Matriz X gaus

#Choose the size D of the square matrix: 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)))