From 7b44722056730d7e7f520b40000dd87eb4caf26b Mon Sep 17 00:00:00 2001
From: xdward <78007088+xdward@users.noreply.github.com>
Date: Mon, 16 Jan 2023 18:58:31 -0500
Subject: [PATCH] Added generator for orthogonal projections (#417)

---
 mathgenerator/_gen_list.py |  1 +
 mathgenerator/algebra.py   | 24 ++++++++++++++++++++++++
 2 files changed, 25 insertions(+)

diff --git a/mathgenerator/_gen_list.py b/mathgenerator/_gen_list.py
index 6f0f36b..8d2b18a 100644
--- a/mathgenerator/_gen_list.py
+++ b/mathgenerator/_gen_list.py
@@ -127,4 +127,5 @@ gen_list = [
     ("complementary_and_supplementary_angle", "geometry"),
     ("simplify_square_root", "basic_math"),
     ("line_equation_from_2_points", "algebra"),
+    ("orthogonal_projection", "algebra"),
 ]
diff --git a/mathgenerator/algebra.py b/mathgenerator/algebra.py
index 0133d0a..5120ee7 100644
--- a/mathgenerator/algebra.py
+++ b/mathgenerator/algebra.py
@@ -765,3 +765,27 @@ def vector_dot(min_val=-20, max_val=20):
     problem = rf'${a}\cdot{b}=$'
     solution = f'${c}$'
     return problem, solution
+
+
+def orthogonal_projection(min_val=-10, max_val=10):
+    r"""Orthogonal Projection
+
+    | Ex. Problem | Ex. Solution |
+    | --- | --- |
+    | Find the orthogonal projection of $[2, 3]$ onto $[4, -7]$ | $[\frac{-4}{5}, \frac{7}{5}]$ |
+    """
+    v = [random.randint(min_val, max_val) for _ in range(2)]
+    u = [random.randint(min_val, max_val) for _ in range(2)]
+    dot_t = v[0] * u[0] + v[1] * u[1]
+    dot_b = u[0] * u[0] + u[1] * u[1]
+    frac = fractions.Fraction(dot_t, dot_b).limit_denominator()
+    y = [frac * u[0], frac * u[1]]
+
+    if y[0].denominator != 1:
+        y[0] = rf'\frac{{{y[0].numerator}}}{{{y[0].denominator}}}'
+    if y[1].denominator != 1:
+        y[1] = rf'\frac{{{y[1].numerator}}}{{{y[1].denominator}}}'
+
+    problem = f'Find the orthogonal projection of ${v}$ onto ${u}$'
+    solution = f'$[{y[0]}, {y[1]}]$'
+    return problem, solution