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APL Wiki - Changes related to "Index" [en-gb]
2024-03-28T17:46:21Z
Related changes
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https://aplwiki.com/index.php?title=Laminate&diff=11355&oldid=10759
Laminate
2024-03-18T01:30:48Z
<p>History</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 01:30, 18 March 2024</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Built-in|Laminate|,[0.5]}} is a case of the [[Catenate]] function [[function axis|with axis]] that joins its argument arrays along a new length-2 [[axis]]. It applies whenever the function axis is non-integral, but is typically written with a half-integer axis. Possible choices of axis range from <syntaxhighlight lang=apl inline>,[⎕IO-0.5]</syntaxhighlight>, which places the new axis before any argument axis, to <syntaxhighlight lang=apl inline>,[r+⎕IO-0.5]</syntaxhighlight>, where <syntaxhighlight lang=apl inline>r</syntaxhighlight> is the shared argument [[rank]], which places it after all argument axes. Laminate appears as a stand-alone function in some languages, with the name Laminate in [[A+]] (<syntaxhighlight lang=apl inline>~</syntaxhighlight>) and [[J]] (<syntaxhighlight lang=j inline>,:</syntaxhighlight>), and Couple in [[BQN]] (<code>≍</code>) and [[Uiua]] (<code>⊟</code>). These languages implement the <syntaxhighlight lang=apl inline>,[⎕IO-0.5]</syntaxhighlight> case only, as the [[Rank operator]] can be used to add the axis in a later position, in accordance with [[leading axis theory]].</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Built-in|Laminate|,[0.5]}} is a case of the [[Catenate]] function [[function axis|with axis]] that joins its argument arrays along a new length-2 [[axis]]. It applies whenever the function axis is non-integral, but is typically written with a half-integer axis. Possible choices of axis range from <syntaxhighlight lang=apl inline>,[⎕IO-0.5]</syntaxhighlight>, which places the new axis before any argument axis, to <syntaxhighlight lang=apl inline>,[r+⎕IO-0.5]</syntaxhighlight>, where <syntaxhighlight lang=apl inline>r</syntaxhighlight> is the shared argument [[rank]], which places it after all argument axes. Laminate appears as a stand-alone function in some languages, with the name Laminate in [[A+]] (<syntaxhighlight lang=apl inline>~</syntaxhighlight>) and [[J]] (<syntaxhighlight lang=j inline>,:</syntaxhighlight>), and Couple in [[BQN]] (<code>≍</code>) and [[Uiua]] (<code>⊟</code>). These languages implement the <syntaxhighlight lang=apl inline>,[⎕IO-0.5]</syntaxhighlight> case only, as the [[Rank operator]] can be used to add the axis in a later position, in accordance with [[leading axis theory]].</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Laminate was defined as an extension to Catenate in [[APL\360]] in 1970.<ref>"Report of the APL SHARE conference" ([https://dl.acm.org/action/showBmPdf?doi=10.1145%2F987461 pdf]). [[APL Quote-Quad]] Volume 2, Number 3. 1970-09.</ref></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Examples ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Examples ==</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [https://www.uiua.org/docs/couple Uiua]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [https://www.uiua.org/docs/couple Uiua]</div></td></tr>
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<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">== References ==</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><references/></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{APL built-ins}}[[Category:Primitive functions]][[Category:Leading axis theory]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{APL built-ins}}[[Category:Primitive functions]][[Category:Leading axis theory]]</div></td></tr>
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Marshall