Prefix: Difference between revisions
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Miraheze>Marshall (Created page with "A '''prefix''' of a vector is another vector which is no longer than that vector, and shares all of its leading elements. In leading axis theory, an array may be c...") |
Miraheze>Adám Brudzewsky No edit summary |
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A vector is a prefix of another vector if its length is [[Less than or Equal to]] that vector's length, and every [[element]] in the prefix vector [[match]]es the corresponding element of the other vector (the one at the same [[index]]). This may be tested using [[Take]] and [[Match]]: | A vector is a prefix of another vector if its length is [[Less than or Equal to]] that vector's length, and every [[element]] in the prefix vector [[match]]es the corresponding element of the other vector (the one at the same [[index]]). This may be tested using [[Take]] and [[Match]]: | ||
<source lang=apl> | <source lang=apl> | ||
isPrefix ← {(≢⍺)≤(≢⍵) ∧ ⍺≡(≢⍺)↑⍵} | isPrefix ← {((≢⍺)≤(≢⍵)) ∧ ⍺≡(≢⍺)↑⍵} | ||
'pre' isPrefix 'prefix' | 'pre' isPrefix 'prefix' | ||
1 | 1 | ||
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In [[leading axis theory]], the [[frame]] for k-cells of an array is a prefix of that array's [[shape]], while the [[cell shape]] is a [[suffix]]. | In [[leading axis theory]], the [[frame]] for k-cells of an array is a prefix of that array's [[shape]], while the [[cell shape]] is a [[suffix]]. | ||
[[Iverson notation]] included the notion of a prefix vector <math>\alpha^j(n)</math> consisting of <math>j</math> ones followed by <math>n-j</math> zeros; such a vector could be used to produce a length-<math>j</math> prefix of a length-<math>n</math> vector using [[Compress]]. | [[Iverson notation]] included the notion of a prefix vector <math>\alpha^j(n)</math> consisting of <math>j</math> ones followed by <math>n-j</math> zeros; such a vector could be used to produce a length-<math>j</math> prefix of a length-<math>n</math> vector using [[Compress]]. A prefix function <source lang=apl inline>n ⍺ j</source> was included in early versions of [[APL\360]]. | ||
In [[Dyalog APL's]] [[Total array ordering]], a prefix of another array always orders earlier than that array; this is a consequence of the | In [[Dyalog APL's]] [[Total array ordering]], a prefix of another array always orders earlier than that array; this is a consequence of the principally "nothing is less than something" used as the foundation for Dyalog's TAO. | ||