From 78d941b4509e04cf5fc031207b727eab0142daf5 Mon Sep 17 00:00:00 2001
From: billpaps <37051006+billpaps@users.noreply.github.com>
Date: Sun, 9 Feb 2020 15:15:31 +0200
Subject: [PATCH 01/12] Create Bisection.py

Find root of
---
 maths/Bisection.py | 50 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 50 insertions(+)
 create mode 100644 maths/Bisection.py

diff --git a/maths/Bisection.py b/maths/Bisection.py
new file mode 100644
index 000000000000..33d6c39471ee
--- /dev/null
+++ b/maths/Bisection.py
@@ -0,0 +1,50 @@
+'''Given a function f(x) on floating number x and two numbers ‘a’ and ‘b’ 
+such that f(a)*f(b) < 0 and f(x) is continuous in [a, b]. Here f(x) represents algebraic or transcendental equation. 
+Find root of function in interval [a, b] (Or find a value of x such that f(x) is 0)
+'''
+
+
+import math
+
+def equation(x):
+    return math.cos(x) + x
+
+def bisection(a, b):
+    #Bolzano theory in order to find if there is a root between a and b
+    if equation(a) * equation(b) >= 0:
+        print("There is not a root between a and b\n")
+        return
+
+    half = a
+    while ((b - a) >= 0.01):
+
+        # Find middle point
+        c = (a + b) / 2
+
+        # Check if middle point is root
+        if equation(c) == 0.0:
+            break
+
+        # Decide the side to repeat the steps
+        if equation(c) * equation(a) < 0:
+            b = c
+        else:
+            a = c
+
+    print("The value of root is : ", "%.4f" % c)
+
+#Testing
+print("Testing for a = -3 and b = 2")
+a = -3
+b = 2
+bisection(a, b)
+
+a = 1
+b = 3
+print("\nTesting for a = 1 and b = 3")
+bisection(a, b)
+
+print("\nTesting for a = -5 and b = 0")
+a = -5
+b=0
+bisection(a,b)

From 95b39cbcdf0f9a33bfda33f96a74775f2ca0e81b Mon Sep 17 00:00:00 2001
From: billpaps <37051006+billpaps@users.noreply.github.com>
Date: Sun, 9 Feb 2020 15:20:27 +0200
Subject: [PATCH 02/12] Update Bisection.py

---
 maths/Bisection.py | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/maths/Bisection.py b/maths/Bisection.py
index 33d6c39471ee..b0cf914c43ae 100644
--- a/maths/Bisection.py
+++ b/maths/Bisection.py
@@ -1,14 +1,15 @@
-'''Given a function f(x) on floating number x and two numbers ‘a’ and ‘b’ 
-such that f(a)*f(b) < 0 and f(x) is continuous in [a, b]. Here f(x) represents algebraic or transcendental equation. 
-Find root of function in interval [a, b] (Or find a value of x such that f(x) is 0)
+'''Given a function f(x) on floating number x and two numbers ‘a’ and ‘b’ we test if there is 
+a root between a and b. The bisection theory can be applied for algebraic or transcendental equations.
 '''
 
 
 import math
 
+#Put here the equation you want
 def equation(x):
     return math.cos(x) + x
 
+#Finds the root and prints it
 def bisection(a, b):
     #Bolzano theory in order to find if there is a root between a and b
     if equation(a) * equation(b) >= 0:

From 984985f256d55be9470a33ee5b6c28df37c5a2bf Mon Sep 17 00:00:00 2001
From: billpaps <37051006+billpaps@users.noreply.github.com>
Date: Mon, 10 Feb 2020 20:57:05 +0200
Subject: [PATCH 03/12] Update Bisection.py

i changed the given function with one that i could make the doctests.
---
 maths/Bisection.py | 62 ++++++++++++++++++++++------------------------
 1 file changed, 30 insertions(+), 32 deletions(-)

diff --git a/maths/Bisection.py b/maths/Bisection.py
index b0cf914c43ae..da26fd904f91 100644
--- a/maths/Bisection.py
+++ b/maths/Bisection.py
@@ -1,23 +1,30 @@
-'''Given a function f(x) on floating number x and two numbers ‘a’ and ‘b’ we test if there is 
-a root between a and b. The bisection theory can be applied for algebraic or transcendental equations.
-'''
-
-
-import math
-
-#Put here the equation you want
-def equation(x):
-    return math.cos(x) + x
-
-#Finds the root and prints it
-def bisection(a, b):
-    #Bolzano theory in order to find if there is a root between a and b
+"""Given a function f(x) on floating number x and two numbers ‘a’ and ‘b’
+such that f(a)*f(b) < 0 and f(x) is continuous in [a, b]. Here f(x) represents algebraic or transcendental equation.
+Find root of function in interval [a, b] (Or find a value of x such that f(x) is 0)
+"""
+import doctest
+
+
+def equation(x: int) -> float:
+    return 10 - x * x
+
+
+def bisection(a: int, b: int) -> float:
+    """
+    >>> bisection(-2,5)
+    3.1611328125
+    >>> bisection(0, 6)
+    3.158203125
+    >>> bisection(2,3)
+    False
+    """
+    c = False
+    # Bolzano theory in order to find if there is a root between a and b
     if equation(a) * equation(b) >= 0:
-        print("There is not a root between a and b\n")
-        return
+        return c
 
     half = a
-    while ((b - a) >= 0.01):
+    while (b - a) >= 0.01:
 
         # Find middle point
         c = (a + b) / 2
@@ -32,20 +39,11 @@ def bisection(a, b):
         else:
             a = c
 
-    print("The value of root is : ", "%.4f" % c)
-
-#Testing
-print("Testing for a = -3 and b = 2")
-a = -3
-b = 2
-bisection(a, b)
+    return c
 
-a = 1
-b = 3
-print("\nTesting for a = 1 and b = 3")
-bisection(a, b)
 
-print("\nTesting for a = -5 and b = 0")
-a = -5
-b=0
-bisection(a,b)
+if __name__ == '__main__':
+    print(bisection(-2, 5))
+    print(bisection(0, 6))
+    print(bisection(2, 3))
+    doctest.testmod()

From a87330d7fdb3b3bca18eb0eaef4bb09b012f65ef Mon Sep 17 00:00:00 2001
From: billpaps <37051006+billpaps@users.noreply.github.com>
Date: Mon, 10 Feb 2020 20:58:30 +0200
Subject: [PATCH 04/12] Rename Bisection.py to bisection.py

---
 maths/{Bisection.py => bisection.py} | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename maths/{Bisection.py => bisection.py} (100%)

diff --git a/maths/Bisection.py b/maths/bisection.py
similarity index 100%
rename from maths/Bisection.py
rename to maths/bisection.py

From b6f8bebb16bd55a6e345da8e88117eaee54a4834 Mon Sep 17 00:00:00 2001
From: billpaps <37051006+billpaps@users.noreply.github.com>
Date: Mon, 10 Feb 2020 21:13:31 +0200
Subject: [PATCH 05/12] Update bisection.py

---
 maths/bisection.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/maths/bisection.py b/maths/bisection.py
index da26fd904f91..eeb775c0bf68 100644
--- a/maths/bisection.py
+++ b/maths/bisection.py
@@ -5,7 +5,7 @@
 import doctest
 
 
-def equation(x: int) -> float:
+def equation(x: int) -> int:
     return 10 - x * x
 
 

From 9cdef1bc5127ae63fc4563e51dbb691359edddee Mon Sep 17 00:00:00 2001
From: billpaps <37051006+billpaps@users.noreply.github.com>
Date: Mon, 10 Feb 2020 21:31:03 +0200
Subject: [PATCH 06/12] Update bisection.py

---
 maths/bisection.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/maths/bisection.py b/maths/bisection.py
index eeb775c0bf68..d506f4e7472b 100644
--- a/maths/bisection.py
+++ b/maths/bisection.py
@@ -23,7 +23,7 @@ def bisection(a: int, b: int) -> float:
     if equation(a) * equation(b) >= 0:
         return c
 
-    half = a
+    c = a
     while (b - a) >= 0.01:
 
         # Find middle point

From 0eea8a7caf7ba48167fbb2a913519906d9c61859 Mon Sep 17 00:00:00 2001
From: billpaps <37051006+billpaps@users.noreply.github.com>
Date: Mon, 10 Feb 2020 21:51:18 +0200
Subject: [PATCH 07/12] Update bisection.py

---
 maths/bisection.py | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/maths/bisection.py b/maths/bisection.py
index d506f4e7472b..af750497da96 100644
--- a/maths/bisection.py
+++ b/maths/bisection.py
@@ -18,10 +18,9 @@ def bisection(a: int, b: int) -> float:
     >>> bisection(2,3)
     False
     """
-    c = False
     # Bolzano theory in order to find if there is a root between a and b
     if equation(a) * equation(b) >= 0:
-        return c
+        return False
 
     c = a
     while (b - a) >= 0.01:

From 8c6b55c72bedc977c2da49e2e9bd0992f1848e5d Mon Sep 17 00:00:00 2001
From: billpaps <37051006+billpaps@users.noreply.github.com>
Date: Mon, 10 Feb 2020 22:07:30 +0200
Subject: [PATCH 08/12] Update bisection.py

---
 maths/bisection.py | 22 +++++++++++-----------
 1 file changed, 11 insertions(+), 11 deletions(-)

diff --git a/maths/bisection.py b/maths/bisection.py
index af750497da96..6bbb7145d90c 100644
--- a/maths/bisection.py
+++ b/maths/bisection.py
@@ -1,43 +1,43 @@
 """Given a function f(x) on floating number x and two numbers ‘a’ and ‘b’
-such that f(a)*f(b) < 0 and f(x) is continuous in [a, b]. Here f(x) represents algebraic or transcendental equation.
-Find root of function in interval [a, b] (Or find a value of x such that f(x) is 0)
+such that f(a)*f(b) < 0 and f(x) is continuous in [a, b]. Here f(x) represents
+ algebraic or transcendental equation.
+Find root of function in interval [a, b] (Or find a value of x such
+that f(x) is 0)
 """
 import doctest
 
-
 def equation(x: int) -> int:
-    return 10 - x * x
+    """
+    >>> equation(0)
+    10
 
+    """
+    return 10 - x * x
 
 def bisection(a: int, b: int) -> float:
     """
-    >>> bisection(-2,5)
+    >>> bisection(-2, 5)
     3.1611328125
     >>> bisection(0, 6)
     3.158203125
-    >>> bisection(2,3)
+    >>> bisection(2, 3)
     False
     """
     # Bolzano theory in order to find if there is a root between a and b
     if equation(a) * equation(b) >= 0:
         return False
-
     c = a
     while (b - a) >= 0.01:
-
         # Find middle point
         c = (a + b) / 2
-
         # Check if middle point is root
         if equation(c) == 0.0:
             break
-
         # Decide the side to repeat the steps
         if equation(c) * equation(a) < 0:
             b = c
         else:
             a = c
-
     return c
 
 

From 8bbee80266c422bff4916b30ecc84ab834a0fc0e Mon Sep 17 00:00:00 2001
From: billpaps <37051006+billpaps@users.noreply.github.com>
Date: Mon, 10 Feb 2020 22:31:36 +0200
Subject: [PATCH 09/12] Update bisection.py

Made the changes that were requested
---
 maths/bisection.py | 9 ++++++---
 1 file changed, 6 insertions(+), 3 deletions(-)

diff --git a/maths/bisection.py b/maths/bisection.py
index 6bbb7145d90c..9fb333a2e403 100644
--- a/maths/bisection.py
+++ b/maths/bisection.py
@@ -21,11 +21,14 @@ def bisection(a: int, b: int) -> float:
     >>> bisection(0, 6)
     3.158203125
     >>> bisection(2, 3)
-    False
+    Traceback (most recent call last):
+    ...
+    ValueError: Wrong space!
     """
     # Bolzano theory in order to find if there is a root between a and b
     if equation(a) * equation(b) >= 0:
-        return False
+        raise ValueError('Wrong space!')
+
     c = a
     while (b - a) >= 0.01:
         # Find middle point
@@ -44,5 +47,5 @@ def bisection(a: int, b: int) -> float:
 if __name__ == '__main__':
     print(bisection(-2, 5))
     print(bisection(0, 6))
-    print(bisection(2, 3))
+
     doctest.testmod()

From be56af2109132be5dc357683cbf58f21a16d6b09 Mon Sep 17 00:00:00 2001
From: Christian Clauss <cclauss@me.com>
Date: Mon, 10 Feb 2020 21:48:08 +0100
Subject: [PATCH 10/12] Update bisection.py

---
 maths/bisection.py | 21 +++++++++++++--------
 1 file changed, 13 insertions(+), 8 deletions(-)

diff --git a/maths/bisection.py b/maths/bisection.py
index 9fb333a2e403..ad806a0beaa2 100644
--- a/maths/bisection.py
+++ b/maths/bisection.py
@@ -1,19 +1,23 @@
-"""Given a function f(x) on floating number x and two numbers ‘a’ and ‘b’
+"""Given a function on floating point number f(x) and two numbers ‘a’ and ‘b’
 such that f(a)*f(b) < 0 and f(x) is continuous in [a, b]. Here f(x) represents
- algebraic or transcendental equation.
-Find root of function in interval [a, b] (Or find a value of x such
+algebraic or transcendental equation.
+Find root of the function in the interval [a, b] (Or find a value of x such
 that f(x) is 0)
-"""
-import doctest
 
+https://en.wikipedia.org/wiki/Bisection_method
+"""
 def equation(x: int) -> int:
     """
+    >>> equation(5)
+    -15
     >>> equation(0)
     10
-
+    >>> equation(-5)
+    -15
     """
     return 10 - x * x
 
+
 def bisection(a: int, b: int) -> float:
     """
     >>> bisection(-2, 5)
@@ -45,7 +49,8 @@ def bisection(a: int, b: int) -> float:
 
 
 if __name__ == '__main__':
-    print(bisection(-2, 5))
-    print(bisection(0, 6))
+    import doctest
 
     doctest.testmod()
+    print(bisection(-2, 5))
+    print(bisection(0, 6))

From de6e494bfd8bee9ae598a340c2c332ac063a4703 Mon Sep 17 00:00:00 2001
From: billpaps <37051006+billpaps@users.noreply.github.com>
Date: Mon, 10 Feb 2020 23:27:35 +0200
Subject: [PATCH 11/12] Update bisection.py

---
 maths/bisection.py | 25 ++++++++++---------------
 1 file changed, 10 insertions(+), 15 deletions(-)

diff --git a/maths/bisection.py b/maths/bisection.py
index ad806a0beaa2..484125bd478b 100644
--- a/maths/bisection.py
+++ b/maths/bisection.py
@@ -1,24 +1,20 @@
-"""Given a function on floating point number f(x) and two numbers ‘a’ and ‘b’
+"""Given a function f(x) on floating number x and two numbers ‘a’ and ‘b’
 such that f(a)*f(b) < 0 and f(x) is continuous in [a, b]. Here f(x) represents
-algebraic or transcendental equation.
-Find root of the function in the interval [a, b] (Or find a value of x such
+ algebraic or transcendental equation.
+Find root of function in interval [a, b] (Or find a value of x such
 that f(x) is 0)
-
-https://en.wikipedia.org/wiki/Bisection_method
 """
-def equation(x: int) -> int:
+import doctest
+
+def equation(x: float) -> float:
     """
-    >>> equation(5)
-    -15
     >>> equation(0)
     10
-    >>> equation(-5)
-    -15
+
     """
     return 10 - x * x
 
-
-def bisection(a: int, b: int) -> float:
+def bisection(a: float, b: float) -> float:
     """
     >>> bisection(-2, 5)
     3.1611328125
@@ -49,8 +45,7 @@ def bisection(a: int, b: int) -> float:
 
 
 if __name__ == '__main__':
-    import doctest
-
-    doctest.testmod()
     print(bisection(-2, 5))
     print(bisection(0, 6))
+
+    doctest.testmod()

From 0f0928b367fa488972768b8a0cce36ae794e5f95 Mon Sep 17 00:00:00 2001
From: Christian Clauss <cclauss@me.com>
Date: Tue, 11 Feb 2020 09:20:09 +0100
Subject: [PATCH 12/12] Add wiki url

---
 maths/bisection.py | 32 +++++++++++++++++++++-----------
 1 file changed, 21 insertions(+), 11 deletions(-)

diff --git a/maths/bisection.py b/maths/bisection.py
index 484125bd478b..a9df15b775b3 100644
--- a/maths/bisection.py
+++ b/maths/bisection.py
@@ -1,19 +1,27 @@
-"""Given a function f(x) on floating number x and two numbers ‘a’ and ‘b’
-such that f(a)*f(b) < 0 and f(x) is continuous in [a, b]. Here f(x) represents
- algebraic or transcendental equation.
-Find root of function in interval [a, b] (Or find a value of x such
-that f(x) is 0)
 """
-import doctest
+Given a function on floating number f(x) and two floating numbers ‘a’ and ‘b’ such that
+f(a) * f(b) < 0 and f(x) is continuous in [a, b].
+Here f(x) represents algebraic or transcendental equation.
+Find root of function in interval [a, b] (Or find a value of x such that f(x) is 0)
 
+https://en.wikipedia.org/wiki/Bisection_method
+"""
 def equation(x: float) -> float:
     """
+    >>> equation(5)
+    -15
     >>> equation(0)
     10
-
+    >>> equation(-5)
+    -15
+    >>> equation(0.1)
+    9.99
+    >>> equation(-0.1)
+    9.99
     """
     return 10 - x * x
 
+
 def bisection(a: float, b: float) -> float:
     """
     >>> bisection(-2, 5)
@@ -27,7 +35,7 @@ def bisection(a: float, b: float) -> float:
     """
     # Bolzano theory in order to find if there is a root between a and b
     if equation(a) * equation(b) >= 0:
-        raise ValueError('Wrong space!')
+        raise ValueError("Wrong space!")
 
     c = a
     while (b - a) >= 0.01:
@@ -44,8 +52,10 @@ def bisection(a: float, b: float) -> float:
     return c
 
 
-if __name__ == '__main__':
-    print(bisection(-2, 5))
-    print(bisection(0, 6))
+if __name__ == "__main__":
+    import doctest
 
     doctest.testmod()
+
+    print(bisection(-2, 5))
+    print(bisection(0, 6))