# -*- coding: utf-8 -*-
"""
Created on Tue Dec 16 12:09:51 2014

@author: grivet

Exercice 4-5 : Construction d'une table de différences latérales

"""
import numpy as np

blanc = "              "
nval = eval(input("nombre de valeurs de la fonction: "))
dmax = eval(input("ordre maximal des differences: "))
xi = float(input("valeur initiale de l'argument: "))
h = float(input("intervalle  tabulaire: "))
table = np.zeros([nval,dmax+1])
#création d'une tabe de valeurs
x = xi
for i in range(nval):
    table[i,0] = np.sqrt(x)
    x = x + h
#remplissage de la table
for j in range(1,dmax+1):
    for i in range(j,nval):
        table[i,j] = table[i,j-1] - table[i-1,j-1]
x = xi
for i in range(nval):
    #lignes impaires
    k = 0; l = i
    print ('%4.1f' %x,end = '')
    while (k <= dmax) & (l < nval):
        if k <= l:
            print ('%12.4f' %table[l,k],end = '')
        print (blanc,end = '')
        k = k+2; l = l+1
    print()
    #lignes paires
    x += h
    k = 1; l = i+1
    print ('    ',end = '')
    while (k <= dmax) & (l < nval):
        if k <= l:
            print ('%s%12.4f' %(blanc,table[l,k]),end = '')
        k += 2; l += 1
    print()