Update taylor.py

src/taylor.py

@@ -7,15 +7,13 @@ from src.differentiation import evaluate_diff
 
 from math import factorial, ceil
 
-N = 10
-
 @cache
 def nth_derivative(func, n):
     """self explanatory for now..."""
     return None
 
 @cache
-def taylor(func, x):
+def taylor(func, x, N):
     """
         Returns the taylor expansion of func as a function of x, centered at 'b'.
         Since the 0th term is just the function itself (which we don't have the answer for yet),
@@ -25,13 +23,13 @@ def taylor(func, x):
     """
     return None
 
-def taylor_at(func, b, f_at_b):
+def taylor_at(func, b, f_at_b, N):
     """
         Returns taylor(-), evaluated by plugging in f_at_b for 'q' and b for 'b'.
     """
     return None
 
-def max_error(func, a, x, n=N):
+def max_error(func, a, x, n):
     """
     Calculates the maximum error of the estimate below using Taylor's Theorem
     in the following way.
@@ -55,7 +53,7 @@ def max_error(func, a, x, n=N):
     return None
 
 @cache
-def estimate(func, x, a, func_at_a):
+def estimate(func, x, a, func_at_a, N):
     """
         Uses the taylor expansion centered around a to compute an estimate for func(x).
     """
@@ -64,19 +62,20 @@ def estimate(func, x, a, func_at_a):
 PI = 3.14159265358979323846264338327950288419716939937510582097494
 
 def arctan(x):
+    N = 10
     if x == 0:
         return 0, 0
     elif x == 1:
-        return PI/4, Decimal(10**-16)
+        return pi/4, Decimal(10**-16)
 
     a = 0
     total_error = Decimal(0)
     prev_value = 0
     while a + 1 <= x:
-        prev_value = estimate('arctan', a + 1, a, prev_value)
-        total_error += max_error('arctan', a, a + 1)
+        prev_value = estimate('arctan', a + 1, a, prev_value, N)
+        total_error += max_error('arctan', a, a + 1, N)
         a += 1
-    return estimate('arctan', x, floor(x), prev_value), total_error + max_error('arctan', floor(x), x)
+    return estimate('arctan', x, floor(x), prev_value, N), total_error + max_error('arctan', floor(x), x, N)
 
 if __name__ == "__main__":
     for i in range(0, 4):