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authorMarshall Lochbaum <mwlochbaum@gmail.com>2022-06-27 22:00:55 -0400
committerMarshall Lochbaum <mwlochbaum@gmail.com>2022-06-27 22:00:55 -0400
commit8389e763344637c01d0d7161091e5f2cd9b14251 (patch)
tree5406113f6711c6b1222650228cba453c2e4641fa /docs/doc/shift.html
parentb6185d5029e2adcc721c0cc2097f591d9a09f135 (diff)
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</pre>
<h2 id="definition"><a class="header" href="#definition">Definition</a></h2>
<p>In any instance of <code><span class='Function'>ยป</span></code> or <code><span class='Function'>ยซ</span></code>, <code><span class='Value'>๐•ฉ</span></code> must have rank at least 1.</p>
-<p>For a dyadic shift function, <code><span class='Value'>๐•จ</span></code> must be <a href="join.html#join-to">Join</a>-compatible with <code><span class='Value'>๐•ฉ</span></code> (that is, <code><span class='Value'>๐•จ</span><span class='Function'>โˆพ</span><span class='Value'>๐•ฉ</span></code> completes without error) and cannot have greater rank than <code><span class='Value'>๐•ฉ</span></code>. Then Shift Before (<code><span class='Function'>ยป</span></code>) is <code><span class='Brace'>{</span><span class='Paren'>(</span><span class='Function'>โ‰ </span><span class='Value'>๐•ฉ</span><span class='Paren'>)</span><span class='Function'>โ†‘</span><span class='Value'>๐•จ</span><span class='Function'>โˆพ</span><span class='Value'>๐•ฉ</span><span class='Brace'>}</span></code> and Shift After (<code><span class='Function'>ยซ</span></code>) is <code><span class='Brace'>{</span><span class='Paren'>(</span><span class='Function'>-โ‰ </span><span class='Value'>๐•ฉ</span><span class='Paren'>)</span><span class='Function'>โ†‘</span><span class='Value'>๐•ฉ</span><span class='Function'>โˆพ</span><span class='Value'>๐•จ</span><span class='Brace'>}</span></code></p>
+<p>For a dyadic shift function, <code><span class='Value'>๐•จ</span></code> must be <a href="join.html#join-to">Join</a>-compatible with <code><span class='Value'>๐•ฉ</span></code> (that is, <code><span class='Value'>๐•จ</span><span class='Function'>โˆพ</span><span class='Value'>๐•ฉ</span></code> completes without error) and can't have greater rank than <code><span class='Value'>๐•ฉ</span></code>. Then Shift Before (<code><span class='Function'>ยป</span></code>) is <code><span class='Brace'>{</span><span class='Paren'>(</span><span class='Function'>โ‰ </span><span class='Value'>๐•ฉ</span><span class='Paren'>)</span><span class='Function'>โ†‘</span><span class='Value'>๐•จ</span><span class='Function'>โˆพ</span><span class='Value'>๐•ฉ</span><span class='Brace'>}</span></code> and Shift After (<code><span class='Function'>ยซ</span></code>) is <code><span class='Brace'>{</span><span class='Paren'>(</span><span class='Function'>-โ‰ </span><span class='Value'>๐•ฉ</span><span class='Paren'>)</span><span class='Function'>โ†‘</span><span class='Value'>๐•ฉ</span><span class='Function'>โˆพ</span><span class='Value'>๐•จ</span><span class='Brace'>}</span></code></p>
<p>When called monadically, the default argument is a cell of fills <code><span class='Number'>1</span><span class='Function'>โ†‘</span><span class='Number'>0</span><span class='Function'>โ†‘</span><span class='Value'>๐•ฉ</span></code>. That is, Nudge (<code><span class='Function'>ยป</span></code>) is <code><span class='Paren'>(</span><span class='Number'>1</span><span class='Function'>โ†‘</span><span class='Number'>0</span><span class='Function'>โ†‘โŠข</span><span class='Paren'>)</span><span class='Modifier2'>โŠธ</span><span class='Function'>ยป</span></code> and Nudge Back (<code><span class='Function'>ยซ</span></code>) is <code><span class='Paren'>(</span><span class='Number'>1</span><span class='Function'>โ†‘</span><span class='Number'>0</span><span class='Function'>โ†‘โŠข</span><span class='Paren'>)</span><span class='Modifier2'>โŠธ</span><span class='Function'>ยซ</span></code>. This default argument always satisfies the compatibility requirement above and so the only conditions for nudge are that <code><span class='Value'>๐•ฉ</span></code> has rank at least 1 and has a fill element.</p>