Fix doc bug

doc_src/overviews/collation_tool.rst

@@ -112,8 +112,7 @@ two strings: *the quick brown fox jumps over the lazy dog* and *sick fox is craz
 .. raw:: html
    :file: ../_static/super-collator-phase1.html
 
-Every cell in the table contains three values, referred to as `D`, `P`, and `Q` in
-Gotoh's paper, and an arrow, like this:
+Every cell in the table contains three values: `D`, `P`, and `Q`, and an arrow, like this:
 
 .. raw:: html
     :align: center
@@ -128,22 +127,28 @@ Gotoh's paper, and an arrow, like this:
    </tr>
    </table>
 
+We define the score `S` for each cell as:
+
+.. math::
+
+    S = \max(D, P, Q)
+
 The grayed cells in the first row and first column are initialized using the *gap start*
 and *gap extension* penalties.  The numbers for each remaining cell are calculated using
 only values from the three cells, to the top-left, the top, and the left, of the current
 cell:
 
 .. math::
 
-   D = \max(D_↖, P_↖, Q_↖) + \mbox{similarity}(word_←, word_↑)
+   D = S_↖ + \mbox{similarity}(word_←, word_↑)
 
 .. math::
 
-   P = \max(D_↑ + openingpenalty, P_↑ + extensionpenalty)
+   P = \max(S_↑ + openingpenalty, P_↑ + extensionpenalty)
 
 .. math::
 
-   Q = \max(D_← + openingpenalty, Q_← + extensionpenalty)
+   Q = \max(S_← + openingpenalty, Q_← + extensionpenalty)
 
 Finally the arrow in the current cell is set to point to that cell which yielded the
 highest of the current cell's `D`, `P`, and `Q` values.

docs/_sources/overviews/collation_tool.rst.txt

@@ -112,8 +112,7 @@ two strings: *the quick brown fox jumps over the lazy dog* and *sick fox is craz
 .. raw:: html
    :file: ../_static/super-collator-phase1.html
 
-Every cell in the table contains three values, referred to as `D`, `P`, and `Q` in
-Gotoh's paper, and an arrow, like this:
+Every cell in the table contains three values: `D`, `P`, and `Q`, and an arrow, like this:
 
 .. raw:: html
     :align: center
@@ -128,22 +127,28 @@ Gotoh's paper, and an arrow, like this:
    </tr>
    </table>
 
+We define the score `S` for each cell as:
+
+.. math::
+
+    S = \max(D, P, Q)
+
 The grayed cells in the first row and first column are initialized using the *gap start*
 and *gap extension* penalties.  The numbers for each remaining cell are calculated using
 only values from the three cells, to the top-left, the top, and the left, of the current
 cell:
 
 .. math::
 
-   D = \max(D_↖, P_↖, Q_↖) + \mbox{similarity}(word_←, word_↑)
+   D = S_↖ + \mbox{similarity}(word_←, word_↑)
 
 .. math::
 
-   P = \max(D_↑ + openingpenalty, P_↑ + extensionpenalty)
+   P = \max(S_↑ + openingpenalty, P_↑ + extensionpenalty)
 
 .. math::
 
-   Q = \max(D_← + openingpenalty, Q_← + extensionpenalty)
+   Q = \max(S_← + openingpenalty, Q_← + extensionpenalty)
 
 Finally the arrow in the current cell is set to point to that cell which yielded the
 highest of the current cell's `D`, `P`, and `Q` values.

docs/overviews/collation_tool.html

@@ -325,8 +325,7 @@ <h3>Phase 1 - Build Table<a class="headerlink" href="#phase-1-build-table" title
 <tr><th class='left'>dog</th><td class='outer prefilled'><table><tr><td class='d inner'>-2.10</td><td class='p inner em'>-2.10</td></tr><tr><td class='q inner'>-2.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.90</td><td class='p inner em'>-1.74</td></tr><tr><td class='q inner'>-2.30</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.54</td><td class='p inner em'>-0.84</td></tr><tr><td class='q inner'>-2.24</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.64</td><td class='p inner em'>-0.46</td></tr><tr><td class='q inner'>-1.34</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.26</td><td class='p inner em'>-0.10</td></tr><tr><td class='q inner'>-0.96</td><td class='inner arrow'>↑</td></tr></table></td></tr>
 </table>
 
-<p>Every cell in the table contains three values, referred to as <span class="math notranslate nohighlight">\(D\)</span>, <span class="math notranslate nohighlight">\(P\)</span>, and <span class="math notranslate nohighlight">\(Q\)</span> in
-Gotoh’s paper, and an arrow, like this:</p>
+<p>Every cell in the table contains three values: <span class="math notranslate nohighlight">\(D\)</span>, <span class="math notranslate nohighlight">\(P\)</span>, and <span class="math notranslate nohighlight">\(Q\)</span>, and an arrow, like this:</p>
 <table class='super-collator super-collator-debug-matrix' style="margin-left: auto; margin-right: auto">
 <tr><td class='outer'>
 <table>
@@ -335,16 +334,19 @@ <h3>Phase 1 - Build Table<a class="headerlink" href="#phase-1-build-table" title
 </table>
 </td>
 </tr>
-</table><p>The grayed cells in the first row and first column are initialized using the <em>gap start</em>
+</table><p>We define the score <span class="math notranslate nohighlight">\(S\)</span> for each cell as:</p>
+<div class="math notranslate nohighlight">
+\[S = \max(D, P, Q)\]</div>
+<p>The grayed cells in the first row and first column are initialized using the <em>gap start</em>
 and <em>gap extension</em> penalties.  The numbers for each remaining cell are calculated using
 only values from the three cells, to the top-left, the top, and the left, of the current
 cell:</p>
 <div class="math notranslate nohighlight">
-\[D = \max(D_↖, P_↖, Q_↖) + \mbox{similarity}(word_←, word_↑)\]</div>
+\[D = S_↖ + \mbox{similarity}(word_←, word_↑)\]</div>
 <div class="math notranslate nohighlight">
-\[P = \max(D_↑ + openingpenalty, P_↑ + extensionpenalty)\]</div>
+\[P = \max(S_↑ + openingpenalty, P_↑ + extensionpenalty)\]</div>
 <div class="math notranslate nohighlight">
-\[Q = \max(D_← + openingpenalty, Q_← + extensionpenalty)\]</div>
+\[Q = \max(S_← + openingpenalty, Q_← + extensionpenalty)\]</div>
 <p>Finally the arrow in the current cell is set to point to that cell which yielded the
 highest of the current cell’s <span class="math notranslate nohighlight">\(D\)</span>, <span class="math notranslate nohighlight">\(P\)</span>, and <span class="math notranslate nohighlight">\(Q\)</span> values.</p>
 </section>