inv: 2 imaginary root system: A1 real root system: A1 complex factor: empty atlas> set params=all_parameters_Cartan_gamma (H,G,rho(G)) Identifier params: [Param] atlas> #params Value: 2 atlas> for p in params do prints(p) G > od final parameter (x=4,lambda=[2,1]/1,nu=[1,-1]/2) final parameter (x=9,lambda=[2,1]/1,nu=[3,3]/2) Value: [(),()] atlas> set H=Cartan_class(G,2) Identifier H: CartanClass (hiding previous one of type CartanClass) atlas> set params=all_parameters_Cartan_gamma (H,G,rho(G)) Identifier params: [Param] (hiding previous one of type [Param]) atlas> #params Value: 8 atlas> for p in params do prints(p) G > od final parameter (x=5,lambda=[2,1]/1,nu=[0,1]/1) final parameter (x=5,lambda=[2,2]/1,nu=[0,1]/1) final parameter (x=6,lambda=[2,1]/1,nu=[0,1]/1) final parameter (x=6,lambda=[2,2]/1,nu=[0,1]/1) final parameter (x=7,lambda=[2,1]/1,nu=[2,0]/1) final parameter (x=7,lambda=[3,1]/1,nu=[2,0]/1) final parameter (x=8,lambda=[2,1]/1,nu=[2,0]/1) final parameter (x=8,lambda=[3,1]/1,nu=[2,0]/1) Value: [(),(),(),(),(),(),(),()] atlas> p:=params[7] Value: final parameter (x=8,lambda=[3,1]/1,nu=[2,0]/1) atlas> p Value: final parameter (x=8,lambda=[3,1]/1,nu=[2,0]/1) atlas> set others=all_parameters(p) Identifier others: [Param] atlas> for p in others do prints(p) od final parameter (x=8,lambda=[3,0]/1,nu=[2,0]/1) final parameter (x=8,lambda=[2,0]/1,nu=[2,0]/1) Value: [(),()] atlas>