from sympy import *
x0=0
x1=25000
x2=50000
x3=75000
x4=100000
x5=125000

y0=9.8100
y1=9.7335
y2=9.6578
y3=9.5830
y4=9.5091
y5=9.4361

v=62500

C0=y0
C1=(y1-C0)/(x1-x0)
C2=(y2-C0-C1*(x2-x0))/((x2-x0)*(x2-x1))
C3=(y3-C0-C1*(x3-x0)-C2*(x3-x0)*(x3-x1))/((x3-x0)*(x3-x1)*(x3-x2))
C4=(y4-C0-C1*(x4-x0)-C2*(x4-x0)*(x4-x1)-C3*(x4-x0)*(x4-x1)*(x4-x2))/((x4-x0)*(x4-x1)*(x4-x2)*(x4-x3))
C5=(y5-C0-C1*(x5-x0)-C2*(x5-x0)*(x5-x1)-C3*(x5-x0)*(x5-x1)*(x5-x2)-C4*(x5-x0)*(x5-x1)*(x5-x2)*(x5-x3))/((x5-x0)*(x5-x1)*(x5-x2)*(x5-x3)*(x5-x4))

x=Symbol("x")
P=C0+C1*(x-x0)+C2*(x-x0)*(x-x1)+C3*(x-x0)*(x-x1)*(x-x2)+C4*(x-x0)*(x-x1)*(x-x2)*(x-x3)+C5*(x-x0)*(x-x1)*(x-x2)*(x-x3)*(x-x4)
P_ec=expand(P)

s=P_ec.subs(x,v)
print("La gravedad para una altura de",v,"es",s)

print("El polinomio interpolador es",P_ec)