From d3ebe8e5fb01015d27b5076a1430b872c779c6b0 Mon Sep 17 00:00:00 2001
From: Akash Saravanan <akashsara@outlook.com>
Date: Fri, 16 Oct 2020 23:48:19 +0530
Subject: [PATCH] Add intersection of two lines.

---
 mathgenerator/mathgen.py | 56 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 56 insertions(+)

diff --git a/mathgenerator/mathgen.py b/mathgenerator/mathgen.py
index bd22657..a85d7c3 100644
--- a/mathgenerator/mathgen.py
+++ b/mathgenerator/mathgen.py
@@ -1,4 +1,5 @@
 import random
+import fractions
 
 genList = []
 
@@ -464,6 +465,60 @@ def commonFactorsFunc(maxVal=100):
     problem = f"Common Factors of {a} and {b} = "
     solution = arr
     return problem, solution
+
+def intersectionOfTwoLinesFunc(
+    minM=-10, maxM=10, minB=-10, maxB=10, minDenominator=1, maxDenominator=6
+):
+    def generateEquationString(m, b):
+        """
+        Generates an equation given the slope and intercept.
+        It handles cases where m is fractional.
+        It also ensures that we don't have weird signs such as y = mx + -b.
+        """
+        if m[1] == 1:
+            m = m[0]
+        else:
+            m = f"{m[0]}/{m[1]}"
+        base = f"y = {m}x"
+        if b > 0:
+            return f"{base} + {b}"
+        elif b < 0:
+            return f"{base} - {b * -1}"
+        else:
+            return base
+
+    def fractionToString(x):
+        """
+        Converts the given fractions.Fraction into a string.
+        """
+        if x.denominator == 1:
+            x = x.numerator
+        else:
+            x = f"{x.numerator}/{x.denominator}"
+        return x
+        
+    m1 = (random.randint(minM, maxM), random.randint(minDenominator, maxDenominator))
+    m2 = (random.randint(minM, maxM), random.randint(minDenominator, maxDenominator))
+    b1 = random.randint(minB, maxB)
+    b2 = random.randint(minB, maxB)
+    equation1 = generateEquationString(m1, b1)
+    equation2 = generateEquationString(m2, b2)
+    problem = "Find the point of intersection of the two lines: "
+    problem += f"{equation1} and {equation2}"
+    m1 = fractions.Fraction(*m1)
+    m2 = fractions.Fraction(*m2)
+    # if m1 == m2 then the slopes are equal
+    # This can happen if both line are the same
+    # Or if they are parallel
+    # In either case there is no intersection
+    if m1 == m2:
+        solution = "No Solution"
+    else:
+        intersection_x = (b1 - b2) / (m2 - m1)
+        intersection_y = ((m2 * b1) - (m1 * b2)) / (m2 - m1)
+        solution = f"({fractionToString(intersection_x)}, {fractionToString(intersection_y)})"
+    return problem, solution
+
 # || Class Instances
 
 #Format is:
@@ -502,3 +557,4 @@ angleRegularPolygon = Generator("Angle of a Regular Polygon",29,"Find the angle
 combinations = Generator("Combinations of Objects",30, "Combinations available for picking 4 objects at a time from 6 distinct objects ="," 15", combinationsFunc)
 factorial = Generator("Factorial", 31, "a! = ", "b", factorialFunc)
 commonFactors = Generator("Common Factors", 32, "Common Factors of {a} and {b} = ","[c, d, ...]",commonFactorsFunc)
+intersectionOfTwoLines = Generator("Intersection of Two Lines", 33, "Find the point of intersection of the two lines: y = m1*x + b1 and y = m2*x + b2", "(x, y)", intersectionOfTwoLinesFunc)