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test if v.norm <> zero pb

HI I do not understand why if v.norm !=0 does not work here.

ZeroDivisionError: rational division by zero

def normalizeVectorL(vectorList) :
    vNormList=[]
    for l in vectorList :
        lMatrixList=[]
        for v in l :
            v=vector(v)
            z=zero_vector(v.length())
            #if v != z  :
            if v.norm() != 0 :

                show("v :\t",v,"v.norm() :\t",v.norm())
                lMatrixList.append(matrix(v/v.norm()).transpose())
            else :
                lMatrixList.append(matrix(v).transpose())

        vNormList.append(lMatrixList)
    return vNormList

VVVlist=[]
VVVlist0=[]
VVVlist0.append([1,1,1])
VVVlist0.append([1,1,2])
VVVlist0.append([1,0,0])
VVVlist.append(VVVlist0)

VVVlist1=[]
VVVlist1.append([1,3,1])
VVVlist1.append([1,2,2])
VVVlist1.append([0,0,0])
VVVlist.append(VVVlist1)

show(VVVlist)
show(normalizeVectorList(VVVlist))