Taylor/Mclaurian expansion

Author: redxz5

taylor_mclaurian_expansion/README.md

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+# **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

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+import math
+from sympy import *
+
+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 denotes number of terms and should be a natural number")
+            return ''
+        expansion = expansion.subs(t_y,var)
+        return expansion
+    except TypeError:
+        print("3rd argument denotes number of terms and should be 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 point x=0 with 5 terms differentiating with respect to x
+    pprint(taylorexpansion(exp(x),0,5,x))
+
+    # e^x approximation at point x=1 with 10 terms differentiating with respect to x
+    print(taylorvalue(exp(x),1,10,x))
+
+    # log(1+x) expansion at point x=0 with 5 terms differentiating with respect to x
+    pprint(taylorexpansion(log(x+1),0,5,x))
+
+    # sin(x) expansion at point x=0 with 5 terms differentiating with respect to x
+    pprint(taylorexpansion(sin(x),0,5,x))
+
+    # expansion for expression at point x=0 with 3 terms differentiating with respect to x
+    pprint(taylorexpansion((5*x**2)+(3*x)+(7),0,3,x))
+
+    # e^(xy) expansion at point x=1 with 5 terms differentiating with respect to x
+    pprint(taylorexpansion(exp(x*y),1,5,x))
+
+examples()

taylor_mclaurian_expansion/requirements.txt

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+mpmath==1.3.0
+sympy==1.13.3