Differences between revisions 1 and 125 (spanning 124 versions)
 ⇤ ← Revision 1 as of 2008-03-11 18:14:23 → Size: 505 Editor: was Comment: ← Revision 125 as of 2011-06-06 00:14:17 → ⇥ Size: 2005 Editor: joseluissegura Comment: Deletions are marked like this. Additions are marked like this. Line 1: Line 1: = Sage Interactions = #Choose the size D of the square matrix:D = 3 Line 3: Line 4: Post code (and screen shots) of the use of interact in Sage here. We'll likely restructure and reorganize this, or move it out of the wiki (?) once we have some nontrivial content and get a sense of how it is laid out. example = [[1 if k==j else 0 for k in range(D)] for j in range(D)]example[0][-1] = 2example[-1][0] = 3 Line 5: Line 8: == Graphics ==== Calculus ==== Number Theory =={{{html('

Cuspidal Subgroups of Modular Jacobians J0(N)

') Line 14: Line 9: def _(N=selector([1..8*13], ncols=8, width=10, default=10)):    A = J0(N)    print A.cuspidal_subgroup()}}} def _(M=input_grid(D,D, default = example,                   label='Matrix to invert', to_value=matrix),      tt = text_control('Enter the bits of precision used'                        ' (only if you entered floating point numbers)'),       precision = slider(5,100,5,20),      auto_update=False):    if det(M)==0:        print 'Failure: Matrix is not invertible'        return    if M.base_ring() == RR:        M = M.apply_map(RealField(precision))    N=M    M=M.augment(identity_matrix(D))    print 'We construct the augmented matrix'    show(M)    for m in range(0,D-1):        if M[m,m] == 0:            lista = [(M[j,m],j) for j in range(m,D)]            maxi, c = max(lista)            M[c,:],M[m,:]=M[m,:],M[c,:]            print 'We permute rows %d and %d'%(m+1,c+1)            show(M)        for n in range(m+1,D):            a=M[m,m]            if M[n,m]!=0:                print "We add %s times row %d to row %d"%(-M[n,m]/a, m+1, n+1)                M=M.with_added_multiple_of_row(n,m,-M[n,m]/a)                show(M)    for m in range(D-1,-1,-1):        for n in range(m-1,-1,-1):            a=M[m,m]            if M[n,m]!=0:                print "We add %s times row %d to the row %d"%(-M[n,m]/a, m+1, n+1)                M=M.with_added_multiple_of_row(n,m,-M[n,m]/a)                show(M)     for m in range(0,D):        if M[m,m]!=1:            print 'We divide row %d by %s'%(m+1,M[m,m])            M = M.with_row_set_to_multiple_of_row(m,m,1/M[m,m])            show(M)     M=M.submatrix(0,D,D)    print 'We keep the right submatrix, which contains the inverse'     html('\$\$M^{-1}=%s\$\$'%latex(M))    print 'We check it actually is the inverse'    html('\$\$M^{-1}*M=%s*%s=%s\$\$'%(latex(M),latex(N),latex(M*N)))

D = 3

example = [[1 if k==j else 0 for k in range(D)] for j in range(D)] example[0][-1] = 2 example[-1][0] = 3

@interact def _(M=input_grid(D,D, default = example,

• label='Matrix to invert', to_value=matrix),
• tt = text_control('Enter the bits of precision used'
• ' (only if you entered floating point numbers)'),
precision = slider(5,100,5,20), auto_update=False):
• if det(M)==0:
• print 'Failure: Matrix is not invertible' return
if M.base_ring() == RR: N=M M=M.augment(identity_matrix(D)) print 'We construct the augmented matrix' show(M) for m in range(0,D-1):
• if M[m,m] == 0:
• lista = [(M[j,m],j) for j in range(m,D)] maxi, c = max(lista) M[c,:],M[m,:]=M[m,:],M[c,:] print 'We permute rows %d and %d'%(m+1,c+1) show(M)
for n in range(m+1,D):
• a=M[m,m] if M[n,m]!=0:
• print "We add %s times row %d to row %d"%(-M[n,m]/a, m+1, n+1) M=M.with_added_multiple_of_row(n,m,-M[n,m]/a) show(M)
for m in range(D-1,-1,-1):
• for n in range(m-1,-1,-1):
• a=M[m,m] if M[n,m]!=0:
• print "We add %s times row %d to the row %d"%(-M[n,m]/a, m+1, n+1) M=M.with_added_multiple_of_row(n,m,-M[n,m]/a) show(M)
for m in range(0,D):
• if M[m,m]!=1:
• print 'We divide row %d by %s'%(m+1,M[m,m]) M = M.with_row_set_to_multiple_of_row(m,m,1/M[m,m]) show(M)
M=M.submatrix(0,D,D) print 'We keep the right submatrix, which contains the inverse'

html('

M^{-1}=%s
'%latex(M)) print 'We check it actually is the inverse' html('
M^{-1}*M=%s*%s=%s
'%(latex(M),latex(N),latex(M*N)))

interact (last edited 2021-08-23 15:58:42 by anewton)