Typhoons01 main (#415)

* Create simplify_square_roots_generator

* Adopt simplify_square_root to standards

* lint fixes

* lint fix

* standardize line_equation_from_2_points

* Fix some lint issues

* Fix formatting/lint errors

* update docs

Co-authored-by: Hardik Gupta <96004638+typhoons01@users.noreply.github.com>

docs/mathgenerator/_gen_list.html

@@ -201,7 +201,8 @@
 </span><span id="L-126"><a href="#L-126"><span class="linenos">126</span></a>    <span class="p">(</span><span class="s2">&quot;is_composite&quot;</span><span class="p">,</span> <span class="s2">&quot;basic_math&quot;</span><span class="p">),</span>
 </span><span id="L-127"><a href="#L-127"><span class="linenos">127</span></a>    <span class="p">(</span><span class="s2">&quot;complementary_and_supplementary_angle&quot;</span><span class="p">,</span> <span class="s2">&quot;geometry&quot;</span><span class="p">),</span>
 </span><span id="L-128"><a href="#L-128"><span class="linenos">128</span></a>    <span class="p">(</span><span class="s2">&quot;simplify_square_root&quot;</span><span class="p">,</span> <span class="s2">&quot;basic_math&quot;</span><span class="p">),</span>
-</span><span id="L-129"><a href="#L-129"><span class="linenos">129</span></a><span class="p">]</span>
+</span><span id="L-129"><a href="#L-129"><span class="linenos">129</span></a>    <span class="p">(</span><span class="s2">&quot;line_equation_from_2_points&quot;</span><span class="p">,</span> <span class="s2">&quot;algebra&quot;</span><span class="p">),</span>
+</span><span id="L-130"><a href="#L-130"><span class="linenos">130</span></a><span class="p">]</span>
 </span></pre></div>
 
 

docs/mathgenerator/basic_math.html

@@ -552,11 +552,11 @@
 </span><span id="L-411"><a href="#L-411"><span class="linenos">411</span></a>            <span class="n">f</span> <span class="o">+=</span> <span class="mi">1</span>
 </span><span id="L-412"><a href="#L-412"><span class="linenos">412</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">b</span> <span class="o">=</span> <span class="mi">1</span>
 </span><span id="L-413"><a href="#L-413"><span class="linenos">413</span></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">factors</span><span class="o">.</span><span class="n">keys</span><span class="p">():</span>
-</span><span id="L-414"><a href="#L-414"><span class="linenos">414</span></a>        <span class="k">if</span> <span class="n">factors</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">&amp;</span><span class="mi">1</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+</span><span id="L-414"><a href="#L-414"><span class="linenos">414</span></a>        <span class="k">if</span> <span class="n">factors</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&amp;</span> <span class="mi">1</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
-</span><span id="L-415"><a href="#L-415"><span class="linenos">415</span></a>           <span class="n">a</span> <span class="o">*=</span> <span class="n">i</span> <span class="o">**</span> <span class="p">(</span><span class="n">factors</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
+</span><span id="L-415"><a href="#L-415"><span class="linenos">415</span></a>            <span class="n">a</span> <span class="o">*=</span> <span class="n">i</span> <span class="o">**</span> <span class="p">(</span><span class="n">factors</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
 </span><span id="L-416"><a href="#L-416"><span class="linenos">416</span></a>        <span class="k">else</span><span class="p">:</span>
-</span><span id="L-417"><a href="#L-417"><span class="linenos">417</span></a>           <span class="n">a</span> <span class="o">*=</span> <span class="n">i</span> <span class="o">**</span> <span class="p">((</span><span class="n">factors</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
+</span><span id="L-417"><a href="#L-417"><span class="linenos">417</span></a>            <span class="n">a</span> <span class="o">*=</span> <span class="n">i</span> <span class="o">**</span> <span class="p">((</span><span class="n">factors</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
-</span><span id="L-418"><a href="#L-418"><span class="linenos">418</span></a>           <span class="n">b</span> <span class="o">*=</span> <span class="n">i</span>
+</span><span id="L-418"><a href="#L-418"><span class="linenos">418</span></a>            <span class="n">b</span> <span class="o">*=</span> <span class="n">i</span>
 </span><span id="L-419"><a href="#L-419"><span class="linenos">419</span></a>    <span class="k">if</span> <span class="n">a</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">b</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
 </span><span id="L-420"><a href="#L-420"><span class="linenos">420</span></a>        <span class="k">return</span> <span class="n">simplify_square_root</span><span class="p">(</span><span class="n">max_variable</span><span class="p">)</span>
 </span><span id="L-421"><a href="#L-421"><span class="linenos">421</span></a>    <span class="k">else</span><span class="p">:</span>
@@ -1642,11 +1642,11 @@
 </span><span id="simplify_square_root-412"><a href="#simplify_square_root-412"><span class="linenos">412</span></a>            <span class="n">f</span> <span class="o">+=</span> <span class="mi">1</span>
 </span><span id="simplify_square_root-413"><a href="#simplify_square_root-413"><span class="linenos">413</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">b</span> <span class="o">=</span> <span class="mi">1</span>
 </span><span id="simplify_square_root-414"><a href="#simplify_square_root-414"><span class="linenos">414</span></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">factors</span><span class="o">.</span><span class="n">keys</span><span class="p">():</span>
-</span><span id="simplify_square_root-415"><a href="#simplify_square_root-415"><span class="linenos">415</span></a>        <span class="k">if</span> <span class="n">factors</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">&amp;</span><span class="mi">1</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+</span><span id="simplify_square_root-415"><a href="#simplify_square_root-415"><span class="linenos">415</span></a>        <span class="k">if</span> <span class="n">factors</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&amp;</span> <span class="mi">1</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
-</span><span id="simplify_square_root-416"><a href="#simplify_square_root-416"><span class="linenos">416</span></a>           <span class="n">a</span> <span class="o">*=</span> <span class="n">i</span> <span class="o">**</span> <span class="p">(</span><span class="n">factors</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
+</span><span id="simplify_square_root-416"><a href="#simplify_square_root-416"><span class="linenos">416</span></a>            <span class="n">a</span> <span class="o">*=</span> <span class="n">i</span> <span class="o">**</span> <span class="p">(</span><span class="n">factors</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
 </span><span id="simplify_square_root-417"><a href="#simplify_square_root-417"><span class="linenos">417</span></a>        <span class="k">else</span><span class="p">:</span>
-</span><span id="simplify_square_root-418"><a href="#simplify_square_root-418"><span class="linenos">418</span></a>           <span class="n">a</span> <span class="o">*=</span> <span class="n">i</span> <span class="o">**</span> <span class="p">((</span><span class="n">factors</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
+</span><span id="simplify_square_root-418"><a href="#simplify_square_root-418"><span class="linenos">418</span></a>            <span class="n">a</span> <span class="o">*=</span> <span class="n">i</span> <span class="o">**</span> <span class="p">((</span><span class="n">factors</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
-</span><span id="simplify_square_root-419"><a href="#simplify_square_root-419"><span class="linenos">419</span></a>           <span class="n">b</span> <span class="o">*=</span> <span class="n">i</span>
+</span><span id="simplify_square_root-419"><a href="#simplify_square_root-419"><span class="linenos">419</span></a>            <span class="n">b</span> <span class="o">*=</span> <span class="n">i</span>
 </span><span id="simplify_square_root-420"><a href="#simplify_square_root-420"><span class="linenos">420</span></a>    <span class="k">if</span> <span class="n">a</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">b</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
 </span><span id="simplify_square_root-421"><a href="#simplify_square_root-421"><span class="linenos">421</span></a>        <span class="k">return</span> <span class="n">simplify_square_root</span><span class="p">(</span><span class="n">max_variable</span><span class="p">)</span>
 </span><span id="simplify_square_root-422"><a href="#simplify_square_root-422"><span class="linenos">422</span></a>    <span class="k">else</span><span class="p">:</span>

mathgenerator/_gen_list.py

@@ -126,4 +126,5 @@ gen_list = [
     ("is_composite", "basic_math"),
     ("complementary_and_supplementary_angle", "geometry"),
     ("simplify_square_root", "basic_math"),
+    ("line_equation_from_2_points", "algebra"),
 ]

mathgenerator/algebra.py

@@ -487,6 +487,48 @@ def linear_equations(n=2, var_range=20, coeff_range=20):
     return f'Given the equations ${problem}$, solve for $x$ and $y$', f'${solution}$'
 
 
+def line_equation_from_2_points(max_val=20):
+    r"""Equation of Line from Two Points
+
+    | Ex. Problem | Ex. Solution |
+    | --- | --- |
+    | Find the equation of the line passing through the points $(-19,-8)$ and $(-2,0)$. | $y=\frac{8}{17}x+\frac{16}{17}$ |
+    """
+    x1 = random.randint(-max_val, max_val)
+    x2 = random.randint(-max_val, max_val)
+    if x1 == x2:
+        return line_equation_from_2_points(max_val=max_val)
+    y1 = random.randint(-max_val, max_val)
+    y2 = random.randint(-max_val, max_val)
+    m1 = (y2 - y1) // math.gcd(y2 - y1, x2 - x1)
+    m2 = (x2 - x1) // math.gcd(y2 - y1, x2 - x1)
+    c1 = (y1 * (x2 - x1) - (y2 - y1) * x1) // math.gcd(y1 * (x2 - x1) - (y2 - y1) * x1, (x2 - x1))
+    c2 = (x2 - x1) // math.gcd(y1 * (x2 - x1) - (y2 - y1) * x1, (x2 - x1))
+    c = rf"{'+' if c1 >= 0 else '-'}\frac{{{abs(c1)}}}{{{c2}}}" if c1 != 0 else ""
+    if c2 < 0:
+        c2 = -c2
+        c1 = -c1
+        c = rf"{'+' if c1 >= 0 else '-'}\frac{{{abs(c1)}}}{{{c2}}}"
+    if c2 == 1:
+        c = f"{c1:+}"
+
+    problem = f'Find the equation of the line passing through the points $({x1},{y1})$ and $({x2},{y2})$.'
+
+    if m1 == 0:
+        return problem, f"$y={c}$"
+    if m2 < 0:
+        m1 = -m1
+        m2 = -m2
+    if m2 == 1:
+        if m1 == 1:
+            return problem, f"$y=x{c}$"
+        if m1 == -1:
+            return problem, f"$y=-x{c}$"
+        return problem, f"y={m1}x{c}"
+
+    return problem, rf"$y=\frac{{{m1}}}{{{m2}}}x{c}$"
+
+
 def log(max_base=3, max_val=8):
     r"""Logarithm