Q:

TypeError: can't convert expression to float, with symbolic x, polynomial interpolation

I'm trying to run the following code but an error appears at the line with S[i][0].

TypeError: can't convert expression to float

I'm am sure that my variables D[][], h[], age[], A[], B[] and n are ok (they are floats). I think it has something to do with the symbolic figure x.
At the end, S is supposed to be a (7,1) vector of polynomes.
import numpy as np
import sympy as sp
age = np.arange(15,55,5)  
N = np.array([0, 7.442, 26.703, 41.635, 49.785, 50.209, 50.226])
n = len(N)

h = np.zeros(n)
for i in range(n) :
    h[i] = age[i+1] - age[i]

mu = np.zeros(n)
lamda = np.zeros(n)
F = np.zeros((n,1))
A = np.zeros(n)
B = np.zeros(n)

for i in range(n) :
    mu[i] = h[i-1]/(h[i]+h[i-1])
    lamda[i] = h[i]/(h[i]+h[i-1])
    F[i][0] = (6*(N[i]*h[i-1] - h[i]*N[i-1]))/((h[i]+h[i-1])*h[i]*h[i-1])   

M = 2*np.eye(n,n) + 0.5*np.diag(np.ones((n-1)),1)+ 0.5*np.diag(np.ones((n-1)),1).T

D = np.dot(np.linalg.inv(M),F)

for i in range(n-1) :
    A[i] = (N[i+1] - N[i])/h[i] - (h[i]*(D[i+1][0] - D[i][0]))/6
    B[i] = N[i] - (((h[i])**2)*D[i][0])/6

def s(D, h, age, A, B, n) :
    S = np.zeros((n,1))
    x = sp.Symbol("x")
    for i in range(n) :
        S[i][0] = (D[i+1][0]*((x - age[i])**3))/(6*h[i]) - (D[i][0]*((x - age[i+1])**3))/(6*h[i]) + (A[i])*(x - age[i]) + B[i]
    return sp.simplify(S)

S = s(D, h, age, A, B, n)

A:

The problem is that while most of your variables are floats, x is symbolic, which causes all of those calculations in the end to be a symbolic object. Such objects are handled at python-level with classes, while numpy requires numbers, so it tries to apply float() to it. For example,
>> float(sp.Add(1, 1))
2.0

>> float(s.Add(1 + x))
Traceback (most recent call last):
  File "<pyshell#85>", line 1, in <module>
    float(sp.Add(1, x))
  File "C:\Users\ip507\AppData\Local\Programs\Python\Python36\lib\site-packages\sympy\core\expr.py", line 239, in __float__
    raise TypeError("can't convert expression to float")
TypeError: can't convert expression to float

Since you don't intend to use an calcuations with the "array-like" S object, it can just be a list, where you collect the expressions.
def s(D, h, age, A, B, n):
    x = sp.Symbol("x")
    S = []
    for i in range(n):
        S.append((D[i+1][0]*((x - age[i])**3))/(6*h[i]) - (D[i][0]*((x - age[i+1])**3))/(6*h[i]) + (A[i])*(x - age[i]) + B[i])
    return S

Having said that, you have an error which causes an IndexError. D has a shape of (7, 1), but you call D[i+1]. It's something you'll need to address since I don't know your intentions.

