New branch

taylor_mclaurian_expansion/README.md

@@ -0,0 +1,25 @@
+# **Taylor and Mclaurian Expansions**
+
+[![python 3](https://img.shields.io/badge/python-3.8-blue)](https://python.org)
+
+ This is a small convenient program to use to approximate values of expresstions using taylor expansions or
+ mclaurian expansions
+
+ **Python** has a great library [*sympy*](https://github.com/sympy/sympy) which allows us to do many calculations,
+ and display them in a manner we are used to.
+
+
+### Before you import sympy you need to install it:
+
+  ```python 
+ pip3 install sympy
+ ```
+
+
+### You can also do the same through the requirements.txt file
+
+```python
+pip install requirements.txt
+```
+
+Some examples have been included for easier use.

taylor_mclaurian_expansion/main.py

@@ -0,0 +1,69 @@
+from sympy import symbols, factorial, diff, pprint, exp, log, sin
+
+x = symbols('x')
+y = symbols('y')
+
+
+def taylorexpansion(func, a, n, var):
+    t_y = symbols('t_y')
+    expansion = func.subs(var, a)
+    d = func
+    if (expansion == 0):
+        n += 1
+    try:
+        k = 1
+        while (k < n):
+            d = diff(d, var)
+            term = (d * ((t_y - a) ** k)) / factorial(k)
+            term = term.subs(var, a)
+            if (term == 0):
+                continue
+            term = term.subs(t_y, var)
+            expansion = term + expansion
+            k += 1
+            if (d == 0 and k < n):
+                print("only ", k - 1, " terms present")
+        if (n < 1):
+            print("3rd argument is for no. of terms, provide a natural number")
+            return ''
+        expansion = expansion.subs(t_y, var)
+        return expansion
+    except TypeError:
+        print("3rd argument denotes number of terms, provide a natural number")
+        return ''
+
+
+def taylorvalue(func, a, n, x):
+    f = taylorexpansion(func, a, n, x)
+    return f.evalf(subs={x: a})
+
+
+def mclaurianexpansion(func, steps, variable):
+    taylorexpansion(func, 0, steps, variable)
+
+
+def mclaurianvalue(func, steps, variable):
+    taylorvalue(func, 0, steps, variable)
+
+
+def examples():
+    # e^x expansion at x=0 with 5 terms differentiating with respect to x
+    pprint(taylorexpansion(exp(x), 0, 5, x))
+
+    # e^x approximation at x=1 with 10 terms differentiating with respect to x
+    print(taylorvalue(exp(x), 1, 10, x))
+
+    # log(1+x) expansion at x=0 with 5 terms differentiating with respect to x
+    pprint(taylorexpansion(log(x + 1), 0, 5, x))
+
+    # sin(x) expansion at x=0 with 5 terms differentiating with respect to x
+    pprint(taylorexpansion(sin(x), 0, 5, x))
+
+    # expansion for expression at x=0 with 3 terms differentiating wrt to x
+    pprint(taylorexpansion((5 * x ** 2) + (3 * x) + (7), 0, 3, x))
+
+    # e^(xy) expansion at x=1 with 5 terms differentiating with respect to x
+    pprint(taylorexpansion(exp(x * y), 1, 5, x))
+
+
+examples()

taylor_mclaurian_expansion/requirements.txt

@@ -0,0 +1,2 @@
+mpmath==1.3.0
+sympy==1.13.3