! quote dot symbol, binomial and factorial ! binomial, 3!5 is 10 ! factorial, !5 is 120 " cap null symbol, comment " comment # left arrow symbol, specification, assignment # specification, a#1 2 3 # assignment, a#1 2 3 $ right arrow symbol, branch $ branch, $0 % divide symbol, divide and reciprocal % divide, 2%3.2 is 0.625 % reciprocal, %4 is 0.25 & and, 0 0 1 1 & 0 1 0 1 is 0 0 0 1 ' quote, 'abc' ( left parenthesis, (12%3)X2 is 8, 12%3X2 is 2 ) right parenthesis ) )clear, empties workspace ) )copy wsid, copies all objects from named workspace ) )copy wsid names, copies specified objects ) )drop wsid, delete named workspace ) )erase names, erases objects in workspace ) )fns [alphabetic] list defined functions ) )group name names, gathers objects into a group ) )grp name, list members of named group ) )grps [alphabetic], list groups ) )lib [alphabetic[, list workspace names ) )load wsid, load named workspace into memory ) )off, end use of apl ) )pcopy wsid, copies all objects without matching names ) )pcopy wsid names, copies specified objects w/o matching names ) )read fileid, reads file into character matrix named 'file' ) )run fileid, executes APL expressions in named file ) )save [wsid], save workspace to named file. ) )si, list halted functions ) )sinl, list halted functions and local names ) )vars [alphabetic] list variables ) )write fileid, writes character matrix named 'file' to file ) )wsid [wsid], assign or list workspace name * star symbol, exponential and power * exponential, *1 2 is 2.7183 7.3891 * power, 2*3 is 8 + plus symbol, plus and conjugate + plus, 2+3 is 5 + conjugate, +4 is 4 , comma symbol, catenate, laminate, ravel , catenate, 2 3 , 4 5 is 2 3 4 5 , laminate, 1 2,[.5]3 4 is 2 2RI4 , ravel, (,2 2RI4) is 1 2 3 4 - overbar, negative numbers, -5 . dot symbol, inner product, outer product . inner product (2 2RI4)+.X2 2RI4 is 2 2R7 10 15 22 . outer product 1 2J.XI3 is 2 3R1 2 3 2 4 6 / slash symbol, compress and reduction / compress, 1 0 1/I3 is 1 3 / reduction, +/I3 is 6 0 digit zero 1 digit one 2 digit two 3 digit three 4 digit four 5 digit five 6 digit six 7 digit seven 8 digit eight 9 digit nine : colon (labels) ; semicolon symbol ; indexing, (2 2RI4)[2;2] is 4 < less, 3 5<5 3 is 1 0 = equal 3 5=1 5 is 0 1 > greater, 3 5>5 3 is 0 1 ? query symbol, deal, roll ? deal, w?y is random deal of w elements from Iy ? roll ?y is random selection from Iy @ log symbol, general logarithm, natural logarithm @ general logarithm, a@b is log b base a @ natural logarithm, @2 is .6931471806 A delta stile symbol, grade up A grade up, A3 5 3 2 is 4 1 3 2 B base symbol, decode B decode, 10B1 7 7 6 is 1776 C base null symbol, execute C execute, C'1+2' is 3 D downstile symbol, floor, minimum D floor, D2.718 is 2 D minimum, 2D3 is 2 E epsilon symbol, membership E membership, 'abcdefgh'E'coffee' is 0 0 1 0 1 0 0 F top null symbol, format F format, 5 3F1%3 is 0.333 G del symbol (function editing) H delta symbol (function editing, ok in names) I iota symbol, index generator, index of I index generator, I5 is 1 2 3 4 5 I index of, 'abc 'I'b c a' is 2 4 3 4 1 J null symbol, inner product, outer product J inner product, (2 2RI4)+.X2 2RI4 is 2 2R7 10 15 22 J outer product, 1 2J.XI3 is 2 3R1 2 3 2 4 6 K not greater, 1 2 3 K 2 is 1 1 0 K less than or equal, 1 2 3 K 2 is 1 1 0 L quad symbol (input/output) Lav atomic vector, 256-element character vector, all possible characters Lcr a, canonical representation of defined function named in a Lct comparison tolerance, default 1e-13 Lex a, expunge objects named by rows of a Lfx a, fix defined function represented by a Lio index origin, either 0 or 1 Llx latent expression, executed automatically when workspace loaded. Lnc a, returns numerical classification of objects named by rows of a Lnl n, returns character matrix of names with classifications in n M domino symbol, matrix divide, matrix inverse M matrix divide, M2 2R5 0 0 2 is 2 2R.2 0 0 .5 M matrix inverse, M2 2R5 0 0 2 is 2 2R.2 0 0 .5 N top symbol, encode N encode, 10N1776 is 1 7 7 6 O circle symbol, circular, hyperbolic, pi times, pythagorean O circular O hyperbolic O pi times, O 1 2 is 3.14159 6.28319 O pythagorean, 4Ox is (1+x*2)*.5 P nand, 0 0 1 1 P 0 1 0 1 is 1 1 1 0 Q quote-quad (character input) R rho symbol, reshape, shape R reshape, 2 2RI4 is 2-by-2 matrix of 1 2 3 4 R shape, R2 2RI4 is 2 2 S upstile symbol, ceiling, maximum S ceiling, S-3.14 3.14 is -3 4 S maximum, 2S3 is 3 T circle slope symbol, transpose T transpose, T2 2RI4 is 2 2R1 3 2 4 U down arrow symbol, drop U drop, 1U'abc' is 'bc' V or, 0 0 1 1 V 0 1 0 1 is 0 1 1 1 W del stile symbol, grade down W grade down, A3 5 3 2 is 2 1 3 4 X times symbol, times, signum X times, 2X3 is 6 X signum, X-3 0 4 is -1 0 1 Y up arrow symbol, take Y take, 2Y'abc' is 'ab' Z not less 1 2 3 Z 2 is 0 1 1 Z greater than or equal, 1 2 3 Z 2 is 0 1 1 [ bracket, left (axis, indexing) \ slope symbol, expand, scan \ expand 1 0 1 \ 'ab' is 'a b' \ scan +\1 2 3 is 1 3 6 ] bracket, right (axis, indexing) ^= not equal 1 2 3^=2 is 0 1 0 _ bar symbol, minus, negative _ minus, 1_2 is -1 _ negative, _1 -2 3 is -1 2 -3 `/ slash bar symbol, compress, reduction `/ compress, 1 0 1`/3 3R'abcdefghi' is 2 3R'abcghi' `/ reduction, +`/3 4RI12 is 15 18 21 24 `1 dieresis symbol `A alpha symbol `C cap symbol `G del tilde symbol `I i-beam symbol `O circle stile symbol, reverse, rotate `O reverse, `O2 3RI6 is 2 3R3 2 1 6 5 4 `O rotate, 1 2`O2 3RI6 is 2 3R2 3 1 6 4 5 `R circle bar symbol, reverse `R reverse, `R2 3RI6 is 2 3R4 5 6 1 2 3 `U cup symbol `V nor, 0 0 1 1 V 0 1 0 1 is 1 0 0 0 `W omega symbol `X shoe, right, symbol `Z shoe, left, symbol `\ slope bar symbol, expand, scan `\ expand, 1 0 1`\2 2RI4 is 3 2R1 2 0 0 3 4 `\ scan, +`\2 3RI6 is 2 3 R 1 2 3 5 7 9 `a alphabetic a underscored `b alphabetic b underscored `c alphabetic c underscored `d alphabetic d underscored `e alphabetic e underscored `f alphabetic f underscored `g alphabetic g underscored `h alphabetic h underscored `i alphabetic i underscored `j alphabetic j underscored `k alphabetic k underscored `l alphabetic l underscored `m alphabetic m underscored `n alphabetic n underscored `o alphabetic o underscored `p alphabetic p underscored `q alphabetic q underscored `r alphabetic r underscored `s alphabetic s underscored `t alphabetic t underscored `u alphabetic u underscored `v alphabetic v underscored `w alphabetic w underscored `x alphabetic x underscored `y alphabetic y underscored `z alphabetic z underscored a alphabetic a b alphabetic b c alphabetic c d alphabetic d e alphabetic e f alphabetic f g alphabetic g h alphabetic h i alphabetic i j alphabetic j k alphabetic k l alphabetic l m alphabetic m n alphabetic n o alphabetic o p alphabetic p q alphabetic q r alphabetic r s alphabetic s t alphabetic t u alphabetic u v alphabetic v w alphabetic w x alphabetic x y alphabetic y z alphabetic z { left brace symbol (not used) | stile symbol, magnitude, residue | magnitude, |-3 0 4 is 3 0 4 | residue, 1|2.385 is 0.385 } right brace symbol (not used) ~ tilde (not), ~0 1 is 1 0