Diff for "interact" - Sagemath Wiki

Differences between revisions 104 and 125 (spanning 21 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 104 as of 2008-05-08 09:48:26 → 
  Size: 730
  Editor: schilly
  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 to just scroll through and paste examples out of here into their own sage notebooks.If you have suggestions on how to improve interact, add them [:interactSuggestions: here] or email [email protected].
+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:
- * [:interact/graph_theory:Graph Theory]
 * [:interact/calculus:Calculus]
 * [:interact/diffeq:Differential Equations]
 * [:interact/linear_algebra:Linear Algebra]
 * [:interact/algebra:Algebra]
 * [:interact/number_theory:Number Theory]
 * [:interact/web:Web Applications]
 * [:interact/bio:Bioinformatics]
 * [:interact/graphics:Drawing Graphics]
 * [:interact/misc:Miscellaneous]
+@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)))