StackOverflow2013

Note that there are some explanatory texts on larger screens.

plurals

PO
text
Body
copied!<p>The answer is documented under <a href="http://www.jsoftware.com/help/dictionary/d630n.htm" rel="noreferrer"><strong>Bond (&)</strong></a> where the following identity is noted for dyadic use:</p> <p><strong>x m&v y ↔ m&v^:x y</strong></p> <p>In your example m is <code>2</code>, v is <code>*</code>, and both x and y are the list of four numbers <code>15 7 3 1</code> .</p> <p>The phrasing on the right-hand side of the equality includes <code>^:x</code> ("to the power x") which is the same as taking the verb and applying it x times. The verb is <code>2&*</code> so it is applied fifteen times. And also seven times. And also three times. And also once. The results of those four applications make up the four rows of the output.</p> <p>Focusing on the third one and using parentheses for emphasis, here's what's happening.</p> <pre><code> (2&* (2&* (2&* (15 7 3 1)))) 120 56 24 8 </code></pre> <p>which is the same as </p> <pre><code> (2&*)^:3 (15 7 3 1) 120 56 24 8 </code></pre> <p>which is the same as </p> <pre><code> (3) 2&* (15 7 3 1) 120 56 24 8 </code></pre> <p>Let's apply all the non-negative integers through 3 to see a pattern:</p> <pre><code> (0 1 2 3) 2&* (15 7 3 1) 15 7 3 1 30 14 6 2 60 28 12 4 120 56 24 8 </code></pre> <p>At this point the similarity to your original table may make the meaning of that table accessible:</p> <pre><code> (15 7 3 1) 2&* (15 7 3 1) 491520 229376 98304 32768 1920 896 384 128 120 56 24 8 30 14 6 2 </code></pre> <p>The same thing is happening, it's just happening more often because you've given some higher numbers.</p>

Querying!

Guidance

An individual column

Larger individual text columns get their own page to allow for proper reading.

SQuiL has stopped working due to an internal error.

If you are curious you may find further information in the browser console, which is accessible through the devtools (F12).

Reload