Diff for "interact" - Sagemath Wiki

Differences between revisions 2 and 125 (spanning 123 versions)

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:
- 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)))

-  ⇤ ← Revision 2 as of 2008-03-11 18:15:48 → 
  Size: 629
  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:
-= Sage Interactions =
+#Choose the size D of the square matrix:
D = 3
-Line 3:
+Line 4:
-Post code that demonstrates the use of the interact command in Sage here.    It should be easy for people to just scroll through and paste examples out of here into their own sage notebooks.
+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
-Line 5:
+Line 8:
-We'll likely restructure and reorganize this once we have some nontrivial content and get a sense of how it is laid out. 

== Graphics ==

== Calculus ==

== Number Theory ==

{{{
html('<h1>Cuspidal Subgroups of Modular Jacobians J0(N)</h1>')
-Line 16:
+Line 9:
-def _(N=selector([1..8*13], ncols=8, width=10, default=10)):
    A = J0(N)
    print A.cuspidal_subgroup()
}}}

attachment:cuspgroup.png
+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)))