From e02b8e963189d786ac80960ac043bd5b79eb22a8 Mon Sep 17 00:00:00 2001
From: redxz5 <mridul240205@gmail.com>
Date: Tue, 1 Oct 2024 20:49:09 +0530
Subject: [PATCH 1/3] Taylor/Mclaurian expansion

---
 taylor_mclaurian_expansion/README.md        | 25 ++++++++
 taylor_mclaurian_expansion/main.py          | 64 +++++++++++++++++++++
 taylor_mclaurian_expansion/requirements.txt |  2 +
 3 files changed, 91 insertions(+)
 create mode 100644 taylor_mclaurian_expansion/README.md
 create mode 100644 taylor_mclaurian_expansion/main.py
 create mode 100644 taylor_mclaurian_expansion/requirements.txt

diff --git a/taylor_mclaurian_expansion/README.md b/taylor_mclaurian_expansion/README.md
new file mode 100644
index 000000000..033a27172
--- /dev/null
+++ b/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.
\ No newline at end of file
diff --git a/taylor_mclaurian_expansion/main.py b/taylor_mclaurian_expansion/main.py
new file mode 100644
index 000000000..b0dd7c894
--- /dev/null
+++ b/taylor_mclaurian_expansion/main.py
@@ -0,0 +1,64 @@
+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()
diff --git a/taylor_mclaurian_expansion/requirements.txt b/taylor_mclaurian_expansion/requirements.txt
new file mode 100644
index 000000000..c9ae7aa06
--- /dev/null
+++ b/taylor_mclaurian_expansion/requirements.txt
@@ -0,0 +1,2 @@
+mpmath==1.3.0
+sympy==1.13.3

From 3941c0b02cef9f78043112ada547597f963fd24a Mon Sep 17 00:00:00 2001
From: redxz5 <mridul240205@gmail.com>
Date: Tue, 1 Oct 2024 21:18:37 +0530
Subject: [PATCH 2/3] flake8 linting

---
 taylor_mclaurian_expansion/main.py | 83 ++++++++++++++++--------------
 1 file changed, 44 insertions(+), 39 deletions(-)

diff --git a/taylor_mclaurian_expansion/main.py b/taylor_mclaurian_expansion/main.py
index b0dd7c894..83e69d7ae 100644
--- a/taylor_mclaurian_expansion/main.py
+++ b/taylor_mclaurian_expansion/main.py
@@ -1,64 +1,69 @@
-import math
-from sympy import *
+from sympy import symbols, factorial, diff, pprint, exp, log, sin
 
 x = symbols('x')
 y = symbols('y')
 
-def taylorexpansion(func,a,n,var):
+
+def taylorexpansion(func, a, n, var):
     t_y = symbols('t_y')
-    expansion = func.subs(var,a)
+    expansion = func.subs(var, a)
     d = func
-    if(expansion==0):
-        n+=1
+    if (expansion == 0):
+        n += 1
     try:
-        k=1
-        while (k<n):
-            d = diff(d,var)
+        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):
+            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")
+            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)
+        expansion = expansion.subs(t_y, var)
         return expansion
     except TypeError:
-        print("3rd argument denotes number of terms and should be a natural number")
+        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 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 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 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))
 
-    # 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 x=0 with 5 terms differentiating with respect to x
+    pprint(taylorexpansion(log(x+1), 0, 5, 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 x=0 with 5 terms differentiating with respect to x
+    pprint(taylorexpansion(sin(x), 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 x=0 with 3 terms differentiating wrt to x
+    pprint(taylorexpansion((5*x**2)+(3*x)+(7), 0, 3, 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 x=1 with 5 terms differentiating with respect to x
+    pprint(taylorexpansion(exp(x*y), 1, 5, 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()

From 4f2dd031407081c7082ce68a4cfc44c822923b46 Mon Sep 17 00:00:00 2001
From: redxz5 <mridul240205@gmail.com>
Date: Tue, 1 Oct 2024 21:32:50 +0530
Subject: [PATCH 3/3] flake8 linting

---
 taylor_mclaurian_expansion/main.py | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/taylor_mclaurian_expansion/main.py b/taylor_mclaurian_expansion/main.py
index 83e69d7ae..888a042f6 100644
--- a/taylor_mclaurian_expansion/main.py
+++ b/taylor_mclaurian_expansion/main.py
@@ -14,15 +14,15 @@ def taylorexpansion(func, a, n, var):
         k = 1
         while (k < n):
             d = diff(d, var)
-            term = (d*((t_y-a)**k))/factorial(k)
+            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
+            expansion = term + expansion
             k += 1
             if (d == 0 and k < n):
-                print("only ", k-1, " terms present")
+                print("only ", k - 1, " terms present")
         if (n < 1):
             print("3rd argument is for no. of terms, provide a natural number")
             return ''
@@ -54,16 +54,16 @@ def examples():
     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))
+    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))
+    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))
+    pprint(taylorexpansion(exp(x * y), 1, 5, x))
 
 
 examples()