How I do randomly select a element in GO(n,RR)?

In these form I can recalculate without problems

html("<h1> From Dictionary to Matrix (2)</h1>")
@interact
def newtarph( D=input_box(default={0: {1: 2, 2: 3}, 1: {0: 3, 2: 4}, 2: {3: 2, 4: 1}, 3: {0: 2, 1: 3, 4: 1}}, label='Dictionary')):
    G = DiGraph(D)
    W= G.weighted_adjacency_matrix()
    n=G.num_verts()
    C=[(i,j) for (i,j) in CartesianProduct(range(n),range(n)) if (W[i][j]<>0)]
    E0=matrix(C)
    V=vector([W[i][j] for (i,j) in C])
    E=column_matrix([E0.column(0),E0.column(1),V])
    print E

Hello Jason Grout, Really dont work. The error message is include in the two previus commentaries. for obtain these error I take the dictionary D={0: {1: 2, 2: 3}, 1: {0: 3, 2: 4}, 2: {3: 2, 4: 1}, 3: {0: 2, 1: 3, 4: 1}} and suprime in a second step 0: {1: 2, 2: 3}. Thank you for your help.

AyOiA0fSwgMjogezM6IDIsIDQ6I\ DF9LCAzOiB7MDogMiwgMTogMywgNDogMX19'), globals()); _interact_.recompute('40');" + '\n', '', 'single') File "", line 1, in <module> File "/home/sage/sage/devel/sagenb/sagenb/notebook/interact.py", line 3770, in recompute S['function']() File "/home/sage/sage/devel/sagenb/sagenb/notebook/interact.py", line 2572, in _ z = f(*[variables[arg] for arg in args]) File "/tmp/tmpiy2_h0/___code___.py", line 8, in newtarph for i in range(len(D.values()[u])): IndexError: list index out of range

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_20.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("X2ludGVyYWN0Xy51cGRh\ dGUoJzQwJywgJ0QnLCA0LCBfaW50ZXJhY3RfLnN0YW5kYXJkX2I2NGRlY29kZSgnZXpFNklI\ c3dPaUF6TENBeU9pQTBmU3dnTWpvZ2V6TTZJRElzSURRNklERjlMQ0F6T2lCN01Eb2dNaXdn\ TVRvZ015d2dORG9nTVgxOScpLCBnbG9iYWxzKCkpOyBfaW50ZXJhY3RfLnJlY29tcHV0ZSgn\ NDAnKTs="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpx7r7GI/___code___.py", line 3, in <module> exec compile(u"_interact_.update('40', 'D', _sage_const_4 , _interact_.standard_b64decode('ezE6IHswOiAzLC

Excuse me Shashank and Jason Grout. Perhaps I make a mistake writen the dictionary. Now work also for me. Eusebio Corbacho.

Yes, seems to work, but if you modifie the dictionary, you can obtein an error

These code work fine

html("<h1> From Dictionary to Matrix (1)</h1>")
    @interact
    def newtarph( D=input_box(default={0:{1:3}, 1: {0: 2, 4: 2, 5: 2}, 2: {0: 3, 1: 4}}, label='Dictionary')):
        E=[]
        for u in D.keys():
            for i in range(len(D.values()[u])):        
              E.append([u, D.values()[u].keys()[i], D.values()[u].values()[i]])
        print matrix(E)

These other code d'ont work:

html("<h1> From Dictionary to Matrix (1)</h1>")
    @interact
    def newtarph( D=input_box(default={1: {0: 2, 4: 2, 5: 2}, 2: {0: 3, 1: 4}}, label='Dictionary')):
        E=[]
        for u in D.keys():
            for i in range(len(D.values()[u])):        
              E.append([u, D.values()[u].keys()[i], D.values()[u].values()[i]])
        print matrix(E)

Thank you very much. Sincerely Eusebio Corbacho

The matrix as a list of rows

Given the matrix [0,1,2] [1,0,3] [1,2,4] [0,2,3] [2,4,1] [2,3,2] how to obtain the dictionary D={0:{1:2,2:3},1:{0:3,2:4},2:{3:2,4:1}} ?

how to obtain the real part of u0=b*vector([Xh0[3],Xh0[4],Xh0[5]])

html("

Trajectory of a particle in a viscose medium under a linear oscilator

in two cases:

1) with an external force that annulates the viscosity

2) with a given external force

             RDF
             assume(t>0)
             N=matrix(3)
             U=identity_matrix(3)
             K=diagonal_matrix([K[0],K[1],K[2]])
             A=block_matrix([[N,U],[-K/m, -b*U/m]])
             CI=vector(CI)
             S=exp(A*t)
             Xh=S*CI
             Ss=S(t=t-s)               
             if V==yes:
                 A0=block_matrix([[N,U],[-K/m, N]])
                 S0=exp(A0*t)
                 Xh0=S0*CI
                 u0=b*vector([Xh0[3],Xh0[4],Xh0[5]])
                 FA=parametric_plot3d((lambda t: real(u0[0](t=t).n()), lambda t: real(u0[1](t=t).n()), lambda t: real(u0[2](t=t).n())), (t,0,T),rgbcolor=(0,1,0),thickness=0.3,plot_points=[20*T])
                 C=parametric_plot3d((lambda t: real(Xh0[0](t=t).n()), lambda t: real(Xh0[1](t=t).n()), lambda t: real(Xh0[2](t=t).n())), (t,0,T),rgbcolor=(1,0,0),thickness=0.5,plot_points=[20*T])
                 show(FA+C)
             else: 
                 u=t^0*vector([0,0,0,F[0],F[1],F[2]])/m
                 u=u(t=s)
                 B=Ss*u
                 XP=integral(B,s,0,t)
                 X=Xh+XP
                 FC=parametric_plot3d((F[0],F[1],F[2]), (t,0,T),rgbcolor=(0,1,0),thickness=0.3,plot_points=[20*T])

                 C=parametric_plot3d((lambda t: real(X[0](t=t).n()), lambda t: real(X[1](t=t).n()), lambda t: real(X[2](t=t).n())), (t,0,T),rgbcolor=(1,0,0),thickness=0.5,plot_points=[20*T])
                 show(FC+C)

The program not calculates a good answer for exp(A*t)

html("<h1>Partícula bajo oscilador lineal</h1>")
var('t s')
@interact
def newtraph(m = input_box(default=1, label='masa'),
             b = input_box(default=1, label='viscosidad aire'),
             T = input_box(default=10, label='tiempo total'),
             k1 =input_box(default=1, label='primer autovalor'),
             k2 =input_box(default=1, label='segundo autovalor'),
             k3 =input_box(default=1, label='tercer autovalor'),
             Fx =input_box(default=0, label='Impulso unitario x'),
             Fy =input_box(default=0, label='Impulso unitario y'),
             Fz =input_box(default=0, label='Impulso unitario z'),
             CI= input_box(default=[1,1,0,1,1,-2], label='CI')):

                 N=matrix(3)
                 U=identity_matrix(3)
                 K=diagonal_matrix([k1,k2,k3])
                 A=block_matrix([[N,U],[-K/m, -b*U/m]])
                 S=exp(A*t)
                 Ss=exp(A*(t-s))
                 u=vector([0,0,0,Fx,Fy,Fz])
                 B=Ss*u
                 CI=vector(CI)
                 Xh=S*CI
                 XP=integral(B,s,0,t)
                 X=Xh+XP
                 parametric_plot3d((X[0],X[1],X[2]),(t,0,T))

What is the maximum size of a square matrix A to calculate exp(A)

exactly, for introduce a concrete graph I need know the number of vertices, the number of arcs and use these inputs for introduce other inputs of second level

Concretely, how tranlate the following MATLAB program to SAGE:

n=input('number of vertices n= ');
m=input('number of edges m= ');
disp('write weighted edges as [v1 v2 w12]');
for i=1:m
    E(i,:)=input(['arco ',num2str(i), '= ']);
end
disp(E)