R.<x>=RR[]
x0 = 0.1
fx0 = 10.98
x1 = 0.2
fx1 = 5.49
x2 = 0.4
fx2 = 2.74
x3 = 0.7
fx3 = 1.56
x4 = 0.8
fx4 = 1.37
x5 = 1
fx5 = 1.09
print 'a)'
print 'PRIMERA COLUMNA'
L01 = (((x-x0)*fx1)-((x-x1)*fx0))/(x1-x0)
print 'L01 = ', L01
L12 = (((x-x1)*fx2)-((x-x2)*fx1))/(x2-x1)
print 'L12 = ', L12
L23 = (((x-x2)*fx3)-((x-x3)*fx2))/(x3-x2)
print 'L23 = ', L23
L34 = (((x-x3)*fx4)-((x-x4)*fx3))/(x4-x3)
print 'L34 = ', L34
L45 = (((x-x4)*fx5)-((x-x5)*fx4))/(x5-x4)
print 'L45 = ', L45
print '----------------------------------'
print 'SEGUNDA COLUMNA'
L012 = (((x-x0)*L12)-((x-x2)*L01))/(x2-x0)
print 'L012 = ', L012
L123 = (((x-x1)*L23)-((x-x3)*L12))/(x3-x1)
print 'L123 = ', L123
L234 = (((x-x2)*L34)-((x-x4)*L23))/(x4-x2)
print 'L234 = ', L234
L345 = (((x-x3)*L45)-((x-x5)*L34))/(x5-x3)
print 'L345 = ', L345
print '----------------------------------'
print 'TERCERA COLUMNA'
L0123 = (((x-x0)*L123)-((x-x3)*L012))/(x3-x0)
print 'L0123 = ', L0123
L1234 = (((x-x1)*L234)-((x-x4)*L123))/(x4-x1)
print 'L1234 = ', L1234
L2345 = (((x-x2)*L345)-((x-x5)*L234))/(x5-x2)
print 'L2345 = ', L2345
print '----------------------------------'
print 'CUARTA COLUMNA'
L01234 = (((x-x0)*L1234)-((x-x4)*L0123))/(x4-x0)
print 'L01234 = ', L01234
L12345 = (((x-x1)*L2345)-((x-x5)*L1234))/(x5-x1)
print 'L12345 = ', L12345
print '----------------------------------'
print 'QUINTA COLUMNA'
L012345 = (((x-x0)*L12345)-((x-x5)*L01234))/(x5-x0)
print 'L012345 = ', L012345
print '----------------------------------'
print 'b)'
print
print 'f(0.3) = ', L012345.subs(x=0.3)
print 'f(0.5) = ', L012345.subs(x=0.5)
a)
PRIMERA COLUMNA
L01 = -54.9000000000000*x + 16.4700000000000
L12 = -13.7500000000000*x + 8.24000000000000
L23 = -3.93333333333333*x + 4.31333333333333
L34 = -1.90000000000000*x + 2.89000000000000
L45 = -1.40000000000000*x + 2.49000000000000
----------------------------------
SEGUNDA COLUMNA
L012 = 137.166666666667*x^2 - 96.0500000000000*x + 19.2133333333333
L123 = 19.6333333333333*x^2 - 25.5300000000000*x + 9.81066666666667
L234 = 5.08333333333334*x^2 - 9.52500000000000*x + 5.73666666666667
L345 = 1.66666666666666*x^2 - 4.39999999999999*x + 3.82333333333333
----------------------------------
TERCERA COLUMNA
L0123 = -195.888888888889*x^3 + 274.288888888889*x^2 - 123.474444444444*x + 20.7804444444444
L1234 = -24.2500000000000*x^3 + 51.1583333333333*x^2 - 37.6550000000000*x + 11.1686666666667
L2345 = -5.69444444444447*x^3 + 15.9027777777778*x^2 - 16.1305555555556*x + 7.01222222222222
----------------------------------
CUARTA COLUMNA
L01234 = 245.198412698413*x^4 - 539.166666666667*x^3 + 428.763888888889*x^2 - 149.465476190476*x + 22.1535555555556
L12345 = 23.1944444444444*x^4 - 72.9583333333333*x^3 + 86.8777777777778*x^2 - 48.2316666666667*x + 12.2077777777778
----------------------------------
QUINTA COLUMNA
L012345 = -246.671075837743*x^5 + 787.874779541447*x^4 - 970.841049382716*x^3 + 579.233245149912*x^2 - 171.764541446208*x + 23.2586419753086
----------------------------------
b)
f(0.3) = 3.42993827160493
f(0.5) = 2.36325396825396
