use utf8; ( # dyadic, monadic # arithmetic ["+\n-", "add\nSum of A and B", "conjugate\nNo change to B"], ["−\n_", "subtract\nA minus B", "negate\nChanges sign of B"], ["×\n-", "multiply\nA multiplied by B", "sign\n¯1 if B<0; 0 if B=0; 1 if B>0"], ["÷\n=", "divide\nA divided by B", "reciprocal\n1 divided by B"], ["∣\nm", "residue\nRemainder of division: B modulo A", "magnitude\nAbsolute value of B"], ["⋆\np", "power\nA raised to the B power", "exponential\ne to the B power"], ["⍟\n*", "logarithm\nLogarithm of B to base A", "natural logarithm\nNatural logarithm of B"], ["○\no", "circle\nTrigonometric functions of B selected by A\nA=1: sin(B) A=2: cos(B) A=3: tan(B)", "pi times\nMultiply by π"], ["⌈\ns", "maximum\nThe greater value of A or B", "ceiling\nLeast integer greater than or equal to B"], ["⌊\nd", "minimum\nThe smaller value of A or B", "floor\nGreatest integer less than or equal to B"], ["!", "binomial\nNumber of combinations of B taken A at a time", "factorial\nProduct of integers 1 to B"], ["?\nq", "deal\nA distinct integers selected randomly from the first B integers", "roll\nOne integer selected randomly from the first B integers"],undef, # logical ["∼\nt", "difference\nItems found in B are removed from A", "not\nLogical: ∼1 is 0, ∼0 is 1"], ["∨\n9", "or\nLogic: 0 if A and B are 0; 1 otherwise"], ["∧\n0", "and\nLogic: 1 if A and B are 1; 0 otherwise"], ["⍱\n(", "nor\nLogic: 1 if both A and B are 0; otherwise 0"], ["⍲\n)", "nand\nLogic: 0 if both A and B are 1; otherwise 1"], # comparative ["<\n3", "less than\nComparison: 1 if true, 0 if false"], ["≤\n4", "less than or equal\nComparison: 1 if true, 0 if false"], ["=\n5", "equal\nComparison: 1 if true, 0 if false"], ["≥\n6", "greater than or equal\nComparison: 1 if true, 0 if false"], [">\n7", "greater than\nComparison: 1 if true, 0 if false"], ["≠\n8", "not equal\nComparison: 1 if true, 0 if false"], ["≡\n:", "match\n1 if arguments are the same in every respect, 0 if not", "depth\nLevel of nesting: 1 + maximum array depth or 0 if scalar"], ["≢\n\"", "not match\n1 if arguments are different if any respect, 0 if not", "tally\nNumber of major cells in B, equivalent to {⍬⍴ (⍴⍵),1}"],undef, # vector ["∈\ne", "membership\n1 for elements of A present in B; 0 where not", "enlist\nEvery element in B as simple vector"], ["⍷\nE", "find\nElements of A within B, returning 1 if the start of A is found in B"], ["⌷\nL", "index", "materialise"], ["⍬\n}",undef, "zilde\nEmpty numeric vector, equivalent to ⍳0 or 0⍴0"], ["⍳\ni", "index of\nThe location (index) of B in A; 1+⌈/⍳⍴A if not found", "count\nVector of the first B integers"], ["⍸\nI", "string index\nThe index of B in A using ⍷ as primary function"], ["⍴\nr", "reshape\nArray of shape A with data B", "shape\nNumber of components in each dimension of B"], # selection ["⊢\n\\", "right\nDiscard A and pass B unchanged", "pass\nPasses argument unchanged, useful to force display of non-printing result"], ["⊣\n|", "left\nDiscard B and pass A unchanged", "stop\nDiscard argument and return empty matrix"], ["⋄\n`", "statement separator\nSeparates multiple statements on a single line"], ["↑\ny", "take\nSelect the first (or last) A elements of B according to ×A", "nub"], ["↓\nu", "drop\nRemove the first (or last) A elements of B according to ×A", "split"], # set ["⊂\nz", "partition\nDivide B into an array of vectors according to specification in A", "enclose\nProduce a scalar of vector B"], ["⊃\nx", "pick\nSelect item A from vector B", "disclose\nProduce an array made up of the items in B"], ["⊆", "subset\nElements in both A and B: (∧/A∈B)∧(∧/B∈A)"], ["∩\nc", "intersection\nElements of A that are in B: (A∈B)/A"], ["∪\nv", "union\nCatenate A and B determined by combining ranks: A,(∼A∈B)/A", "unique"], [",", "catenate\nElements of B appended to the elements of A", "ravel\nReshapes B into a vector"], ["⍪\n<", "catenate first\nCatenate across the first axis"], # transform ["⌹\n+", "matrix divide\nSolution to system of linear equations, multiple regression Ax = B", "matrix inverse\nInverse of matrix B"], ["⌽\n%", "rotate first\nThe elements of B are rotated A positions", "reverse first\nReverse elements of B along last axis"], ["⊖\n&", "rotate\nThe elements of B are rotated A positions along the first axis", "reverse\nReverse elements of B along first axis"], ["⍉\n^", "general transpose\nThe axes of B are ordered by A", "monadic transpose\nReverse the axes of B"],undef, # sorting and coding ["⍋\n\$", "grade up\nArrange B according to collating sequence specified by A", "grade up\nIndices of B which will arrange B in ascending order"], ["⍒\n#", "grade down\nArrange B according to inverse collating sequence specified by A", "grade down\nIndices of B which will arrange B in descending order"], ["⊤\nn", "encode\nBase-A representation of the value of B"], ["⊥\nb", "decode\nValue of a polynomial whose coefficients are B at A"], # miscellaneous ["⍺", "picture format\nDisplays the numbers in B according to the instructions in A", "alpha"], ["⍕\n'", "specified format\nFormat B into a character matrix according to A", "format\nConvert to characters according to default display rules"], ["⍎\n;", "execute", "execute\nExecute an APL expression"], ["⎕\nl",undef, "evaluated I/O\nRead number or expression typed on the keyboard or display result with newline"], ["⍞\n{",undef, "bare I/O\nRead data typed on the keyboard as characters or display without terminating newline"], [")",undef, "hook"], ["→\n]",undef, "goto\n→This_Label sends APL execution to This_Label:"], ["←\n[",undef, "assign\nB←A sets values and shape of B to match A"], ["⍝\n,",undef, "comment\nEverything to the right of ⍝ denotes a comment"], ["_\nf"], ["∆\nh", "difference", "derivative"], ["∇\ng",undef, "edit\nToggle function definition mode"], ["⍫\n@",undef, "lock\nEdit a function which cannot be edited or displayed"], ["'\nk"], ["⍙\n>"],undef, # operators ["\\","expand\nInsert zeros (or blanks) in B corresponding to zeros in A", "scan\nRunning sum across B"], ["⍀\n.", "expand first", "scan first\nRunning sum down B"], ["/", "replicate\nSelect elements in B corresponding to ones in A", "reduce\nSum across B"], ["⌿\n/", "replicate first", "reduce first\nSum down B"], # array ["¯\n2",undef, "negative\nDenotes a negative number"], ["∝\na"], ["⍵\nw", "omega"], # monadic ["¨\n1", "each\nOver each, or perform each separately; B = on these; A = operation to perform or using (e.g. iota)"], ["⍨\nT", "commute\nExchanges the arguments of a dyadic function: A+⍨B ↔ B+A"], ["&",undef, "spawn"], ["⌶\n!",undef, "I-beam"], # dyadic ["⍠\n?", "variant"], ["⌸", "key\nApply function to each unique key in A and major cells of B having that key", "key\nApply function A to each unique key in B and elements of ⍳≢B having that key"], ["⍣\nP", "reapply\nThe function A is applied B times"], [".", "inner product\nMatrix product of A and B"], ["∘.\nj", "outer product\nOuter product of A and B"], ["∘\nj", "compose"], ["⍤\nJ", "rank\nApply function successively to the sub-arrays in B specified by k"], ["⍥\nO", "coax"], );