Revision history [back]

Let B be a basis of the inner product space V defined on GF(p), and B' be the orthogonal set of B. My goal is to find B' for a given B.

     I use the following #fnc to get n linear independent vectors over GF(p);

       def gen_basis(p,d):
             V=VectorSpace(GF(p),d)
             B=[]
             while True:
                 t=V.random_element()
                 if not V.linear_dependence(B + [t]):
                     B.append(t)
             if len(B)==d:
                 break
         return B
     B=gen_basis(11,3)

 case 1:
 m=Matrix(GF(11),b)
 m
 [ 7  1  7]
 [ 5  1  9]
 [ 1  7 10]
 G,M=m.gram_schmidt() #i get the error as follow
 #AttributeError:'sage.rings.finite_rings.integer_mod.IntegerMod_int' object has no attribute 'conjugate' 

 case 2:
 If i use;
 from sage.modules.misc import gram_schmidt 
 G,M=gram_schmidt(b)

 # in this case orthogonalization works, but in some cases ;
     B'={w1,w2,....wk}
     <wi,w_>= 0 for some i values.
 what could be the reason for this?
 What does it mean <w_i,w_i> is zero

Let B be a basis of the inner product space V defined on GF(p), and B' be the orthogonal set of B. My goal is to find B' for a given B.

         I use the following #fnc to get n linear independent vectors over GF(p);

           def gen_basis(p,d):
                 V=VectorSpace(GF(p),d)
                 B=[]
                 while True:
                     t=V.random_element()
                     if not V.linear_dependence(B + [t]):
                         B.append(t)
                 if len(B)==d:
                     break
             return B
         B=gen_basis(11,3)

     case 1:
     m=Matrix(GF(11),b)
     m
     [ 7  1  7]
     [ 5  1  9]
     [ 1  7 10]
     G,M=m.gram_schmidt() #i get the error as follow
     #AttributeError:'sage.rings.finite_rings.integer_mod.IntegerMod_int' object has no attribute 'conjugate' 

     case 2:
     If i use;
     from sage.modules.misc import gram_schmidt 
     G,M=gram_schmidt(b)

     # in this case orthogonalization works, but in some cases ;
         B'={w1,w2,....wk}
         <wi,w_>= 0 for some i values.
     what could be the reason for this?
     What does it mean <w_i,w_i> is zero

Let B be a basis of the inner product space V defined on GF(p), and B' be the orthogonal set of B. My goal is to find B' for a given B.

 
I use the following #fnc to get n linear independent vectors over GF(p);

              GF(p);
 
def gen_basis(p,d):
     V=VectorSpace(GF(p),d)
     B=[]
     while True:
         t=V.random_element()
         if not V.linear_dependence(B + [t]):
             B.append(t)
         if len(B)==d:
                        break
            len(B)==d:break
    return B
 B=gen_basis(11,3)

        case #case 1:
 m=Matrix(GF(11),b)
        m
print(m)
            [ 7  1  7]
         [ 5  1  9]
         [ 1  7 10]
 G,M=m.gram_schmidt() #i get the error as follow
 #AttributeError:'sage.rings.finite_rings.integer_mod.IntegerMod_int' object has no attribute 'conjugate' 

        case #case 2:
        If #If i use;
 from sage.modules.misc import gram_schmidt 
 G,M=gram_schmidt(b)

        # in  '''               
In  this case orthogonalization works, but in some cases ;
 B'={w1,w2,....wk}
 <wi,w_>= 0 for some i values.
        values, what could be the reason for this?
 What does it mean <w_i,w_i> is zero
'''