       
   to find the other packages : http://www.simtel.net/
              The news groups : http://groups.yahoo.com/group/mathc/
      
 
                   Verify with numeric applications :
                   --------------------------------
     
   vectaa01.zip : Some vector space axioms on (rows, 
                  columns) vectors and  on polynomials. 

                   *        u + v = v + u          
                   *  (u + v) + w = u + (v + w)
                   *        0 + u = u + 0    = u        
                   *     u + (-u) = (-u) + u = 0          
                   *     k( u+ v) = ku + kv
                   *    (k + l) u = ku + lu
                   *       k (lu) = (kl) u


   vectab01.zip :  * Properties of Euclidian inner product in R**n.
                   * Properties of length   in R**n.
                   * Properties of distance in R**n.
                   * u.v = 1/4 ||u+v||**2  -  1/4 ||u-v||**2. 
                   * Cauchy-Schwarz inequality in R**n.
                   * If u.v =0 :  ||u+v||**2 = ||u||**2 + ||v||**2.


   vectac01.zip :    You can see the result in Gnuplot.

                   * Reflection about the x-axis.
                   * Reflection about the y-axis.
                   * Reflection about the line y = x.
                   * Orthogonal projection on the x-axis. 
                   * Orthogonal projection on the y-axis.


   vectae01.zip :    You can see the result in Gnuplot.

                   * Reflection about the xy-plan.
                   * Reflection about the xz-plan.
                   * Reflection about the yz-plan.
                   * Orthogonal projection on the xy-plan. 
                   * Orthogonal projection on the xz-plan. 
                   * Orthogonal projection on the yz-plan.  