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heyredhat · Nov 5, 2020 · e6a409e · e6a409e
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diff --git a/docs/_build/doctrees/environment.pickle b/docs/_build/doctrees/environment.pickle
diff --git a/docs/_build/doctrees/index.doctree b/docs/_build/doctrees/index.doctree
diff --git a/docs/_build/html/_modules/index.html b/docs/_build/html/_modules/index.html
@@ -144,6 +144,7 @@
 
   <h1>All modules for which code is available</h1>
 <ul><li><a href="spheres/stars.html">spheres.stars</a></li>
+<li><a href="spheres/symmetrization.html">spheres.symmetrization</a></li>
 <li><a href="spheres/utils.html">spheres.utils</a></li>
 </ul>
 

diff --git a/docs/_build/html/_modules/spheres/stars.html b/docs/_build/html/_modules/spheres/stars.html
@@ -459,7 +459,7 @@ <h1>Source code for spheres.stars</h1><div class="highlight"><pre>
     <span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Takes a spin-j state and returns the cartesian coordinates on the unit sphere</span>
 <span class="sd">    corresponding to its &quot;Majorana stars.&quot; Each contributes a quantum of angular </span>
-<span class="sd">    momentum :math:`\\frac{1}{2}` to the overal spin.</span>
+<span class="sd">    momentum :math:`\\frac{1}{2}` to the overall spin.</span>
 
 <span class="sd">    Parameters</span>
 <span class="sd">    ----------</span>
@@ -489,6 +489,96 @@ <h1>Source code for spheres.stars</h1><div class="highlight"><pre>
 <span class="sd">            Spin-j state.</span>
 <span class="sd">    &quot;&quot;&quot;</span>
     <span class="k">return</span> <span class="n">poly_spin</span><span class="p">(</span><span class="n">roots_poly</span><span class="p">([</span><span class="n">xyz_c</span><span class="p">(</span><span class="n">star</span><span class="p">)</span> <span class="k">for</span> <span class="n">star</span> <span class="ow">in</span> <span class="n">xyz</span><span class="p">]))</span></div>
+
+<div class="viewcode-block" id="spin_spinors"><a class="viewcode-back" href="../../index.html#spheres.stars.spin_spinors">[docs]</a><span class="k">def</span> <span class="nf">spin_spinors</span><span class="p">(</span><span class="n">spin</span><span class="p">):</span>
+    <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Takes a spin-j state and returns its decomposition into 2j spinors.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">        spin : qt.Qobj</span>
+<span class="sd">            Spin-j state.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">        spinors : list</span>
+<span class="sd">            2j spinors.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="k">return</span> <span class="p">[</span><span class="n">c_spinor</span><span class="p">(</span><span class="n">c</span><span class="p">)</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">poly_roots</span><span class="p">(</span><span class="n">spin_poly</span><span class="p">(</span><span class="n">spin</span><span class="p">))]</span></div>
+
+<div class="viewcode-block" id="spinors_spin"><a class="viewcode-back" href="../../index.html#spheres.stars.spinors_spin">[docs]</a><span class="k">def</span> <span class="nf">spinors_spin</span><span class="p">(</span><span class="n">spinors</span><span class="p">):</span>
+    <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Given 2j spinors constructs corresponding spin-j state (up to phase).</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">        spinors : list</span>
+<span class="sd">            2j spinors.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">        spin : qt.Qobj</span>
+<span class="sd">            Spin-j state.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="k">return</span> <span class="n">poly_spin</span><span class="p">(</span><span class="n">roots_poly</span><span class="p">([</span><span class="n">spinor_c</span><span class="p">(</span><span class="n">spinor</span><span class="p">)</span> <span class="k">for</span> <span class="n">spinor</span> <span class="ow">in</span> <span class="n">spinors</span><span class="p">]))</span></div>
+
+<div class="viewcode-block" id="mobius"><a class="viewcode-back" href="../../index.html#spheres.stars.mobius">[docs]</a><span class="k">def</span> <span class="nf">mobius</span><span class="p">(</span><span class="n">abcd</span><span class="p">):</span>
+    <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Given parameters :math:`\\begin{pmatrix} a &amp; b \\\\ b &amp; c \\end{pmatrix}`,</span>
+<span class="sd">    arranged in a 2x2 matrix, returns a function which implements the </span>
+<span class="sd">    corresponding `Möbius transformation &lt;https://en.wikipedia.org/wiki/M%C3%B6bius_transformation&gt;`_</span>
+
+<span class="sd">    .. math::</span>
+
+<span class="sd">        f(z) = \\frac{az+b}{cz+d}</span>
+
+<span class="sd">    which acts on the extended complex plane. Note that if :math:`c \\neq 0`, we have:</span>
+
+<span class="sd">    .. math::</span>
+
+<span class="sd">        f(-\\frac{d}{c}) = \\infty</span>
+
+<span class="sd">        f(\\infty) = \\frac{a}{c}</span>
+
+<span class="sd">    And if :math:`c = 0`, we have:</span>
+
+<span class="sd">    .. math::</span>
+
+<span class="sd">        f(\\infty) = \\infty</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">        abcd : np.ndarray or qt.Qobj</span>
+<span class="sd">            2x2 matrix representing Möbius parameters.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">        mobius : func</span>
+<span class="sd">            A function which takes an extended complex coordinate as input, </span>
+<span class="sd">            and returns an extended complex coordinate as output.</span>
+
+<span class="sd">    Raises</span>
+<span class="sd">    ------</span>
+<span class="sd">        Exception</span>
+<span class="sd">            If :math:`ad = bc`, then :math:`f(z) = \\frac{a}{c}`, a constant function,</span>
+<span class="sd">            which doesn&#39;t qualify as a Möbius transformation.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="k">if</span> <span class="nb">type</span><span class="p">(</span><span class="n">abcd</span><span class="p">)</span> <span class="o">==</span> <span class="n">qt</span><span class="o">.</span><span class="n">Qobj</span><span class="p">:</span>
+        <span class="n">abcd</span> <span class="o">=</span> <span class="n">abcd</span><span class="o">.</span><span class="n">full</span><span class="p">()</span>
+    <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="o">=</span> <span class="n">abcd</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+    <span class="k">if</span> <span class="n">a</span><span class="o">*</span><span class="n">d</span> <span class="o">-</span> <span class="n">b</span><span class="o">*</span><span class="n">c</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Möbius transformation doesn&#39;t satisfy ad-bc != 0.&quot;</span><span class="p">)</span>
+    <span class="k">def</span> <span class="nf">__mobius__</span><span class="p">(</span><span class="n">z</span><span class="p">):</span>
+        <span class="k">if</span> <span class="n">c</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="k">if</span> <span class="n">z</span> <span class="o">==</span> <span class="o">-</span><span class="n">d</span><span class="o">/</span><span class="n">c</span><span class="p">:</span>
+                <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">inf</span>
+            <span class="k">if</span> <span class="n">z</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">inf</span><span class="p">:</span>
+                <span class="k">return</span> <span class="n">a</span><span class="o">/</span><span class="n">c</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">if</span> <span class="n">z</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">inf</span><span class="p">:</span>
+                <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">inf</span>
+        <span class="k">return</span> <span class="p">(</span><span class="n">a</span><span class="o">*</span><span class="n">z</span> <span class="o">+</span> <span class="n">b</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">c</span><span class="o">*</span><span class="n">z</span> <span class="o">+</span> <span class="n">d</span><span class="p">)</span>
+    <span class="k">return</span> <span class="n">__mobius__</span></div>
 </pre></div>
 
            </div>