Du zhka Ajversona funkciya sho povertaye 1 dlya istinnogo vislovlyuvannya i 0 yaksho argument hibnij P 1 yaksho P istinne 0 yaksho P hibne displaystyle P begin cases 1 amp text yaksho P text istinne 0 amp text yaksho P text hibne end cases Notaciya yaku Kennet Ajverson vviv dlya movi programuvannya APL viyavilasya duzhe zruchnim matematichnim poznachennyam napriklad z nim mozhna lakonichno viznachiti simvol Kronekera d i j i j displaystyle delta ij i j indikatornu funkciyu 1 A x x A displaystyle mathbf 1 A x x in A funkciyu Gevisajda 8 x x 0 displaystyle theta x x geqslant 0 funkciyu znaka chisla sgn x x gt 0 x lt 0 displaystyle operatorname sgn x x gt 0 x lt 0 Takozh notaciya zruchna pri koristuvanni sumami oskilki dozvolyaye virazhati yih bez obmezhen na indeks pidsumovuvannya napriklad i 1 n a i k a k 1 k n displaystyle sum i 1 n a i sum k a k 1 leqslant k leqslant n tobto indeks k displaystyle k probigaye vsyu mnozhinu Z displaystyle mathbb Z cilih chisel i formalno pidsumovuyetsya neskinchenna kilkist dodankiv ale lishe skinchenne chislo yih vidminne vid nulya Priklad obchislennya z vikoristannyam duzhok Ajversona sumi S i 1 n 1 j i 1 n a i a j displaystyle S sum i 1 n 1 sum j i 1 n a i a j dlya poslidovnosti a i displaystyle a i i lt j i j i gt j 1 displaystyle i lt j i j i gt j 1 i j a i a j i lt j i j a i a j i j i j a i a j i gt j i j a i a j displaystyle sum limits i j a i a j i lt j sum limits i j a i a j i j sum limits i j a i a j i gt j sum limits i j a i a j S i a i 2 S i a i 2 displaystyle S sum limits i a i 2 S biggl sum limits i a i biggr 2 a oskilki dlya pravoyi chastini i j a i a j i j a i a j i a i j a j i a i 2 displaystyle sum limits i j a i a j sum limits i sum limits j a i a j sum limits i a i sum limits j a j biggl sum limits i a i biggr 2 to S 1 i lt j n a i a j 1 2 i 1 n a i 2 1 2 i 1 n a i 2 displaystyle S sum 1 leq i lt j leq n a i a j frac 1 2 biggl sum i 1 n a i biggr 2 frac 1 2 sum i 1 n a i 2 Literatura RedaguvatiGrehem R Knut D Patashnik O Konkretnaya matematika M Mir 1998 703 s ISBN 5 03 001793 3 Kenneth E Iverson A Programming Language the University of California Wiley 1962 286 s ISBN 0471430145 Otrimano z https uk wikipedia org w index php title Duzhka Ajversona amp oldid 37186420
