a1=-3; a2=-2.5;a3=-1.5; a4=-0.5;a5=0.5; a6=1.5; a7=2.5;a8=3;
y1=1;  y2=0;   y3=2;    y4=3;   y5=3;   y6=1;   y7=-2; y8=4
P(x) = (x-a1)*(x-a2)*(x-a3)*(x-a4)*(x-a5)*(x-a6)*(x-a7)*(x-a8)
P1(x) = (x-a2)*(x-a3)*(x-a4)*(x-a5)*(x-a6)*(x-a7)*(x-a8)
P2(x) = (x-a1)*(x-a3)*(x-a4)*(x-a5)*(x-a6)*(x-a7)*(x-a8)
P3(x) = (x-a1)*(x-a2)*(x-a4)*(x-a5)*(x-a6)*(x-a7)*(x-a8)
P4(x) = (x-a1)*(x-a2)*(x-a3)*(x-a5)*(x-a6)*(x-a7)*(x-a8)
P5(x) = (x-a1)*(x-a2)*(x-a3)*(x-a4)*(x-a6)*(x-a7)*(x-a8)
P6(x) = (x-a1)*(x-a2)*(x-a3)*(x-a4)*(x-a5)*(x-a7)*(x-a8)
P7(x) = (x-a1)*(x-a2)*(x-a3)*(x-a4)*(x-a5)*(x-a6)*(x-a8)
P8(x) = (x-a1)*(x-a2)*(x-a3)*(x-a4)*(x-a5)*(x-a6)*(x-a7)
dP(x) = P1(x)+ P2(x)+ P3(x)+ P4(x)+ P5(x) + P6(x)+ P7(x)+ P8(x)
set xrange [a1-0.5:a8+0.5]
set arrow from a1,0 to a1,y1 nohead
set arrow from a2,0 to a2,y2 nohead
set arrow from a3,0 to a3,y3 nohead
set arrow from a4,0 to a4,y4 nohead
set arrow from a5,0 to a5,y5 nohead
set arrow from a6,0 to a6,y6 nohead
set arrow from a7,0 to a7,y7 nohead
set arrow from a8,0 to a8,y8 nohead
## plot P(x),dP(x),0
f(x) = y1*P1(x)/dP(a1) + y2*P2(x)/dP(a2) + y3*P3(x)/dP(a3) +\
	y4*P4(x)/dP(a4) + y5*P5(x)/dP(a5)+\
	y6*P6(x)/dP(a6) + y7*P7(x)/dP(a7)+y8*P8(x)/dP(a8)
set title "Polinomio de Lagrange interpolando pontos do plano"
## set term postscript portrait color enhanced
## set output "exer05.01.03.eps"
plot "pontos.05.01" with points, f(x),0
## pause -2