8020:
8453:
8443:
84:
25:
5956:
Before
Unicode, APL interpreters were supplied with fonts in which APL characters were mapped to less commonly used positions in the ASCII character sets, usually in the upper 128 code points. These mappings (and their national variations) were sometimes unique to each APL vendor's interpreter, which
5949:
block, which are thus usually rendered accurately from the larger
Unicode fonts installed with most modern operating systems. These fonts are rarely designed by typographers familiar with APL glyphs. So, while accurate, the glyphs may look unfamiliar to APL programmers or be difficult to distinguish
3802:
The product operator "." expects a dyadic function on both its left and right, forming a dyadic composite function applied to the vectors on its left and right. If the function to the left of the dot is "∘" (signifying null) then the composite function is an outer product, otherwise it is an inner
5006:
Inside a program or a custom function, control may be conditionally transferred to a statement identified by a line number or explicit label; if the target is 0 (zero) this terminates the program or returns to a function's caller. The most common form uses the APL compression function, as in the
5002:
Custom dyadic functions may usually be applied to parameters with the same conventions as built-in functions, i.e., arrays should either have the same number of elements or one of them should have a single element which is extended. There are exceptions to this, for example a function to convert
5999:
equivalent to 55 APL special symbols (excluding letters, numbers, punctuation, etc. keys). Thus, early APL was then only using about 11% (55/472) of a symbolic language's at-that-time utilization potential, based on keyboard # keys limits, again excluding numbers, letters, punctuation, etc. In
3806:
Some functions can be followed by an axis indicator in (square) brackets, i.e., this appears between a function and an array and should not be confused with array subscripts written after an array. For example, given the ⌽ (reversal) function and a two-dimensional array, the function by default
6024:, which is a triangular array of numbers in which those at the ends of the rows are 1 and each of the other numbers is the sum of the nearest two numbers in the row just above it (the apex, 1, being at the top). The following is an APL one-liner function to visually depict Pascal's triangle:
5178:
since the condition ends up being based on a single element of the SIGN array - on the other hand, the user function could be modified to correctly handle vectorized arguments. Operation can sometimes be unpredictable since APL defines that computers with vector-processing capabilities
161:
function has another argument, the first item of data on its left. Many symbols denote both monadic and dyadic functions, interpreted according to use. For example, ⌊3.2 gives 3, the largest integer not above the argument, and 3⌊2 gives 2, the lower of the two arguments.
5994:
character max (256 chars times 2 codes for each keys-combination). Again, in theory the keyboard pictured here would have allowed for about 472 different APL symbols/functions to be keyboard-input, actively used. In practice, early versions were only using something
5265:
A more concise way and sometimes better way - to formulate a function is to avoid explicit transfers of control, instead using expressions which evaluate correctly in all or the expected conditions. Sometimes it is correct to let a function fail when one or both
5194:
particularly if they will be used with vector or even matrix arguments. This affects not only explicit application of a custom function to arrays, but also its use anywhere that a dyadic function may reasonably be used such as in generation of a table of results:
4998:
are distinct is implementation-defined. If allowed, then a function CURVEAREA could be defined twice to replace both monadic CIRCLEAREA and dyadic SEGMENTAREA above, with the monadic or dyadic function being selected by the context in which it was referenced.
136:
to describe algorithms. APL programmers often assign informal names when discussing functions and operators (for example, "product" for ×/) but the core functions and operators provided by the language are denoted by non-textual symbols.
5007:
template (condition)/target which has the effect of evaluating the condition to 0 (false) or 1 (true) and then using that to mask the target (if the condition is false it is ignored, if true it is left alone so control is transferred).
5977:
monadic and dyadic tables) APL symbol keys (55 APL functions (operators) are listed in IBM's 5110 APL Reference Manual), thus with the use of alt, shift and ctrl keys - it would theoretically have allowed a maximum of some
5966:
5973:
Note the APL On/Off Key - topmost-rightmost key, just below. Also note the keyboard had some 55 unique (68 listed per tables above, including comparative symbols but several symbols appear in
3803:
product. An inner product intended for conventional matrix multiplication uses the + and × functions, replacing these with other dyadic functions can result in useful alternative operations.
368:(vector) of items using data types other than just numeric, for example a 2-element vector of character strings {"Apples" "Oranges"} could be substituted for numeric vector {45 67} above.
356:
vector {45 0 67} — note how APL inserted a 0 into the vector. Conversely, the exact opposite occurs on the right side — where a 3-element vector becomes just 2-elements; boolean 0s
4756:
8491:
8797:
8807:
8802:
5274:- precisely to let user know that one or both arguments used were incorrect. The following is more concise than the above SEGMENTAREA function. The below importantly
265:
an array by multiplication. The above case is simplified, imagine multiplying (adding, subtracting or dividing) more than just a few numbers together. (From a vector,
190:, however both terms are used in APL more precisely. Early definitions of APL symbols were very specific about how symbols were categorized. For example, the operator
567:
and evaluate to a dyadic or monadic function. Operators have long left scope. An operator takes as its left operand the longest function to its left. For example:
7400:
8484:
8892:
8887:
7960:
672:
function. The result of ∘.=/ is a monadic function. With a function's usual long right scope, it takes as its right argument the result of ⍳¨3 3. Thus
4791:
defines whether a custom function is niladic (no arguments), monadic (one right argument) or dyadic (left and right arguments), the local name of the
178:’s sense as a moderator of a function as opposed to some other programming language's use of the same term as something that operates on data, ref.
4115:
visually portrays. Compare the result here to the original matrix stored in A, topmost matrix. These types of data transformations are useful in
5942:
4151:
to a symbol/function), it can be used to laminate (interpose) two arrays depending on whether the axis indicator is less than or greater than the
8477:
7636:
APL's "high minus" applies to the single number that follows, while the monadic minus function changes the sign of the entire array to its right.
5466:, veritably "misunderstood and complex idioms" and a "write-only" style, which has done little to endear APL to influential commentators such as
5462:
Avoiding explicit transfers of control also called branching, if not reviewed or carefully controlled - can promote use of excessively complex
3799:
The reduce and scan operators expect a dyadic function on their left, forming a monadic composite function applied to the vector on its right.
5933:
commands or functions due to the use of a leading right parenthesis or hook. There is some standardization of these quad and hook functions.
8675:
5003:
pre-decimal UK currency to dollars would expect to take a parameter with precisely three elements representing pounds, shillings and pence.
6950:⍝Generate a Fibonacci sequenced number where Nth is the position # of the Fibonacci number in the sequence. << function description
8447:
590:
Beginning rightmost: ⍳¨3 3 produces a 2-element nested APL vector { {1 2 3} {1 2 3} } where each element is itself a vector {1 2 3}.
5010:
Hence function SEGMENTAREA may be modified to abort (just below), returning zero if the parameters (DEGREES and RADIUS below) are of
408:
8922:
8457:
8124:
6000:
another sense keyboard symbols utilization was closer to 100%, highly efficient, since EBCDIC only allowed 256 distinct chars, and
4361:) two arrays (vectors in this case) depending on whether the axis indicator is less than or greater than the index origin(1). The
8542:
8508:
5112:⍝ << APL logic TEST/determine whether DEGREES and RADIUS do NOT (≠ used) have same SIGN 1-yes different(≠), 0-no(same sign)
49:
5391:⍝ this APL statement is more complex, as a one-liner - but it solves vectorized arguments: a tradeoff - complexity vs. branching
157:
function takes as its argument the result of evaluating everything to its right. (Moderated in the usual way by parentheses.) A
8835:
8680:
7953:
7127:
5876:
for the APL workspace and program to process using. If this number gets low or approaches zero - the computer may need more
8917:
8724:
8719:
8277:
380:
for functions or operators is strictly positional: expressions are evaluated right-to-left. APL does not follow the usual
8698:
8690:
8388:
8243:
8167:
8028:
7061:⍝ This APL statement says: Generate the Fibonacci sequence over each(¨) integer number(iota or ⍳) for the integers 1..14.
5657:
104:
7801:
8830:
7901:
7844:
7526:
7188:
7165:
7146:
8612:
7946:
67:
432:
419:: it takes as its left arguments the first piece of data to its left. For example, (leftmost column below is actual
8872:
8840:
8659:
8654:
8641:
8547:
8361:
8132:
4404:
885:
6947:⍝ Funct header, funct name=Fibonacci, monadic funct with 1 right hand arg Nth;local var IOwas, and a returned num.
8312:
7994:
7411:
183:
5990:(with tri-key pressing, e.g., ctrl-alt-del) or some 472 different maximum key combinations, approaching the 512
5139:⍝ branching(here, exiting) occurs when SIGN=1 while SIGN=0 does NOT branch to 0. Branching to 0 exits function.
8877:
8322:
581:
8205:
8004:
6012:
APL has proved to be extremely useful in solving mathematical puzzles, several of which are described below.
199:
5664:) variable, since while the original IBM APL based its arrays on 1 some newer variants base them on zero:
8238:
4056:
1162:
1130:
8591:
8271:
8097:
8078:
7969:
2789:
2373:
2336:
746:
424:
117:
91:
8469:
7729:
7611:
7570:
5484:
4087:. The result is that variable A has been reflected across the horizontal axis, instead of vertically.
8512:
5644:
Most APL implementations support a number of system variables and functions, usually preceded by the
40:
7931:
7874:
7556:
5953:
Some
Unicode fonts have been designed to display APL well: APLX Upright, APL385 Unicode, and SimPL.
1039:
Iota finds letter "C" at position 3 in
Letters, it finds "A" at position 1, and "B" at position 2.
8157:
8120:
8109:
7786:
full-featured, no restrictions, free downloadable APL/2 with nested arrays by Sudley Place
Software
5812:
now changed to 0. Thus, the 'first index position' in vector X changes from 1 to 0. Consequently,
8768:
8729:
7204:
7106:⍝ Generated sequence, i.e., the Fibonacci sequence of numbers generated by APL's interpreter.
5957:
made the display of APL programs on the Web, in text files and manuals - frequently problematic.
5946:
2793:
100:
8222:
7210:
4412:
4120:
3121:
2074:
1465:
881:
617:(in human i.e., reversed terms, the APL interpreter reads 3 3 over each use iota), concisely:
194:
is denoted by a forward slash and reduces an array along one axis by interposing its function
8825:
8552:
8504:
8148:
7734:
7233:
Proceedings of the May 1-3, 1962, spring joint computer conference on - AIEE-IRE '62 (Spring)
6401:
6197:
5478:, for example including source and intended meaning and function of the idiom(s). Here is an
877:
864:
and then used monadically, its right argument is taken as its left argument as well. Thus, a
133:
8436:
8382:
8249:
7795:
7756:
7646:
7319:
6021:
5877:
5661:
4408:
4399:
4152:
826:
404:
345:
5921:
There are also system functions available to users for saving the current workspace e.g.,
1036:
through its left argument(Letters) for the search string (iota's right argument, FindIt).
8:
8348:
8070:
7724:
7720:
7716:
7712:
7583:
4124:
3297:
3231:
1883:
1391:
750:
415:: that is, they take as right arguments everything to their right. A dyadic function has
381:
377:
179:
7292:
5480:
327:
8622:
8617:
8343:
7919:
7907:
7862:
7850:
7806:
7738:
7544:
7532:
7459:
7246:
6206:
833:
8882:
8307:
7897:
7840:
7522:
7184:
7177:
7161:
7142:
7123:
35:
7854:
7463:
7250:
6915:
sequence, where each subsequent number in the sequence is the sum of the prior two:
6399:
Examining the converse or opposite of a mathematical solution is frequently needed (
8627:
8353:
8297:
8009:
7911:
7887:
7830:
7777:
7536:
7512:
7449:
7236:
6912:
5656:=close parenthesis) character. Note that the quad character is not the same as the
2591:
175:
8019:
4799:
arrow), and whether it has any local variables (each separated by semicolon ';').
4304:
At left, variable 'B' is first assigned a vector of 4 consecutive integers (e.g.,
563:
8371:
8302:
7999:
7988:
5881:
5467:
4552:
set = to matrix with 4 rows by 5 columns, consisting of 20 consecutive integers.
735:
186:. Other programming languages also sometimes use this term interchangeably with
7667:
7507:
Benkard, J. Philip (1992). "Nested arrays and operators: Some issues in depth".
7478:
6439:⍝ i.e., prove Non-Prime. String 'prime' is returned for a Prime integer.
8649:
8637:
7691:
5885:
3713:
3384:
2109:
1528:
1326:
1260:
428:
7819:
3807:
operates along the last axis but this can be changed using an axis indicator:
848:, for example, could be a hypothetical function that applies defined function
8911:
8596:
8409:
6205:
that has no positive divisors other than 1 and itself) up to some number N.
3753:
1424:
8737:(Mathematical signs and symbols for use in physical sciences and technology)
7241:
995:
is assigned a vector of 5-elements, in this case - letters of the alphabet.
8703:
8327:
7265:
6235:⍝ Function takes one right arg N (e.g., show prime numbers for 1 ... int N)
5085:⍝ this APL code statement calls user function CIRCLEAREA, defined up above.
7835:
7749:
7517:
7454:
7437:
6667:⍝ Prove non primes for each(¨) of the integers from 1 through 15 (iota 15)
6556:⍝ If result has zero shape, it has no other factors and is therefore prime
8501:
8396:
8366:
8317:
4419:. Array structures containing elements which are also arrays are called
4116:
3347:
2004:
742:
420:
365:
94:
7892:
7373:
5488:
8499:
8227:
8200:
7046:⍝ In order for this function to work correctly ⎕IO must be set to zero.
3633:
7346:
6604:⍝ Show the number R, its factors(except 1,itself), and a new line char
6209:
is credited with the following one-liner APL solution to the problem:
8792:
8734:
8338:
5474:
APL idioms can be fun, educational and useful - if used with helpful
2891:
1851:
1819:
1591:
7789:
6405:): Prove for the subset of integers from 1 through 15 that they are
4111:
to a 3 row by 4 col matrix such that rows-cols become exchanged, as
860:
existing function. In cases where a dyadic function is moderated by
8524:
7743:
6436:⍝Show all factors of an integer R - except 1 and the number itself,
5965:
5869:
5865:
4415:, etc.). Arrays containing both characters and numbers are termed
2039:
1968:
1359:
1227:
7938:
4755:
8572:
8526:
4995:
1050:
anywhere in variable
Letters so it returns the number 6 which is
7117:
6101:⍝ Run function Pascal for seven rows and show the results below:
3495:
exactly with respect to value, shape, and nesting; otherwise 1.
8232:
6413:. What are their non-one factors (#'s divisible by, except 1)?
5991:
844:
664:. Its left operand is the function expression to its left: the
7798:
uploaded by Jimin Park, 8 intro/beginner instructional videos.
7160:(Paperback) (Reprint of the original 1st ed.). Springer.
648:
is used monadically and takes as its right operand the vector
8530:
8115:
6394:⍝ There are twenty-five prime numbers in the range up to 100.
6001:
5915:
shows user variable names existing in the current workspace.
1231:
552:
Step 4) Divide 1 by -3 = -0.3333333333 = final result.
7884:
Conference proceedings on APL as a tool of thought - APL '89
7827:
Proceedings of the international conference on APL - APL '83
7509:
Proceedings of the international conference on APL - APL '92
7231:
Iverson, Kenneth E. (1962-01-01). "A programming language".
5660:. Particularly important and widely implemented is the ⎕IO (
4369:) is a 2 row by 4 column matrix, vertically joining 'B' and
341:
to produce exactly opposite results. On the left side, the
8757:
8048:
7783:
7374:"D-functions and operators loosely grouped into categories"
6529:⍝ Delete 1 and the number as factors for the number from Z.
5960:
2729:
1755:
1293:
6190:
2212:
Negatives produce the inverse of the respective functions
392:. Instead of operator precedence, APL defines a notion of
8217:
7882:
Gffer, M. (1989). "A future APL: Examples and problems".
7792:
free downloadable interpreter for APL by Jürgen
Sauermann
7649:. Microapl.co.uk. p. (toward bottom of the web page)
4994:
Whether functions with the same identifier but different
2411:
1195:
330:
values (0s and 1s) can be used as left arguments for the
7825:
Iverson, Kenneth E. (1983). "APL syntax and semantics".
132:, not words. These symbols were originally devised as a
7573:, IBM Research, Thomas J. Watson Research Center, 1969.
4403:
are structures which have elements grouped linearly as
4069:
is now reflected or flipped along its vertical axis as
1561:
876:
at left) is used in the APL user session to return a 9-
537:
Step 1{of topmost APL code entered at left}) 4-5 = -1.
7757:"How to Create an APL or Math Symbols Keyboard Layout"
4720:
Element in X, formerly integer 14, now becomes a mini
4314:
is then assigned 4 more consecutive integers (such as
261:
evaluates to a scalar (1 element only) result through
7563:
5187:
reorder array operations as far as possible - thus,
1024:
1 2 3 4 5 << vector positions or index #'s in
45:
This article has non-standard layout and formatting.
8893:
List of typographical symbols and punctuation marks
6487:⍝ Determine all factors for integer R, store into Z
2243:distinct integers selected randomly from the first
388:does not bind its operands any more "tightly" than
16:
Set of rules defining correctly structured programs
8888:Table of mathematical symbols by introduction date
7176:
7750:extending APL and its keyboard-symbols-operators.
7272:. Vector - Journal of the British APL Association
7156:Thompson, Norman D.; Polivka, Raymond P. (2013).
5884:space or some combination of the two to increase
4338:). In the particular case at left, if the dyadic
533:<< First note there are no parentheses and
8909:
7488:. MicroAPL - Version 5 .0 June 2009. p. 22
7155:
7137:Reiter, Clifford A.; Jones, William R. (1990).
5594:→This_Label sends APL execution to This_Label:
5564:Everything to the right of ⍝ denotes a comment
3542:
140:
722:The matrix of 1s and 0s similarly produced by
8485:
7954:
7778:A Practical Introduction to APL 1 & APL 2
7213:– More modern APL keyboard layout information
7158:APL2 in Depth (Springer Series in Statistics)
6092:⍝ Create one-line user function called Pascal
2531:Value of a polynomial whose coefficients are
1107:One integer selected randomly from the first
384:of other programming languages; for example,
8570:
7235:. New York, NY, USA: ACM. pp. 345–351.
6652:⍝ function branches here if number was prime
5753:set = to vector of 12 consecutive integers.
4559:in row 2 - column 2 currently is an integer
3047:= operation to perform or using (e.g., iota)
986:(or not find) elements in a character vector
535:APL is going to execute from right-to-left.
7771:
7136:
7118:Polivka, Raymond P.; Pakin, Sandra (1975).
5925:and terminating the APL environment, e.g.,
8492:
8478:
7961:
7947:
7174:
5767:. Thus, the first position in vector X or
5624:B←A sets values and shape of B to match A
4826:function SEGMENTAREA, with local variables
4155:(index origin = 1 in illustration below):
1205:Number of components in each dimension of
269:returns the product of all its elements.)
165:
7891:
7834:
7692:"Miscellaneous Technical (including APL)"
7516:
7453:
7240:
5874:additional total free work area available
5055:⍝ local variables denoted by semicolon(;)
4787:rather than by a non-textual symbol. The
4783:which, like variables, are identified by
2309:1 for starting point of multi-item array
68:Learn how and when to remove this message
7820:Conway's Game Of Life in APL, on YouTube
7175:Gilman, Leonard; Rose, Allen J. (1976).
5964:
5961:APL2 keyboard function to symbol mapping
4754:
741:Identity matrices are useful in solving
8862:
8758:Typographical conventions and notations
8543:List of mathematical symbols by subject
7824:
7784:APL for PCs, Servers and Tablets - NARS
7506:
7230:
6191:Prime numbers, contra proof via factors
4580:Thus, the first element in matrix X or
4385:) is a 4 row by 2 column matrix.
4055:. The 4 x 3 matrix is then stored in a
4047:4 rows by 3 cols matrix created, using
3039:Over each, or perform each separately;
1172:Greatest integer less than or equal to
1140:Least integer greater than or equal to
364:function. APL symbols also operate on
326:symbol, right example) demonstrate how
105:question marks, boxes, or other symbols
8910:
8836:Notation in probability and statistics
8776:
8681:Mathematical Operators (Unicode block)
7344:
6304:⍝ Show all prime numbers from 1 to 100
4724:2x2 matrix of 4 consecutive integers.
4707:Element in X is changed (from 7) to a
3402:are 1, otherwise 1. Alt: ~∧ = not And
3378:APL FUNCTIONAL SYMBOL DOWN CARET TILDE
2989:APL FUNCTIONAL SYMBOL CIRCLE BACKSLASH
2330:APL FUNCTIONAL SYMBOL EPSILON UNDERBAR
1845:APL FUNCTIONAL SYMBOL CIRCLE BACKSLASH
1405:(real numbers are returned unchanged)
561:An operator may have function or data
352:where boolean 0s occur to result in a
8861:
8756:
8569:
8523:
8473:
7942:
7881:
7609:
7435:
6906:
6220:⍝ Show APL user-function PrimeNumbers
4411:—and higher dimensions (3D or cubed,
3365:are 0, otherwise 0. Alt: ~∨ = not Or
2939:into a character matrix according to
1924:into a table, a 2-dimensional array.
1893:Nesting depth: 1 for un-nested array
8442:
8254:Telecompute Integrated Systems, Inc.
7476:
7317:
7290:
7141:(1 ed.). Taylor & Francis.
6015:
4158:
4136:As a particular case, if the dyadic
3810:
3415:APL FUNCTIONAL SYMBOL UP CARET TILDE
1077:
897:
762:
675:
570:
438:
431:, not-indented = result returned by
18:
8699:Supplemental Mathematical Operators
8244:Scientific Time Sharing Corporation
8168:Association for Computing Machinery
7968:
7744:General information about APL chars
7263:
7183:(Paperback) (3rd ed.). Wiley.
5860:, shows how much Work Area remains
4332:together for illustration purposes,
3696:APL FUNCTIONAL SYMBOL BACKSLASH BAR
1944:
1782:APL FUNCTIONAL SYMBOL DOWN TACK JOT
13:
8676:Mathematical operators and symbols
7886:. Vol. 19. pp. 158–163.
7829:. Vol. 13. pp. 223–231.
7730:British APL Association fonts page
7647:"The Workspace - System Functions"
7371:
7207:– Unicode block including APL keys
7111:
6007:
5124:⍝ default value of AREA set = zero
3212:Comparison: 1 if true, 0 if false
3185:Comparison: 1 if true, 0 if false
3158:Comparison: 1 if true, 0 if false
3131:Comparison: 1 if true, 0 if false
3102:Comparison: 1 if true, 0 if false
3075:Comparison: 1 if true, 0 if false
2850:APL FUNCTIONAL SYMBOL CIRCLE STILE
1648:APL FUNCTIONAL SYMBOL CIRCLE STILE
852:to the result of defined function
824:Some APL interpreters support the
14:
8934:
8613:Mathematical Alphanumeric Symbols
7813:
7705:
7179:A. P. L.: An Interactive Approach
6613:⍝ Done with function if non-prime
5671:User session with APL interpreter
5577:APL FUNCTIONAL SYMBOL UP SHOE JOT
4433:User session with APL interpreter
2955:APL FUNCTIONAL SYMBOL UP TACK JOT
2921:APL FUNCTIONAL SYMBOL CIRCLE STAR
2815:APL FUNCTIONAL SYMBOL QUAD DIVIDE
2779:Matrix divide, Dyadic Quad Divide
1812:APL FUNCTIONAL SYMBOL UP TACK JOT
1714:APL FUNCTIONAL SYMBOL DELTA STILE
1617:APL FUNCTIONAL SYMBOL CIRCLE STAR
1555:APL FUNCTIONAL SYMBOL QUAD DIVIDE
715:<< Rightmost expression is
660:operator, denoted by the forward
594:by itself would produce {1 2 3}.
8873:Glossary of mathematical symbols
8841:List of common physics notations
8660:Geometric Shapes (Unicode block)
8655:Miscellaneous Symbols and Arrows
8548:Glossary of mathematical symbols
8452:
8451:
8441:
8133:Polymorphic Programming Language
8018:
7211:APL (codepage) § Keyboard layout
5945:includes the APL symbols in the
5658:Unicode missing character symbol
5495:
5168:scalars or single-element arrays
4393:
3030:Diaeresis, Dieresis, Double-Dot
1021:and its length is 4 characters.
880:identity matrix using its right
128:: its primitives are denoted by
82:
23:
8923:APL programming language family
7754:
7683:
7660:
7639:
7630:
7603:
7576:
7511:. Vol. 23. pp. 7–21.
7500:
7401:"IBM 5100 APL Reference Manual"
7398:
7120:APL: The Language and Its Usage
6577:" factors(except 1) "
5619:
5589:
5559:
5529:
5162:The above function SEGMENTAREA
4770:
3748:
3708:
3675:
3642:
3627:APL FUNCTIONAL SYMBOL SLASH BAR
3606:
3573:
3535:APL FUNCTIONAL SYMBOL COMMA BAR
3517:
3482:
3453:
3424:
3389:
3352:
3302:
3236:
3207:
3180:
3153:
3126:
3097:
3070:
3033:
2998:
2964:
2930:
2896:
2872:positions along the first axis
2859:
2824:
2783:
2748:
2734:
2697:
2663:
2629:
2596:
2569:representation of the value of
2560:
2526:
2488:
2450:
2416:
2379:
2342:
2304:
2269:
2235:
2148:
2114:
2079:
2044:
2009:
1973:
1937:APL FUNCTIONAL SYMBOL COMMA BAR
1915:
1888:
1856:
1824:
1791:
1760:
1749:APL FUNCTIONAL SYMBOL DEL STILE
1723:
1688:
1657:
1626:
1596:
1567:
1534:
1500:
1470:
1429:
1396:
1364:
1331:
1298:
1265:
1236:
1200:
1167:
1135:
1102:
575:∘.=/⍳¨3 3 1 0 0 0 1 0 0 0 1
371:
8878:List of mathematical constants
7802:SIGAPL Compiled Tutorials List
7470:
7438:"In defense of index origin 0"
7429:
7392:
7365:
7338:
7311:
7284:
7257:
7224:
7139:APL with a Mathematical Accent
5489:Finnish APL idiom library here
5278:handles vectorized arguments:
4334:resulting in a single vector (
1796:A character representation of
1002:or character vector-length of
1:
8206:Digital Equipment Corporation
7571:"APL\360 Primer Student Text"
7217:
6201:(prime # is a natural number
5816:then references or points to
5174:if they are multiple-element
4759:Visual representation of the
3522:Concatenate along first axis
8257:Time Sharing Resources (TSR)
6926:⍝ Display function Fibonacci
3562:Unicode code point sequence
3543:Operators and axis indicator
2668:Insert zeros (or blanks) in
2660:Expansion, Dyadic Backslash
2638:appended to the elements of
856:; foo and bar can represent
141:Monadic and dyadic functions
7:
8918:Programming language syntax
8691:Supplemental Math Operators
8239:Science Research Associates
7610:Cason, Stan (13 May 2006).
7408:bitsavers.trailing-edge.com
7198:
6402:integer factors of a number
6295:⍝ The Ken Iverson one-liner
5771:per vector of iota values {
4342:function is followed by an
4143:function is followed by an
4079:is now reflected using the
2493:Remove the first (or last)
2455:Select the first (or last)
2153:Trigonometric functions of
842:functions together so that
701:Equivalent results in APL:
584:or piecemeal sub-analysis (
43:. The specific problem is:
10:
8939:
8592:List of Unicode characters
8272:Carnegie Mellon University
7807:Learn APL: An APL Tutorial
7780:by Graeme Donald Robertson
5911:a system function in APL,
5613:Assign, LeftArrow, Set to
5534:Denotes a negative number
4830:
3567:Reduce (last axis), Slash
3003:Number of combinations of
2790:system of linear equations
2772:APL FUNCTIONAL SYMBOL IOTA
2694:Compression, Dyadic Slash
2672:corresponding to zeros in
1497:Ravel, Catenate, Laminate
1320:APL FUNCTIONAL SYMBOL IOTA
1241:Logical: ∼1 is 0, ∼0 is 1
322:examples (using the same
8868:
8857:
8818:
8785:
8767:
8763:
8752:
8712:
8689:
8668:
8636:
8605:
8584:
8580:
8565:
8538:
8519:
8422:
8405:
8290:
8264:
8187:
8180:
8156:
8147:
8069:
8036:
8027:
8016:
7976:
7737:aka the APL code page on
7711:APL character reference:
7442:ACM SIGAPL APL Quote Quad
5583:RightArrow, Branch, GoTo
5485:IBM APL2 idioms list here
3394:Boolean Logic: 0 if both
3357:Boolean Logic: 1 if both
2706:corresponding to ones in
2441:APL FUNCTIONAL SYMBOL RHO
1861:Product of integers 1 to
1401:The complex conjugate of
1221:APL FUNCTIONAL SYMBOL RHO
1052:1 greater than the length
1032:At left, dyadic function
629:The left operand for the
601:or mini double-dot means
257:function. The expression
116:The programming language
7772:Generic online tutorials
7668:"APL language reference"
6917:
6415:
6211:
6195:Determine the number of
6026:
5943:Basic Multilingual Plane
5936:
5893:
5837:
5781:
5680:
5280:
5197:
5016:
4910:
4865:
4832:
4711:vector "Text" using the
4590:
4442:
4427:Creating a nested array
4162:
4085:first dimension modifier
3814:
3171:GREATER-THAN OR EQUAL TO
2739:The location (index) of
901:
766:
540:Step 2) 3 times -1 = -3.
442:
120:is distinctive in being
8233:Micro Computer Machines
8173:British APL Association
7242:10.1145/1460833.1460872
7205:Miscellaneous Technical
6421:'ProveNonPrime'
5947:Miscellaneous Technical
3636:(last axis), Backslash
2301:Find, Epsilon Underbar
687:1 0 0 0 1 0 0 0 1
611:perform each separately
360:items using the dyadic
307:used at right >>
241:In the above case, the
166:Functions and operators
8777:APL syntax and symbols
8278:University of Maryland
8223:I. P. Sharp Associates
7984:APL syntax and symbols
7479:"APLX Language Manual"
6217:'PrimeNumbers'
5986:(with 2-key pressing)
5970:
5501:Miscellaneous symbols
4763:
4093:is now reflected both
3328:, 0 (False) otherwise
3150:Greater than or equal
1531:, Monadic Quad Divide
888:or operand = 3.
90:This article contains
8826:Mathematical notation
8808:Latin letters in STEM
8803:Greek letters in STEM
8553:List of logic symbols
7836:10.1145/800062.801221
7796:YouTube APL Tutorials
7612:"APL2 Idioms Library"
7518:10.1145/144045.144065
7455:10.1145/586050.586053
7410:. IBM. Archived from
7293:"Primitive Operators"
7270:archive.vector.org.uk
7266:"Sharp APL Operators"
6411:decomposition factors
5968:
5515:Meaning (of example)
4811:function PI or π(pi)
4758:
4413:4D or cubed over time
4353:), it can be used to
4123:, just two examples,
3559:Meaning (of example)
3115:LESS-THAN OR EQUAL TO
2384:The smaller value of
2347:The greater value of
1601:Natural logarithm of
978:Example using APL to
656:is terminated by the
134:mathematical notation
8533:mathematical symbols
8437:Open-source software
8383:Edward H. Sussenguth
8250:Soliton Incorporated
8194:Analogic Corporation
6616:ProveNonPrimeIsPrime
6553:ProveNonPrimeIsPrime
5878:random-access memory
5164:works as expected if
4795:(to the left of the
4722:enclosed or ⊂ nested
4407:or in table form as
4073:visually indicates.
3600:Reduce (first axis)
3260:, 1 otherwise. Alt:
2266:Membership, Epsilon
1829:Reverse the axes of
1736:in descending order
1662:Reverse elements of
1631:Reverse elements of
1303:Vector of the first
1013:is assigned what to
695:1 0 0 0 1 0 0 0 1
652:. The left scope of
427:, indented = actual
378:precedence hierarchy
311:1 0 1/45 0 67 45 67
277:1 0 1\45 67 45 0 67
145:Most symbols denote
50:improve this article
39:to meet Knowledge's
8863:Meanings of symbols
7893:10.1145/75144.75166
7436:Brown, Jim (1978).
6923:'Fibonacci'
5929:- sometimes called
5518:Unicode code point
5502:
5166:the parameters are
4818:function CIRCLEAREA
4804:
4428:
4121:spatial coordinates
3647:Running sum across
3094:Less than or equal
2794:multiple regression
2702:Select elements in
2068:MULTIPLICATION SIGN
1732:which will arrange
1701:in ascending order
1697:which will arrange
1459:MULTIPLICATION SIGN
1094:Unicode code point
751:multiple regression
743:matrix determinants
382:operator precedence
184:operators generally
180:relational operator
8883:Physical constants
8623:Letterlike Symbols
8344:Kenneth E. Iverson
8332:Patrick E. Hagerty
7486:www.microapl.co.uk
7417:on 14 January 2015
7324:www.microapl.co.uk
7297:www.microapl.co.uk
6907:Fibonacci sequence
6640:" prime"
5971:
5950:from one another.
5856:, another dynamic
5560:⍝This is a comment
5500:
5472:Conversely however
4802:
4779:may define custom
4764:
4426:
3669:Scan (first axis)
2961:General transpose
2274:1 for elements of
1539:Inverse of matrix
691:1 2 3 1 2 3
683:1 2 3 1 2 3
170:APL uses the term
8905:
8904:
8901:
8900:
8853:
8852:
8849:
8848:
8748:
8747:
8744:
8743:
8561:
8560:
8467:
8466:
8418:
8417:
8393:William Yerazunis
8376:J. Henri Schueler
8335:Herbert Hellerman
8286:
8285:
8143:
8142:
7735:IBM code page 293
7591:www.cs.utexas.edu
7129:978-0-13-038885-8
7122:. Prentice-Hall.
6409:by listing their
6022:Pascal's triangle
6016:Pascal's triangle
5919:
5918:
5642:
5641:
4992:
4991:
4768:
4767:
4390:
4389:
4132:
4131:
3794:
3793:
3680:Running sum down
3540:
3539:
3198:GREATER-THAN SIGN
2728:Index of, Dyadic
1942:
1941:
1666:along first axis
1292:Index generator,
1078:Monadic functions
1074:
1073:
910:"ABCDE"
893:
892:
758:
757:
626:
625:
557:
556:
550:of 2 and -3 = -3.
542:Step 3) Take the
411:. Functions have
316:
315:
239:
238:
101:rendering support
78:
77:
70:
41:quality standards
32:This article may
8930:
8859:
8858:
8765:
8764:
8754:
8753:
8642:Geometric Shapes
8628:Symbols for zero
8582:
8581:
8567:
8566:
8521:
8520:
8494:
8487:
8480:
8471:
8470:
8455:
8454:
8445:
8444:
8354:Eugene McDonnell
8185:
8184:
8154:
8153:
8034:
8033:
8022:
8010:Shared Variables
7963:
7956:
7949:
7940:
7939:
7935:
7929:
7925:
7923:
7915:
7895:
7878:
7872:
7868:
7866:
7858:
7838:
7767:
7765:
7763:
7699:
7698:
7696:
7687:
7681:
7680:
7678:
7677:
7672:
7664:
7658:
7657:
7655:
7654:
7643:
7637:
7634:
7628:
7627:
7625:
7623:
7607:
7601:
7600:
7598:
7597:
7588:
7580:
7574:
7567:
7561:
7560:
7554:
7550:
7548:
7540:
7520:
7504:
7498:
7497:
7495:
7493:
7483:
7474:
7468:
7467:
7457:
7433:
7427:
7426:
7424:
7422:
7416:
7405:
7396:
7390:
7389:
7387:
7385:
7369:
7363:
7362:
7360:
7358:
7342:
7336:
7335:
7333:
7331:
7315:
7309:
7308:
7306:
7304:
7288:
7282:
7281:
7279:
7277:
7261:
7255:
7254:
7244:
7228:
7194:
7182:
7171:
7152:
7133:
7107:
7104:
7101:
7098:
7095:
7092:
7089:
7086:
7083:
7080:
7077:
7074:
7071:
7068:
7065:
7062:
7059:
7056:
7053:
7050:
7047:
7044:
7041:
7038:
7035:
7032:
7029:
7026:
7023:
7020:
7017:
7014:
7011:
7008:
7005:
7002:
6999:
6996:
6993:
6990:
6987:
6984:
6981:
6978:
6975:
6972:
6969:
6966:
6963:
6960:
6957:
6954:
6951:
6948:
6945:
6942:
6939:
6936:
6933:
6930:
6927:
6924:
6921:
6913:Fibonacci number
6902:
6899:
6896:
6893:
6890:
6887:
6884:
6881:
6878:
6875:
6872:
6869:
6866:
6863:
6860:
6857:
6854:
6851:
6848:
6845:
6842:
6839:
6836:
6833:
6830:
6827:
6824:
6821:
6818:
6815:
6812:
6809:
6806:
6803:
6800:
6797:
6794:
6791:
6788:
6785:
6782:
6779:
6776:
6773:
6770:
6767:
6764:
6761:
6758:
6755:
6752:
6749:
6746:
6743:
6740:
6737:
6734:
6731:
6728:
6725:
6722:
6719:
6716:
6713:
6710:
6707:
6704:
6701:
6698:
6695:
6692:
6689:
6686:
6683:
6680:
6677:
6674:
6671:
6668:
6665:
6662:
6659:
6656:
6653:
6650:
6647:
6644:
6641:
6638:
6635:
6632:
6629:
6626:
6623:
6620:
6617:
6614:
6611:
6608:
6605:
6602:
6599:
6596:
6593:
6590:
6587:
6584:
6581:
6578:
6575:
6572:
6569:
6566:
6563:
6560:
6557:
6554:
6551:
6548:
6545:
6542:
6539:
6536:
6533:
6530:
6527:
6524:
6521:
6518:
6515:
6512:
6509:
6506:
6503:
6500:
6497:
6494:
6491:
6488:
6485:
6482:
6479:
6476:
6473:
6470:
6467:
6464:
6461:
6458:
6455:
6452:
6449:
6446:
6443:
6440:
6437:
6434:
6431:
6428:
6425:
6422:
6419:
6395:
6392:
6389:
6386:
6383:
6380:
6377:
6374:
6371:
6368:
6365:
6362:
6359:
6356:
6353:
6350:
6347:
6344:
6341:
6338:
6335:
6332:
6329:
6326:
6323:
6320:
6317:
6314:
6311:
6308:
6305:
6302:
6299:
6296:
6293:
6290:
6287:
6284:
6281:
6278:
6275:
6272:
6269:
6266:
6263:
6260:
6257:
6254:
6251:
6248:
6245:
6242:
6239:
6236:
6233:
6230:
6227:
6224:
6221:
6218:
6215:
6186:
6183:
6180:
6177:
6174:
6171:
6168:
6165:
6162:
6159:
6156:
6153:
6150:
6147:
6144:
6141:
6138:
6135:
6132:
6129:
6126:
6123:
6120:
6117:
6114:
6111:
6108:
6105:
6102:
6099:
6096:
6093:
6090:
6087:
6084:
6081:
6078:
6075:
6072:
6069:
6066:
6063:
6060:
6057:
6054:
6051:
6048:
6045:
6042:
6039:
6036:
6033:
6030:
5903:
5900:
5897:
5844:
5841:
5803:
5800:
5797:
5794:
5791:
5788:
5785:
5744:
5741:
5738:
5735:
5732:
5729:
5726:
5723:
5720:
5717:
5714:
5711:
5708:
5705:
5702:
5699:
5696:
5693:
5690:
5687:
5684:
5672:
5667:
5666:
5638:
5635:
5632:
5630:
5621:
5608:
5607:RIGHTWARDS ARROW
5605:
5602:
5600:
5591:
5578:
5575:
5572:
5570:
5561:
5548:
5545:
5542:
5540:
5531:
5503:
5499:
5492:
5458:
5455:
5452:
5449:
5446:
5443:
5440:
5437:
5434:
5431:
5428:
5425:
5422:
5419:
5416:
5413:
5410:
5407:
5404:
5401:
5398:
5395:
5392:
5389:
5386:
5383:
5380:
5377:
5374:
5371:
5368:
5365:
5362:
5359:
5356:
5353:
5350:
5347:
5344:
5341:
5338:
5335:
5332:
5329:
5326:
5323:
5320:
5317:
5314:
5311:
5308:
5305:
5302:
5299:
5296:
5293:
5290:
5287:
5284:
5261:
5258:
5255:
5252:
5249:
5246:
5243:
5240:
5237:
5234:
5231:
5228:
5225:
5222:
5219:
5216:
5213:
5210:
5207:
5204:
5201:
5183:parallelise and
5158:
5155:
5152:
5149:
5146:
5143:
5140:
5137:
5134:
5131:
5128:
5125:
5122:
5119:
5116:
5113:
5110:
5107:
5104:
5101:
5098:
5095:
5092:
5089:
5086:
5083:
5080:
5077:
5074:
5071:
5068:
5065:
5062:
5059:
5056:
5053:
5050:
5047:
5044:
5041:
5038:
5035:
5032:
5029:
5026:
5023:
5020:
4986:
4983:
4980:
4977:
4974:
4971:
4968:
4965:
4962:
4959:
4956:
4953:
4950:
4947:
4944:
4941:
4938:
4935:
4932:
4929:
4926:
4923:
4920:
4917:
4914:
4905:
4902:
4899:
4896:
4893:
4890:
4887:
4884:
4881:
4878:
4875:
4872:
4869:
4860:
4857:
4854:
4851:
4848:
4845:
4842:
4839:
4836:
4827:
4819:
4805:
4801:
4702:
4699:
4696:
4693:
4690:
4687:
4684:
4681:
4678:
4675:
4672:
4669:
4666:
4663:
4660:
4657:
4654:
4651:
4648:
4645:
4642:
4639:
4636:
4633:
4630:
4627:
4624:
4621:
4618:
4615:
4612:
4609:
4606:
4603:
4602:"Text"
4600:
4597:
4594:
4542:
4539:
4536:
4533:
4530:
4527:
4524:
4521:
4518:
4515:
4512:
4509:
4506:
4503:
4500:
4497:
4494:
4491:
4488:
4485:
4482:
4479:
4476:
4473:
4470:
4467:
4464:
4461:
4458:
4455:
4452:
4449:
4446:
4434:
4429:
4425:
4298:
4295:
4292:
4289:
4286:
4283:
4280:
4277:
4274:
4271:
4268:
4265:
4262:
4259:
4256:
4253:
4250:
4247:
4244:
4241:
4238:
4235:
4232:
4229:
4226:
4223:
4220:
4217:
4214:
4211:
4208:
4205:
4202:
4199:
4196:
4193:
4190:
4187:
4184:
4181:
4178:
4175:
4172:
4169:
4166:
4159:
4040:
4037:
4034:
4031:
4028:
4025:
4022:
4019:
4016:
4013:
4010:
4007:
4004:
4001:
3998:
3995:
3992:
3989:
3986:
3983:
3980:
3977:
3974:
3971:
3968:
3965:
3962:
3959:
3956:
3953:
3950:
3947:
3944:
3941:
3938:
3935:
3932:
3929:
3926:
3923:
3920:
3917:
3914:
3911:
3908:
3905:
3902:
3899:
3896:
3893:
3890:
3887:
3884:
3881:
3878:
3875:
3872:
3869:
3866:
3863:
3860:
3857:
3854:
3851:
3848:
3845:
3842:
3839:
3836:
3833:
3830:
3827:
3824:
3821:
3818:
3811:
3790:
3787:
3784:
3782:
3777:
3774:
3771:
3769:
3750:
3737:
3734:
3731:
3729:
3710:
3697:
3694:
3691:
3689:
3677:
3664:
3661:
3658:
3656:
3644:
3628:
3625:
3622:
3620:
3608:
3595:
3592:
3589:
3587:
3575:
3547:
3546:
3536:
3533:
3530:
3528:
3519:
3509:
3506:
3503:
3501:
3484:
3474:
3471:
3468:
3466:
3455:
3445:
3442:
3439:
3437:
3426:
3416:
3413:
3410:
3408:
3391:
3379:
3376:
3373:
3371:
3354:
3342:
3339:
3336:
3334:
3304:
3292:
3289:
3286:
3284:
3238:
3226:
3223:
3220:
3218:
3209:
3199:
3196:
3193:
3191:
3182:
3172:
3169:
3166:
3164:
3155:
3145:
3142:
3139:
3137:
3128:
3116:
3113:
3110:
3108:
3099:
3089:
3086:
3083:
3081:
3072:
3062:
3059:
3056:
3054:
3048:
3035:
3025:
3024:EXCLAMATION MARK
3022:
3019:
3017:
3000:
2990:
2987:
2984:
2982:
2966:
2956:
2953:
2950:
2948:
2932:
2922:
2919:
2916:
2914:
2898:
2886:
2883:
2880:
2878:
2864:The elements of
2861:
2851:
2848:
2845:
2843:
2829:The elements of
2826:
2816:
2813:
2810:
2808:
2785:
2780:
2773:
2770:
2767:
2765:
2758:
2757:
2754:
2751:
2736:
2723:
2720:
2717:
2715:
2699:
2689:
2686:
2683:
2681:
2665:
2655:
2652:
2649:
2647:
2631:
2621:
2618:
2615:
2613:
2598:
2586:
2583:
2580:
2578:
2562:
2552:
2549:
2546:
2544:
2528:
2518:
2515:
2512:
2510:
2490:
2480:
2477:
2474:
2472:
2452:
2442:
2439:
2436:
2434:
2418:
2410:Reshape, Dyadic
2405:
2402:
2399:
2397:
2381:
2368:
2365:
2362:
2360:
2344:
2331:
2328:
2325:
2323:
2306:
2296:
2293:
2290:
2288:
2271:
2261:
2258:
2255:
2253:
2237:
2227:
2224:
2221:
2219:
2150:
2140:
2137:
2134:
2132:
2116:
2104:
2101:
2098:
2096:
2081:
2069:
2066:
2063:
2061:
2046:
2034:
2031:
2028:
2026:
2011:
1999:
1996:
1993:
1991:
1975:
1963:code point
1949:
1948:
1945:Dyadic functions
1938:
1935:
1932:
1930:
1917:
1907:
1904:
1901:
1899:
1890:
1878:
1877:EXCLAMATION MARK
1875:
1872:
1870:
1858:
1846:
1843:
1840:
1838:
1826:
1813:
1810:
1807:
1805:
1793:
1783:
1780:
1777:
1775:
1762:
1750:
1747:
1744:
1742:
1725:
1715:
1712:
1709:
1707:
1690:
1680:
1677:
1674:
1672:
1659:
1649:
1646:
1643:
1641:
1635:along last axis
1628:
1618:
1615:
1612:
1610:
1598:
1586:
1583:
1580:
1578:
1569:
1556:
1553:
1550:
1548:
1536:
1523:
1520:
1517:
1515:
1502:
1492:
1489:
1486:
1484:
1472:
1460:
1457:
1454:
1452:
1431:
1419:
1416:
1413:
1411:
1398:
1386:
1383:
1380:
1378:
1369:Changes sign of
1366:
1354:
1351:
1348:
1346:
1333:
1321:
1318:
1315:
1313:
1300:
1287:
1284:
1281:
1279:
1267:
1255:
1252:
1249:
1247:
1238:
1222:
1219:
1216:
1214:
1202:
1189:
1186:
1183:
1181:
1169:
1157:
1154:
1151:
1149:
1137:
1125:
1122:
1119:
1117:
1104:
1082:
1081:
991:First, variable
971:
968:
965:
962:
959:
956:
953:
950:
947:
944:
941:
938:
935:
934:"CABS"
932:
929:
926:
923:
920:
917:
914:
911:
908:
905:
898:
872:function (named
818:
815:
812:
809:
806:
803:
800:
797:
794:
791:
788:
785:
782:
779:
776:
773:
770:
763:
747:linear equations
733:
727:
718:
714:
712:
706:
690:
676:
651:
647:
643:derived function
636:
586:full explanation
571:
527:
524:
521:
518:
515:
512:
509:
506:
503:
500:
497:
494:
491:
488:
485:
482:
479:
476:
473:
470:
467:
464:
461:
458:
455:
452:
449:
446:
439:
417:short left scope
413:long right scope
391:
387:
320:dyadic functions
303:dyadic function
294:dyadic function
273:
272:
205:
204:
198:. An example of
107: instead of
86:
85:
73:
66:
62:
59:
53:
27:
26:
19:
8938:
8937:
8933:
8932:
8931:
8929:
8928:
8927:
8908:
8907:
8906:
8897:
8864:
8845:
8814:
8798:Letters in STEM
8781:
8759:
8740:
8708:
8685:
8664:
8632:
8618:Blackboard bold
8601:
8576:
8557:
8534:
8515:
8498:
8468:
8463:
8440:
8414:
8401:
8313:Charles Brenner
8282:
8260:
8176:
8159:
8139:
8065:
8029:Implementations
8023:
8014:
8000:Iverson bracket
7989:Direct function
7972:
7970:APL programming
7967:
7927:
7926:
7917:
7916:
7904:
7870:
7869:
7860:
7859:
7847:
7816:
7774:
7761:
7759:
7746:on the APL wiki
7708:
7703:
7702:
7694:
7690:
7688:
7684:
7675:
7673:
7670:
7666:
7665:
7661:
7652:
7650:
7645:
7644:
7640:
7635:
7631:
7621:
7619:
7608:
7604:
7595:
7593:
7586:
7582:
7581:
7577:
7568:
7564:
7552:
7551:
7542:
7541:
7529:
7505:
7501:
7491:
7489:
7481:
7475:
7471:
7434:
7430:
7420:
7418:
7414:
7403:
7397:
7393:
7383:
7381:
7378:dfns.dyalog.com
7370:
7366:
7356:
7354:
7343:
7339:
7329:
7327:
7316:
7312:
7302:
7300:
7289:
7285:
7275:
7273:
7262:
7258:
7229:
7225:
7220:
7201:
7191:
7168:
7149:
7130:
7114:
7112:Further reading
7109:
7108:
7105:
7102:
7099:
7096:
7093:
7090:
7087:
7084:
7081:
7078:
7075:
7072:
7069:
7066:
7063:
7060:
7057:
7054:
7051:
7048:
7045:
7042:
7039:
7036:
7033:
7030:
7027:
7024:
7021:
7018:
7015:
7012:
7009:
7006:
7003:
7000:
6997:
6994:
6991:
6988:
6985:
6982:
6979:
6976:
6973:
6970:
6967:
6964:
6961:
6958:
6955:
6952:
6949:
6946:
6943:
6940:
6937:
6934:
6931:
6928:
6925:
6922:
6919:
6909:
6904:
6903:
6900:
6897:
6894:
6891:
6888:
6885:
6882:
6879:
6876:
6873:
6870:
6867:
6864:
6861:
6858:
6855:
6852:
6849:
6846:
6843:
6840:
6837:
6834:
6831:
6828:
6825:
6822:
6819:
6816:
6813:
6810:
6807:
6804:
6801:
6798:
6795:
6792:
6789:
6786:
6783:
6780:
6777:
6774:
6771:
6768:
6765:
6762:
6759:
6756:
6753:
6750:
6747:
6744:
6741:
6738:
6735:
6732:
6729:
6726:
6723:
6720:
6717:
6714:
6711:
6708:
6705:
6702:
6699:
6696:
6693:
6690:
6687:
6684:
6681:
6678:
6675:
6672:
6669:
6666:
6663:
6660:
6657:
6654:
6651:
6648:
6645:
6642:
6639:
6636:
6633:
6630:
6627:
6624:
6621:
6618:
6615:
6612:
6609:
6606:
6603:
6600:
6597:
6594:
6591:
6588:
6585:
6582:
6579:
6576:
6573:
6570:
6567:
6564:
6561:
6558:
6555:
6552:
6549:
6546:
6543:
6540:
6537:
6534:
6531:
6528:
6525:
6522:
6519:
6516:
6513:
6510:
6507:
6504:
6501:
6498:
6495:
6492:
6489:
6486:
6483:
6480:
6477:
6474:
6471:
6468:
6465:
6462:
6459:
6456:
6453:
6450:
6447:
6444:
6441:
6438:
6435:
6432:
6429:
6426:
6423:
6420:
6417:
6397:
6396:
6393:
6390:
6387:
6384:
6381:
6378:
6375:
6372:
6369:
6366:
6363:
6360:
6357:
6354:
6351:
6348:
6345:
6342:
6339:
6336:
6333:
6330:
6327:
6324:
6321:
6318:
6315:
6312:
6309:
6306:
6303:
6300:
6297:
6294:
6291:
6288:
6285:
6282:
6279:
6276:
6273:
6270:
6267:
6264:
6261:
6258:
6255:
6252:
6249:
6246:
6243:
6240:
6237:
6234:
6231:
6228:
6225:
6222:
6219:
6216:
6213:
6193:
6188:
6187:
6184:
6181:
6178:
6175:
6172:
6169:
6166:
6163:
6160:
6157:
6154:
6151:
6148:
6145:
6142:
6139:
6136:
6133:
6130:
6127:
6124:
6121:
6118:
6115:
6112:
6109:
6106:
6103:
6100:
6097:
6094:
6091:
6088:
6085:
6082:
6079:
6076:
6073:
6070:
6067:
6064:
6061:
6058:
6055:
6052:
6049:
6046:
6043:
6040:
6037:
6034:
6031:
6028:
6018:
6010:
6008:Solving puzzles
5963:
5939:
5905:
5904:
5901:
5898:
5895:
5882:hard disk drive
5858:system variable
5846:
5845:
5842:
5839:
5828:now references
5824:3 4 5 ...} and
5805:
5804:
5801:
5798:
5795:
5792:
5789:
5786:
5783:
5746:
5745:
5742:
5739:
5736:
5733:
5730:
5727:
5724:
5721:
5718:
5715:
5712:
5709:
5706:
5703:
5700:
5697:
5694:
5691:
5688:
5685:
5682:
5670:
5637:LEFTWARDS ARROW
5636:
5633:
5628:
5627:
5606:
5603:
5598:
5597:
5576:
5573:
5568:
5567:
5546:
5543:
5538:
5537:
5498:
5481:APL idioms list
5479:
5468:Edsger Dijkstra
5460:
5459:
5456:
5453:
5450:
5447:
5444:
5441:
5438:
5435:
5432:
5429:
5426:
5423:
5420:
5417:
5414:
5411:
5408:
5405:
5402:
5399:
5396:
5393:
5390:
5387:
5384:
5381:
5378:
5375:
5372:
5369:
5366:
5363:
5360:
5357:
5354:
5351:
5348:
5345:
5342:
5339:
5336:
5333:
5330:
5327:
5324:
5321:
5318:
5315:
5312:
5309:
5306:
5303:
5300:
5297:
5294:
5291:
5288:
5285:
5282:
5263:
5262:
5259:
5256:
5253:
5250:
5247:
5244:
5241:
5238:
5235:
5232:
5229:
5226:
5223:
5220:
5217:
5214:
5211:
5208:
5205:
5202:
5199:
5160:
5159:
5156:
5153:
5150:
5147:
5144:
5141:
5138:
5135:
5132:
5129:
5126:
5123:
5120:
5117:
5114:
5111:
5108:
5105:
5102:
5099:
5096:
5093:
5090:
5087:
5084:
5081:
5078:
5075:
5072:
5069:
5066:
5063:
5060:
5057:
5054:
5051:
5048:
5045:
5042:
5039:
5036:
5033:
5030:
5027:
5024:
5021:
5018:
4988:
4987:
4984:
4981:
4978:
4975:
4972:
4969:
4966:
4963:
4960:
4957:
4954:
4951:
4948:
4945:
4942:
4939:
4936:
4933:
4930:
4927:
4924:
4921:
4918:
4915:
4912:
4907:
4906:
4903:
4900:
4897:
4894:
4891:
4888:
4885:
4882:
4879:
4876:
4873:
4870:
4867:
4862:
4861:
4858:
4855:
4852:
4849:
4846:
4843:
4840:
4837:
4834:
4822:
4814:
4803:User functions
4789:function header
4773:
4752:
4743:, it is both a
4741:nested elements
4718:
4717:
4716:
4704:
4703:
4700:
4697:
4694:
4691:
4688:
4685:
4682:
4679:
4676:
4673:
4670:
4667:
4664:
4661:
4658:
4655:
4652:
4649:
4646:
4643:
4640:
4637:
4634:
4631:
4628:
4625:
4622:
4619:
4616:
4613:
4610:
4607:
4604:
4601:
4598:
4595:
4592:
4548:
4544:
4543:
4540:
4537:
4534:
4531:
4528:
4525:
4522:
4519:
4516:
4513:
4510:
4507:
4504:
4501:
4498:
4495:
4492:
4489:
4486:
4483:
4480:
4477:
4474:
4471:
4468:
4465:
4462:
4459:
4456:
4453:
4450:
4447:
4444:
4432:
4396:
4391:
4333:
4319:
4309:
4300:
4299:
4296:
4293:
4290:
4287:
4284:
4281:
4278:
4275:
4272:
4269:
4266:
4263:
4260:
4257:
4254:
4251:
4248:
4245:
4242:
4239:
4236:
4233:
4230:
4227:
4224:
4221:
4218:
4215:
4212:
4209:
4206:
4203:
4200:
4197:
4194:
4191:
4188:
4185:
4182:
4179:
4176:
4173:
4170:
4167:
4164:
4134:
4133:
4046:
4042:
4041:
4038:
4035:
4032:
4029:
4026:
4023:
4020:
4017:
4014:
4011:
4008:
4005:
4002:
3999:
3996:
3993:
3990:
3987:
3984:
3981:
3978:
3975:
3972:
3969:
3966:
3963:
3960:
3957:
3954:
3951:
3948:
3945:
3942:
3939:
3936:
3933:
3930:
3927:
3924:
3921:
3918:
3915:
3912:
3909:
3906:
3903:
3900:
3897:
3894:
3891:
3888:
3885:
3882:
3879:
3876:
3873:
3870:
3867:
3864:
3861:
3858:
3855:
3852:
3849:
3846:
3843:
3840:
3837:
3834:
3831:
3828:
3825:
3822:
3819:
3816:
3788:
3785:
3780:
3779:
3775:
3772:
3767:
3766:
3735:
3732:
3727:
3726:
3695:
3692:
3687:
3686:
3663:REVERSE SOLIDUS
3662:
3659:
3654:
3653:
3626:
3623:
3618:
3617:
3593:
3590:
3585:
3584:
3545:
3534:
3531:
3526:
3525:
3507:
3504:
3499:
3498:
3491:does not match
3472:
3469:
3464:
3463:
3443:
3440:
3435:
3434:
3414:
3411:
3406:
3405:
3377:
3374:
3369:
3368:
3340:
3337:
3332:
3331:
3307:Boolean Logic:
3290:
3287:
3282:
3281:
3241:Boolean Logic:
3224:
3221:
3216:
3215:
3197:
3194:
3189:
3188:
3170:
3167:
3162:
3161:
3143:
3140:
3135:
3134:
3114:
3111:
3106:
3105:
3087:
3084:
3079:
3078:
3060:
3057:
3052:
3051:
3038:
3023:
3020:
3015:
3014:
2988:
2985:
2980:
2979:
2973:are ordered by
2954:
2951:
2946:
2945:
2920:
2917:
2912:
2911:
2884:
2881:
2876:
2875:
2849:
2846:
2841:
2840:
2814:
2811:
2806:
2805:
2778:
2771:
2768:
2763:
2762:
2755:
2752:
2749:
2721:
2718:
2713:
2712:
2688:REVERSE SOLIDUS
2687:
2684:
2679:
2678:
2653:
2650:
2645:
2644:
2619:
2616:
2611:
2610:
2584:
2581:
2576:
2575:
2550:
2547:
2542:
2541:
2517:DOWNWARDS ARROW
2516:
2513:
2508:
2507:
2478:
2475:
2470:
2469:
2440:
2437:
2432:
2431:
2421:Array of shape
2403:
2400:
2395:
2394:
2366:
2363:
2358:
2357:
2329:
2326:
2321:
2320:
2317:; 0 where not.
2294:
2291:
2286:
2285:
2282:; 0 where not.
2259:
2256:
2251:
2250:
2225:
2222:
2217:
2216:
2210:
2138:
2135:
2130:
2129:
2102:
2099:
2094:
2093:
2067:
2064:
2059:
2058:
2032:
2029:
2024:
2023:
1997:
1994:
1989:
1988:
1962:
1947:
1936:
1933:
1928:
1927:
1905:
1902:
1897:
1896:
1876:
1873:
1868:
1867:
1844:
1841:
1836:
1835:
1811:
1808:
1803:
1802:
1788:Monadic format
1781:
1778:
1773:
1772:
1748:
1745:
1740:
1739:
1713:
1710:
1705:
1704:
1678:
1675:
1670:
1669:
1647:
1644:
1639:
1638:
1616:
1613:
1608:
1607:
1584:
1581:
1576:
1575:
1554:
1551:
1546:
1545:
1521:
1518:
1513:
1512:
1490:
1487:
1482:
1481:
1458:
1455:
1450:
1449:
1417:
1414:
1409:
1408:
1384:
1381:
1376:
1375:
1352:
1349:
1344:
1343:
1319:
1316:
1311:
1310:
1285:
1282:
1277:
1276:
1253:
1250:
1245:
1244:
1220:
1217:
1212:
1211:
1187:
1184:
1179:
1178:
1155:
1152:
1147:
1146:
1123:
1120:
1115:
1114:
1080:
1075:
1069:"S" (6).
1061:"CAB" (3 1 2).
1028:
973:
972:
969:
966:
963:
960:
957:
954:
951:
948:
945:
942:
939:
936:
933:
930:
927:
924:
921:
918:
915:
912:
909:
906:
903:
895:
894:
820:
819:
816:
813:
810:
807:
804:
801:
798:
795:
792:
789:
786:
783:
780:
777:
774:
771:
768:
760:
759:
736:identity matrix
729:
723:
716:
710:
708:
702:
700:
696:
688:
649:
645:
634:
627:
619:iota for each 3
589:
576:
559:
558:
551:
541:
536:
534:
529:
528:
525:
522:
519:
516:
513:
510:
507:
504:
501:
498:
495:
492:
489:
486:
483:
480:
477:
474:
471:
468:
465:
462:
459:
456:
453:
450:
447:
444:
433:APL interpreter
407:determines its
389:
385:
374:
312:
299:
289:
278:
271:
235:
221:
210:
168:
143:
114:
113:
112:
99:Without proper
87:
83:
74:
63:
57:
54:
47:
28:
24:
17:
12:
11:
5:
8936:
8926:
8925:
8920:
8903:
8902:
8899:
8898:
8896:
8895:
8890:
8885:
8880:
8875:
8869:
8866:
8865:
8855:
8854:
8851:
8850:
8847:
8846:
8844:
8843:
8838:
8833:
8828:
8822:
8820:
8816:
8815:
8813:
8812:
8811:
8810:
8805:
8795:
8789:
8787:
8783:
8782:
8780:
8779:
8773:
8771:
8761:
8760:
8750:
8749:
8746:
8745:
8742:
8741:
8739:
8738:
8732:
8727:
8722:
8716:
8714:
8710:
8709:
8707:
8706:
8701:
8695:
8693:
8687:
8686:
8684:
8683:
8678:
8672:
8670:
8666:
8665:
8663:
8662:
8657:
8652:
8646:
8644:
8634:
8633:
8631:
8630:
8625:
8620:
8615:
8609:
8607:
8603:
8602:
8600:
8599:
8594:
8588:
8586:
8578:
8577:
8563:
8562:
8559:
8558:
8556:
8555:
8550:
8545:
8539:
8536:
8535:
8517:
8516:
8497:
8496:
8489:
8482:
8474:
8465:
8464:
8462:
8461:
8432:
8430:= discontinued
8423:
8420:
8419:
8416:
8415:
8413:
8412:
8406:
8403:
8402:
8400:
8399:
8394:
8391:
8389:Arthur Whitney
8386:
8380:
8377:
8374:
8369:
8364:
8359:
8358:Robert Metzger
8356:
8351:
8346:
8341:
8336:
8333:
8330:
8325:
8320:
8315:
8310:
8305:
8300:
8294:
8292:
8288:
8287:
8284:
8283:
8281:
8280:
8275:
8268:
8266:
8262:
8261:
8259:
8258:
8255:
8252:
8247:
8241:
8236:
8230:
8225:
8220:
8215:
8212:
8209:
8203:
8198:
8195:
8191:
8189:
8182:
8178:
8177:
8175:
8174:
8171:
8164:
8162:
8151:
8145:
8144:
8141:
8140:
8138:
8137:
8129:
8128:
8127:
8113:
8107:
8101:
8094:
8088:
8075:
8073:
8067:
8066:
8064:
8063:
8057:
8052:
8044:
8040:
8038:
8031:
8025:
8024:
8017:
8015:
8013:
8012:
8007:
8002:
7997:
7992:
7986:
7980:
7978:
7974:
7973:
7966:
7965:
7958:
7951:
7943:
7937:
7936:
7928:|journal=
7903:978-0897913270
7902:
7879:
7871:|journal=
7846:978-0897910958
7845:
7822:
7815:
7812:
7811:
7810:
7804:
7799:
7793:
7787:
7781:
7773:
7770:
7769:
7768:
7752:
7747:
7741:
7732:
7727:
7707:
7706:External links
7704:
7701:
7700:
7689:Unicode chart
7682:
7659:
7638:
7629:
7616:www-01.ibm.com
7602:
7575:
7562:
7553:|journal=
7528:978-0897914772
7527:
7499:
7469:
7428:
7391:
7364:
7351:progopedia.com
7337:
7310:
7283:
7264:Baronet, Dan.
7256:
7222:
7221:
7219:
7216:
7215:
7214:
7208:
7200:
7197:
7196:
7195:
7190:978-0471093046
7189:
7172:
7167:978-0387942131
7166:
7153:
7148:978-0534128647
7147:
7134:
7128:
7113:
7110:
6918:
6908:
6905:
6416:
6212:
6203:greater than 1
6192:
6189:
6027:
6017:
6014:
6009:
6006:
5962:
5959:
5938:
5935:
5917:
5916:
5906:
5894:
5890:
5889:
5886:virtual memory
5847:
5838:
5834:
5833:
5806:
5782:
5778:
5777:
5775:2 3 4 5 ...}.
5747:
5681:
5677:
5676:
5673:
5640:
5639:
5625:
5622:
5617:
5614:
5610:
5609:
5595:
5592:
5587:
5584:
5580:
5579:
5565:
5562:
5557:
5554:
5553:Lamp, Comment
5550:
5549:
5535:
5532:
5527:
5524:
5520:
5519:
5516:
5513:
5510:
5507:
5497:
5494:
5281:
5270:arguments are
5198:
5192:user functions
5189:test and debug
5017:
4990:
4989:
4911:
4908:
4866:
4863:
4833:
4829:
4828:
4820:
4812:
4772:
4769:
4766:
4765:
4705:
4591:
4587:
4586:
4545:
4443:
4439:
4438:
4435:
4395:
4392:
4388:
4387:
4383:greater than 1
4373:row-wise. The
4344:axis indicator
4301:
4163:
4157:
4145:axis indicator
4130:
4129:
4099:horizontally ⌽
4081:axis indicator
4043:
3815:
3809:
3792:
3791:
3764:
3751:
3746:
3743:
3742:Outer product
3739:
3738:
3724:
3714:Matrix product
3711:
3706:
3703:
3702:Inner product
3699:
3698:
3684:
3678:
3673:
3670:
3666:
3665:
3651:
3645:
3640:
3637:
3630:
3629:
3615:
3609:
3604:
3601:
3597:
3596:
3582:
3576:
3571:
3568:
3564:
3563:
3560:
3557:
3554:
3551:
3544:
3541:
3538:
3537:
3523:
3520:
3515:
3511:
3510:
3496:
3485:
3480:
3476:
3475:
3461:
3456:
3451:
3447:
3446:
3432:
3427:
3422:
3418:
3417:
3403:
3392:
3387:
3381:
3380:
3366:
3355:
3350:
3344:
3343:
3329:
3305:
3300:
3294:
3293:
3279:
3239:
3234:
3228:
3227:
3213:
3210:
3205:
3201:
3200:
3186:
3183:
3178:
3174:
3173:
3159:
3156:
3151:
3147:
3146:
3132:
3129:
3124:
3118:
3117:
3103:
3100:
3095:
3091:
3090:
3088:LESS-THAN SIGN
3076:
3073:
3068:
3064:
3063:
3049:
3036:
3031:
3027:
3026:
3012:
3001:
2996:
2992:
2991:
2977:
2967:
2962:
2958:
2957:
2943:
2933:
2928:
2927:Dyadic format
2924:
2923:
2909:
2899:
2894:
2888:
2887:
2873:
2862:
2857:
2853:
2852:
2838:
2827:
2822:
2818:
2817:
2803:
2786:
2781:
2775:
2774:
2760:
2737:
2732:
2725:
2724:
2710:
2700:
2695:
2691:
2690:
2676:
2666:
2661:
2657:
2656:
2642:
2632:
2627:
2623:
2622:
2608:
2599:
2594:
2588:
2587:
2573:
2563:
2558:
2554:
2553:
2539:
2529:
2524:
2520:
2519:
2505:
2501:according to ×
2491:
2486:
2482:
2481:
2467:
2463:according to ×
2453:
2448:
2444:
2443:
2429:
2419:
2414:
2407:
2406:
2392:
2382:
2377:
2370:
2369:
2355:
2345:
2340:
2333:
2332:
2318:
2307:
2302:
2298:
2297:
2283:
2272:
2267:
2263:
2262:
2248:
2238:
2233:
2229:
2228:
2214:
2161:
2151:
2146:
2142:
2141:
2127:
2122:raised to the
2117:
2112:
2110:Exponentiation
2106:
2105:
2091:
2082:
2077:
2071:
2070:
2056:
2052:multiplied by
2047:
2042:
2036:
2035:
2021:
2012:
2007:
2001:
2000:
1986:
1976:
1971:
1965:
1964:
1959:
1956:
1953:
1946:
1943:
1940:
1939:
1925:
1918:
1913:
1909:
1908:
1894:
1891:
1886:
1880:
1879:
1865:
1859:
1854:
1848:
1847:
1833:
1827:
1822:
1815:
1814:
1800:
1794:
1789:
1785:
1784:
1770:
1763:
1758:
1752:
1751:
1737:
1726:
1721:
1717:
1716:
1702:
1691:
1686:
1682:
1681:
1667:
1660:
1655:
1651:
1650:
1636:
1629:
1624:
1620:
1619:
1605:
1599:
1594:
1588:
1587:
1573:
1572:Multiply by π
1570:
1565:
1558:
1557:
1543:
1537:
1532:
1529:Matrix inverse
1525:
1524:
1510:
1509:into a vector
1503:
1498:
1494:
1493:
1479:
1473:
1468:
1462:
1461:
1447:
1432:
1427:
1421:
1420:
1406:
1399:
1394:
1388:
1387:
1373:
1367:
1362:
1356:
1355:
1341:
1334:
1329:
1323:
1322:
1308:
1301:
1296:
1289:
1288:
1274:
1268:
1263:
1261:Absolute value
1257:
1256:
1254:TILDE OPERATOR
1242:
1239:
1234:
1224:
1223:
1209:
1203:
1198:
1191:
1190:
1176:
1170:
1165:
1159:
1158:
1144:
1138:
1133:
1127:
1126:
1112:
1105:
1100:
1096:
1095:
1092:
1089:
1086:
1079:
1076:
1072:
1071:
1065:correctly did
1058:found letters
974:
902:
896:
891:
890:
821:
767:
761:
756:
755:
697:
679:
674:
641:function. The
624:
623:
577:
574:
569:
555:
554:
530:
443:
437:
373:
370:
314:
313:
310:
308:
286:results in APL
281:<<
279:
276:
237:
236:
233:
231:
218:results in APL
211:
208:
167:
164:
142:
139:
103:, you may see
88:
81:
80:
79:
76:
75:
31:
29:
22:
15:
9:
6:
4:
3:
2:
8935:
8924:
8921:
8919:
8916:
8915:
8913:
8894:
8891:
8889:
8886:
8884:
8881:
8879:
8876:
8874:
8871:
8870:
8867:
8860:
8856:
8842:
8839:
8837:
8834:
8832:
8831:Abbreviations
8829:
8827:
8824:
8823:
8821:
8817:
8809:
8806:
8804:
8801:
8800:
8799:
8796:
8794:
8791:
8790:
8788:
8784:
8778:
8775:
8774:
8772:
8770:
8766:
8762:
8755:
8751:
8736:
8733:
8731:
8728:
8726:
8723:
8721:
8718:
8717:
8715:
8713:Miscellaneous
8711:
8705:
8702:
8700:
8697:
8696:
8694:
8692:
8688:
8682:
8679:
8677:
8674:
8673:
8671:
8667:
8661:
8658:
8656:
8653:
8651:
8648:
8647:
8645:
8643:
8639:
8635:
8629:
8626:
8624:
8621:
8619:
8616:
8614:
8611:
8610:
8608:
8604:
8598:
8597:Unicode block
8595:
8593:
8590:
8589:
8587:
8583:
8579:
8574:
8568:
8564:
8554:
8551:
8549:
8546:
8544:
8541:
8540:
8537:
8532:
8528:
8522:
8518:
8514:
8510:
8506:
8503:
8495:
8490:
8488:
8483:
8481:
8476:
8475:
8472:
8460:
8459:
8450:
8449:
8439:
8438:
8433:
8431:
8428:
8425:
8424:
8421:
8411:
8410:Iverson Award
8408:
8407:
8404:
8398:
8395:
8392:
8390:
8387:
8384:
8381:
8378:
8375:
8373:
8370:
8368:
8365:
8363:
8360:
8357:
8355:
8352:
8350:
8349:Dick Lathwell
8347:
8345:
8342:
8340:
8337:
8334:
8331:
8329:
8326:
8324:
8321:
8319:
8316:
8314:
8311:
8309:
8306:
8304:
8301:
8299:
8296:
8295:
8293:
8289:
8279:
8276:
8273:
8270:
8269:
8267:
8263:
8256:
8253:
8251:
8248:
8245:
8242:
8240:
8237:
8234:
8231:
8229:
8226:
8224:
8221:
8219:
8216:
8213:
8210:
8207:
8204:
8202:
8199:
8196:
8193:
8192:
8190:
8186:
8183:
8181:Organizations
8179:
8172:
8169:
8166:
8165:
8163:
8161:
8155:
8152:
8150:
8146:
8135:
8134:
8130:
8126:
8122:
8119:
8118:
8117:
8114:
8111:
8108:
8105:
8102:
8100:
8099:
8095:
8093:
8089:
8086:
8085:
8081:
8077:
8076:
8074:
8072:
8068:
8061:
8058:
8056:
8053:
8051:
8050:
8045:
8042:
8041:
8039:
8035:
8032:
8030:
8026:
8021:
8011:
8008:
8006:
8003:
8001:
7998:
7996:
7993:
7990:
7987:
7985:
7982:
7981:
7979:
7975:
7971:
7964:
7959:
7957:
7952:
7950:
7945:
7944:
7941:
7933:
7921:
7913:
7909:
7905:
7899:
7894:
7889:
7885:
7880:
7876:
7864:
7856:
7852:
7848:
7842:
7837:
7832:
7828:
7823:
7821:
7818:
7817:
7808:
7805:
7803:
7800:
7797:
7794:
7791:
7788:
7785:
7782:
7779:
7776:
7775:
7758:
7753:
7751:
7748:
7745:
7742:
7740:
7736:
7733:
7731:
7728:
7726:
7722:
7718:
7714:
7710:
7709:
7693:
7686:
7669:
7663:
7648:
7642:
7633:
7617:
7613:
7606:
7592:
7585:
7579:
7572:
7566:
7558:
7546:
7538:
7534:
7530:
7524:
7519:
7514:
7510:
7503:
7487:
7480:
7473:
7465:
7461:
7456:
7451:
7447:
7443:
7439:
7432:
7413:
7409:
7402:
7395:
7379:
7375:
7368:
7352:
7348:
7341:
7325:
7321:
7314:
7298:
7294:
7287:
7271:
7267:
7260:
7252:
7248:
7243:
7238:
7234:
7227:
7223:
7212:
7209:
7206:
7203:
7202:
7192:
7186:
7181:
7180:
7173:
7169:
7163:
7159:
7154:
7150:
7144:
7140:
7135:
7131:
7125:
7121:
7116:
7115:
6916:
6914:
6655:ProveNonPrime
6430:ProveNonPrime
6414:
6412:
6408:
6404:
6403:
6210:
6208:
6204:
6200:
6199:
6198:prime numbers
6025:
6023:
6013:
6005:
6003:
5998:
5993:
5989:
5985:
5981:
5976:
5969:APL2 Keyboard
5967:
5958:
5954:
5951:
5948:
5944:
5934:
5932:
5928:
5924:
5914:
5910:
5907:
5892:
5891:
5887:
5883:
5879:
5875:
5871:
5867:
5863:
5859:
5855:
5851:
5848:
5836:
5835:
5831:
5827:
5823:
5819:
5815:
5811:
5808:Index Origin
5807:
5780:
5779:
5776:
5774:
5770:
5766:
5762:
5759:
5754:
5752:
5748:
5679:
5678:
5674:
5669:
5668:
5665:
5663:
5659:
5655:
5651:
5647:
5626:
5623:
5618:
5615:
5612:
5611:
5596:
5593:
5588:
5585:
5582:
5581:
5566:
5563:
5558:
5555:
5552:
5551:
5536:
5533:
5528:
5525:
5522:
5521:
5517:
5514:
5511:
5508:
5505:
5504:
5496:Miscellaneous
5493:
5490:
5486:
5482:
5477:
5473:
5469:
5465:
5279:
5277:
5273:
5269:
5196:
5193:
5190:
5186:
5182:
5177:
5173:
5169:
5165:
5015:
5013:
5008:
5004:
5000:
4997:
4909:
4864:
4831:
4825:
4821:
4817:
4813:
4810:
4807:
4806:
4800:
4798:
4794:
4790:
4786:
4782:
4778:
4762:
4757:
4753:
4750:
4746:
4742:
4738:
4734:
4730:
4725:
4723:
4714:
4710:
4706:
4589:
4588:
4585:
4583:
4578:
4576:
4572:
4569:
4564:
4562:
4558:
4553:
4551:
4546:
4441:
4440:
4436:
4431:
4430:
4424:
4422:
4421:nested arrays
4418:
4414:
4410:
4406:
4402:
4401:
4394:Nested arrays
4386:
4384:
4380:
4376:
4372:
4368:
4364:
4360:
4356:
4352:
4348:
4345:
4341:
4337:
4331:
4327:
4323:
4317:
4313:
4307:
4302:
4161:
4160:
4156:
4154:
4150:
4149:axis modifier
4146:
4142:
4139:
4128:
4126:
4122:
4119:analysis and
4118:
4114:
4110:
4106:
4102:
4100:
4096:
4092:
4088:
4086:
4082:
4078:
4074:
4072:
4068:
4064:
4062:
4058:
4054:
4050:
4044:
3813:
3812:
3808:
3804:
3800:
3798:
3776:RING OPERATOR
3765:
3763:
3759:
3755:
3754:Outer product
3752:
3747:
3744:
3741:
3740:
3725:
3723:
3719:
3715:
3712:
3707:
3704:
3701:
3700:
3685:
3683:
3679:
3674:
3671:
3668:
3667:
3652:
3650:
3646:
3641:
3638:
3635:
3632:
3631:
3616:
3614:
3610:
3605:
3602:
3599:
3598:
3583:
3581:
3577:
3572:
3569:
3566:
3565:
3561:
3558:
3555:
3552:
3549:
3548:
3524:
3521:
3516:
3513:
3512:
3497:
3494:
3490:
3486:
3481:
3478:
3477:
3462:
3460:
3457:
3452:
3449:
3448:
3433:
3431:
3428:
3423:
3420:
3419:
3404:
3401:
3397:
3393:
3388:
3386:
3383:
3382:
3367:
3364:
3360:
3356:
3351:
3349:
3346:
3345:
3330:
3327:
3323:
3320:
3317:
3314:
3310:
3306:
3301:
3299:
3296:
3295:
3280:
3277:
3273:
3270:
3267:
3263:
3259:
3255:
3251:
3248:
3244:
3240:
3235:
3233:
3230:
3229:
3214:
3211:
3206:
3203:
3202:
3187:
3184:
3179:
3177:Greater than
3176:
3175:
3160:
3157:
3152:
3149:
3148:
3133:
3130:
3125:
3123:
3120:
3119:
3104:
3101:
3096:
3093:
3092:
3077:
3074:
3069:
3066:
3065:
3050:
3046:
3042:
3037:
3032:
3029:
3028:
3013:
3010:
3006:
3002:
2997:
2995:Combinations
2994:
2993:
2978:
2976:
2972:
2968:
2963:
2960:
2959:
2944:
2942:
2938:
2934:
2929:
2926:
2925:
2910:
2908:
2904:
2901:Logarithm of
2900:
2895:
2893:
2890:
2889:
2885:CIRCLED MINUS
2874:
2871:
2867:
2863:
2858:
2855:
2854:
2839:
2836:
2832:
2828:
2823:
2820:
2819:
2804:
2802:
2798:
2795:
2791:
2787:
2782:
2777:
2776:
2761:
2759:if not found
2746:
2742:
2738:
2733:
2731:
2727:
2726:
2711:
2709:
2705:
2701:
2696:
2693:
2692:
2677:
2675:
2671:
2667:
2662:
2659:
2658:
2643:
2641:
2637:
2633:
2628:
2625:
2624:
2609:
2607:
2603:
2600:
2595:
2593:
2590:
2589:
2574:
2572:
2568:
2564:
2559:
2556:
2555:
2540:
2538:
2534:
2530:
2525:
2522:
2521:
2506:
2504:
2500:
2496:
2492:
2487:
2484:
2483:
2479:UPWARDS ARROW
2468:
2466:
2462:
2458:
2454:
2449:
2446:
2445:
2430:
2428:
2424:
2420:
2415:
2413:
2409:
2408:
2393:
2391:
2387:
2383:
2378:
2375:
2372:
2371:
2356:
2354:
2350:
2346:
2341:
2338:
2335:
2334:
2319:
2316:
2312:
2308:
2303:
2300:
2299:
2284:
2281:
2277:
2273:
2268:
2265:
2264:
2260:QUESTION MARK
2249:
2246:
2242:
2239:
2234:
2231:
2230:
2215:
2213:
2208:
2204:
2200:
2196:
2192:
2188:
2184:
2180:
2176:
2172:
2168:
2164:
2160:
2156:
2152:
2147:
2144:
2143:
2139:STAR OPERATOR
2128:
2125:
2121:
2118:
2113:
2111:
2108:
2107:
2103:DIVISION SIGN
2092:
2090:
2086:
2083:
2078:
2076:
2073:
2072:
2057:
2055:
2051:
2048:
2043:
2041:
2038:
2037:
2022:
2020:
2016:
2013:
2008:
2006:
2003:
2002:
1987:
1985:
1981:
1977:
1972:
1970:
1967:
1966:
1960:
1957:
1954:
1951:
1950:
1926:
1923:
1919:
1914:
1911:
1910:
1895:
1892:
1887:
1885:
1882:
1881:
1866:
1864:
1860:
1855:
1853:
1850:
1849:
1834:
1832:
1828:
1823:
1821:
1817:
1816:
1801:
1799:
1795:
1790:
1787:
1786:
1771:
1768:
1764:
1759:
1757:
1754:
1753:
1738:
1735:
1731:
1727:
1722:
1719:
1718:
1703:
1700:
1696:
1692:
1687:
1684:
1683:
1679:CIRCLED MINUS
1668:
1665:
1661:
1656:
1653:
1652:
1637:
1634:
1630:
1625:
1622:
1621:
1606:
1604:
1600:
1595:
1593:
1590:
1589:
1574:
1571:
1566:
1563:
1560:
1559:
1544:
1542:
1538:
1533:
1530:
1527:
1526:
1511:
1508:
1504:
1499:
1496:
1495:
1491:DIVISION SIGN
1480:
1478:
1475:1 divided by
1474:
1469:
1467:
1464:
1463:
1448:
1445:
1441:
1437:
1433:
1428:
1426:
1423:
1422:
1407:
1404:
1400:
1395:
1393:
1390:
1389:
1374:
1372:
1368:
1363:
1361:
1358:
1357:
1353:STAR OPERATOR
1342:
1339:
1335:
1330:
1328:
1325:
1324:
1309:
1306:
1302:
1297:
1295:
1291:
1290:
1275:
1273:
1270:Magnitude of
1269:
1264:
1262:
1259:
1258:
1243:
1240:
1235:
1233:
1229:
1226:
1225:
1210:
1208:
1204:
1199:
1197:
1193:
1192:
1177:
1175:
1171:
1166:
1164:
1161:
1160:
1145:
1143:
1139:
1134:
1132:
1129:
1128:
1124:QUESTION MARK
1113:
1110:
1106:
1101:
1098:
1097:
1093:
1090:
1087:
1084:
1083:
1070:
1068:
1064:
1059:
1057:
1054:of Letters.
1053:
1048:
1046:
1042:
1037:
1035:
1034:iota searches
1030:
1027:
1022:
1020:
1016:
1012:
1007:
1005:
1001:
996:
994:
989:
987:
985:
981:
975:
900:
899:
889:
887:
883:
879:
875:
871:
867:
863:
859:
855:
851:
847:
846:
841:
838:. The former
837:
835:
830:
828:
822:
765:
764:
754:
752:
748:
744:
739:
737:
734:is called an
732:
726:
720:
713:
705:
698:
694:
686:
682:
678:
677:
673:
671:
667:
666:outer product
663:
659:
655:
644:
640:
632:
622:
620:
616:
612:
608:
604:
600:
595:
593:
587:
583:
578:
573:
572:
568:
566:
565:
553:
549:
545:
538:
531:
526:¯0.3333333333
514:¯0.3333333333
496:¯0.3333333333
472:¯0.3333333333
441:
440:
436:
434:
430:
426:
422:
418:
414:
410:
406:
402:
397:
395:
383:
379:
369:
367:
363:
359:
355:
351:
347:
344:
340:
337:
333:
329:
325:
321:
309:
306:
302:
297:
293:
287:
285:
280:
275:
274:
270:
268:
264:
260:
256:
252:
248:
244:
232:
230:used at left
229:
225:
219:
217:
212:
207:
206:
203:
201:
197:
193:
189:
185:
181:
177:
173:
163:
160:
156:
152:
148:
138:
135:
131:
127:
123:
119:
110:
106:
102:
98:
96:
93:
72:
69:
61:
51:
46:
42:
38:
37:
30:
21:
20:
8704:Number Forms
8606:Alphanumeric
8502:mathematical
8456:
8446:
8434:
8429:
8426:
8372:John Scholes
8328:Adin Falkoff
8303:Bob Bernecky
8160:associations
8158:Professional
8131:
8103:
8096:
8091:
8083:
8079:
8059:
8054:
8047:
7983:
7883:
7826:
7814:Syntax rules
7760:. Retrieved
7685:
7674:. Retrieved
7662:
7651:. Retrieved
7641:
7632:
7620:. Retrieved
7615:
7605:
7594:. Retrieved
7590:
7578:
7569:Berry, Paul
7565:
7508:
7502:
7490:. Retrieved
7485:
7472:
7445:
7441:
7431:
7419:. Retrieved
7412:the original
7407:
7394:
7382:. Retrieved
7377:
7367:
7355:. Retrieved
7353:. Progopedia
7350:
7345:Progopedia.
7340:
7328:. Retrieved
7323:
7313:
7301:. Retrieved
7296:
7286:
7274:. Retrieved
7269:
7259:
7232:
7226:
7178:
7157:
7138:
7119:
6977:FibonacciNum
6929:FibonacciNum
6910:
6410:
6406:
6400:
6398:
6385:PrimeNumbers
6298:PrimeNumbers
6229:PrimeNumbers
6202:
6196:
6194:
6019:
6011:
5996:
5987:
5983:
5979:
5974:
5972:
5955:
5952:
5941:The Unicode
5940:
5930:
5926:
5922:
5920:
5912:
5908:
5873:
5868:or about 41
5861:
5857:
5853:
5849:
5829:
5825:
5821:
5817:
5813:
5809:
5772:
5768:
5764:
5760:
5758:index origin
5757:
5755:
5750:
5749:
5675:Description
5662:Index Origin
5653:
5649:
5645:
5643:
5475:
5471:
5463:
5461:
5275:
5271:
5267:
5264:
5191:
5188:
5184:
5180:
5175:
5171:
5167:
5163:
5161:
5011:
5009:
5005:
5001:
4993:
4823:
4815:
4808:
4796:
4792:
4788:
4784:
4780:
4776:
4774:
4771:Flow control
4761:nested array
4760:
4748:
4744:
4740:
4736:
4732:
4728:
4726:
4721:
4719:
4712:
4708:
4581:
4579:
4574:
4570:
4568:index origin
4567:
4565:
4560:
4556:
4554:
4549:
4547:
4437:Explanation
4420:
4417:mixed arrays
4416:
4398:
4397:
4382:
4378:
4374:
4370:
4366:
4362:
4358:
4354:
4350:
4347:
4343:
4340:catenate ","
4339:
4335:
4329:
4326:concatenated
4325:
4321:
4315:
4311:
4305:
4303:
4153:index origin
4148:
4144:
4140:
4137:
4135:
4112:
4109:⍉ transposed
4108:
4104:
4103:
4098:
4095:vertically ⊖
4094:
4090:
4089:
4084:
4080:
4076:
4075:
4070:
4066:
4065:
4060:
4052:
4048:
4045:
3805:
3801:
3796:
3795:
3761:
3757:
3721:
3717:
3681:
3648:
3612:
3579:
3508:IDENTICAL TO
3492:
3488:
3458:
3429:
3399:
3395:
3362:
3358:
3325:
3321:
3318:
3315:
3312:
3308:
3275:
3271:
3268:
3265:
3261:
3257:
3253:
3249:
3246:
3242:
3225:NOT EQUAL TO
3044:
3043:= on these;
3040:
3008:
3004:
2974:
2970:
2969:The axes of
2940:
2936:
2906:
2902:
2869:
2868:are rotated
2865:
2834:
2833:are rotated
2830:
2800:
2796:
2788:Solution to
2744:
2740:
2707:
2703:
2673:
2669:
2639:
2635:
2634:Elements of
2605:
2601:
2570:
2566:
2536:
2532:
2502:
2498:
2497:elements of
2494:
2464:
2460:
2459:elements of
2456:
2426:
2422:
2389:
2385:
2367:LEFT CEILING
2352:
2348:
2314:
2310:
2279:
2275:
2244:
2240:
2226:WHITE CIRCLE
2211:
2206:
2202:
2198:
2194:
2190:
2186:
2182:
2178:
2174:
2170:
2166:
2162:
2158:
2157:selected by
2154:
2123:
2119:
2088:
2084:
2053:
2049:
2018:
2014:
1983:
1979:
1921:
1906:IDENTICAL TO
1862:
1830:
1797:
1766:
1733:
1729:
1698:
1694:
1663:
1632:
1602:
1585:WHITE CIRCLE
1540:
1506:
1476:
1443:
1439:
1438:<0; 0 if
1435:
1402:
1370:
1337:
1304:
1271:
1206:
1173:
1156:LEFT CEILING
1141:
1108:
1066:
1062:
1060:
1055:
1051:
1049:
1044:
1040:
1038:
1033:
1031:
1025:
1023:
1018:
1014:
1010:
1008:
1003:
999:
997:
992:
990:
983:
979:
977:
976:
873:
869:
865:
861:
857:
853:
849:
843:
839:
832:
825:
823:
745:, groups of
740:
730:
724:
721:
717:more concise
709:
703:
699:
692:
684:
680:
669:
665:
661:
657:
653:
642:
638:
630:
628:
618:
615:iota repeats
614:
610:
606:
602:
598:
596:
591:
585:
579:
562:
560:
547:
543:
539:
532:
425:user session
423:from an APL
421:program code
416:
412:
400:
398:
393:
375:
372:Syntax rules
361:
357:
353:
349:
342:
338:
335:
331:
323:
319:
317:
304:
300:
298:used at left
295:
291:
283:
282:
266:
262:
258:
254:
250:
246:
242:
240:
227:
223:
215:
214:
195:
191:
187:
171:
169:
158:
154:
150:
146:
144:
129:
125:
124:rather than
121:
115:
108:
89:
64:
58:October 2015
55:
48:Please help
44:
33:
8397:Rodnay Zaks
8367:Alan Perlis
8362:Roger Moore
8318:Fred Brooks
8308:Larry Breed
8298:Phil Abrams
8214:Dyalog Ltd.
8211:DNA Systems
8062:→ NARS2000°
7809:by MicroAPL
7320:"Operators"
6911:Generate a
6207:Ken Iverson
5843:41226371072
5590:→This_Label
5523:High minus
5454:¯3.14159265
5424:0.785398163
5412:SEGMENTAREA
5295:SEGMENTAREA
5215:SEGMENTAREA
5031:SEGMENTAREA
4925:SEGMENTAREA
4377:result (of
4365:result (of
4351:less than 1
4117:time series
3578:Sum across
3341:LOGICAL AND
3245:(False) if
3144:EQUALS SIGN
2626:Catenation
2313:present in
2278:present in
2087:divided by
1769:expression
1765:Execute an
1728:Indices of
1720:Grade down
1693:Indices of
1327:Exponential
1047:letter "S"
599:diaeresis ¨
376:In APL the
348:{45 67} is
336:/ replicate
209:×/2 3 4 24
109:APL symbols
95:source code
52:if you can.
8912:Categories
8228:Kx Systems
8201:CompuServe
8090:APLNext →
8043:Dyalog APL
7995:Code pages
7762:13 January
7755:Lee, Xah.
7739:mainframes
7676:2018-11-05
7653:2018-11-05
7622:1 February
7596:2019-09-10
7584:"Treatise"
7492:31 January
7477:MicroAPL.
7421:14 January
7384:13 January
7357:13 January
7330:13 January
7326:. MicroAPL
7318:MicroAPL.
7303:13 January
7299:. MicroAPL
7291:MicroAPL.
7276:13 January
7218:References
6004:only 128.
5872:of unused
5864:or 41,226
5476:comments ⍝
5464:one liners
5448:37.6991118
5442:2.35619449
5439:25.1327412
5433:1.57079633
5430:12.5663706
5340:CIRCLEAREA
5079:CIRCLEAREA
4964:CIRCLEAREA
4877:CIRCLEAREA
4125:more exist
3473:RIGHT TACK
3311:(True) if
3291:LOGICAL OR
3264:(True) if
3204:Not equal
3067:Less than
3011:at a time
2837:positions
2425:with data
2404:LEFT FLOOR
2339:, Ceiling
2295:ELEMENT OF
2033:MINUS SIGN
1466:Reciprocal
1385:MINUS SIGN
1188:LEFT FLOOR
1015:search for
836:operator ⍨
829:operator ∘
429:user input
318:The above
216:Equivalent
8793:Diacritic
8735:ISO 31-11
8730:Technical
8669:Operators
8571:Lists of
8525:Lists of
8379:Bob Smith
8339:Roger Hui
8323:Jim Brown
8265:Education
8149:Community
8092:VisualAPL
8055:SHARP APL
7930:ignored (
7920:cite book
7873:ignored (
7863:cite book
7555:ignored (
7545:cite book
7049:Fibonacci
6935:Fibonacci
6407:non-prime
5870:gigabytes
5866:megabytes
5276:correctly
5272:incorrect
5012:different
4781:functions
4731:contains
4715:function.
4713:enclose ⊂
4381:which is
4359:interpose
4349:which is
4324:are then
3789:FULL STOP
3736:FULL STOP
3611:Sum down
3514:Laminate
3444:LEFT TACK
3061:DIAERESIS
2892:Logarithm
2856:Rotation
2821:Rotation
2585:DOWN TACK
2247:integers
2205:=7: tanh(
2189:=6: cosh(
2173:=5: sinh(
1998:PLUS SIGN
1955:Notation
1852:Factorial
1820:transpose
1685:Grade up
1654:Reversal
1623:Reversal
1592:Logarithm
1505:Reshapes
1442:=0; 1 if
1418:PLUS SIGN
1392:Conjugate
1336:e to the
1307:integers
1111:integers
1088:Notation
1009:Variable
886:parameter
731:(⍳3)∘.=⍳3
725:∘.=/⍳¨3 3
693:∘.=/⍳¨3 3
685:(⍳3)∘.=⍳3
633:operator
631:over-each
607:over each
409:arguments
354:3-element
343:2-element
339:functions
301:Replicate
290:<<
251:moderates
249:operator
234:2×3×4 24
226:operator
222:<<
213:<<
176:Heaviside
151:operators
147:functions
8819:Notation
8769:Language
8513:formulas
8505:notation
8458:Category
8188:Business
8170:: SIGAPL
8071:Dialects
7977:Features
7855:16511283
7464:40187000
7448:(2): 7.
7380:. Dyalog
7372:Dyalog.
7251:11777029
7199:See also
5820:from {1
5763:value =
5756:Initial
5646:⎕ (quad)
5634:←
5604:→
5574:⍝
5512:Example
5506:Name(s)
5376:FRACTION
5319:FRACTION
5304:FRACTION
5148:FRACTION
5058:FRACTION
5040:FRACTION
4976:FRACTION
4943:FRACTION
4934:FRACTION
4797:← assign
4573:value =
4566:Initial
4555:Element
4409:matrices
4355:laminate
4320:'B' and
4138:catenate
4127:.
4113:symbol ⍉
4071:symbol ⌽
4057:variable
3773:∘
3693:⍀
3624:⌿
3556:Example
3550:Name(s)
3532:⍪
3505:≡
3470:⊢
3441:⊣
3412:⍲
3375:⍱
3338:∧
3288:∨
3222:≠
3168:≥
3112:≤
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2952:⍕
2918:⍟
2905:to base
2882:⊖
2847:⌽
2812:⌹
2769:⍳
2617:∣
2582:⊤
2548:⊥
2514:↓
2476:↑
2438:⍴
2401:⌊
2376:, Floor
2364:⌈
2327:⍷
2292:∈
2223:○
2197:=3: tan(
2181:=2: cos(
2165:=1: sin(
2136:⋆
2040:Multiply
2030:−
2005:Subtract
1958:Meaning
1952:Name(s)
1934:⍪
1903:≡
1842:⍉
1818:Monadic
1809:⍕
1779:⍎
1746:⍒
1711:⍋
1676:⊖
1645:⌽
1614:⍟
1582:○
1552:⌹
1382:−
1360:Negation
1350:⋆
1317:⍳
1283:∣
1251:∼
1218:⍴
1185:⌊
1153:⌈
1091:Meaning
1085:Name(s)
1067:not find
1045:not find
882:argument
870:composed
831:and the
753:.
704:(⍳3)(⍳3)
681:(⍳3)(⍳3)
621:.
564:operands
405:function
350:expanded
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288:>>
284:Opposite
263:reducing
255:multiply
220:>>
188:function
172:operator
122:symbolic
34:require
8786:Letters
8585:General
8575:symbols
8573:Unicode
8527:Unicode
8509:symbols
8500:Common
8448:Commons
8427:Italics
8197:APL2000
8104:GNU APL
8046:APL2 →
7912:6011221
7790:GNU APL
7537:7760410
6883:factors
6859:factors
6823:factors
6793:factors
6772:factors
6748:factors
6718:factors
6691:factors
5997:roughly
5982:(keys)
5880:(RAM),
5850:Quad WA
5648:and/or
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5325:DEGREES
5292:DEGREES
5100:DEGREES
5064:DEGREES
5028:DEGREES
4996:adicity
4949:DEGREES
4922:DEGREES
4816:Monadic
4809:Niladic
4733:numbers
4405:vectors
4330:raveled
3594:SOLIDUS
3553:Symbol
3278:(True)
2935:Format
2722:SOLIDUS
2620:DIVIDES
2604:modulo
2592:Residue
2557:Encode
2551:UP TACK
2523:Decode
2374:Minimum
2337:Maximum
2145:Circle
1978:Sum of
1961:Unicode
1756:Execute
1286:DIVIDES
1194:Shape,
1131:Ceiling
1026:Letters
1019:Letters
1004:Letters
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993:Letters
980:index ⍳
952:Letters
922:Letters
913:Letters
904:Letters
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866:derived
862:commute
845:foo∘bar
840:∘ glues
834:commute
827:compose
668:of the
639:index ⍳
637:is the
592:Iota ⍳3
362:/ slash
328:boolean
259:×/2 3 4
196:operand
155:monadic
130:symbols
126:lexical
36:cleanup
8650:Arrows
8638:Arrows
8511:, and
8291:People
8246:(STSC)
7910:
7900:
7853:
7843:
7725:Page 4
7721:Page 3
7717:Page 2
7713:Page 1
7535:
7525:
7462:
7249:
7187:
7164:
7145:
7126:
6889:except
6865:except
6829:except
6799:except
6778:except
6754:except
6724:except
6697:except
6238:Primes
6223:Primes
6095:Pascal
6029:Pascal
5992:EBCDIC
5862:unused
5631:
5629:U+2190
5601:
5599:U+2192
5571:
5569:U+235D
5547:MACRON
5544:¯
5541:
5539:U+00AF
5367:RADIUS
5343:RADIUS
5298:RADIUS
5181:should
5176:arrays
5170:, but
5109:RADIUS
5082:RADIUS
5034:RADIUS
5014:sign:
4967:RADIUS
4928:RADIUS
4895:RADIUS
4880:RADIUS
4847:RESULT
4838:RESULT
4824:Dyadic
4793:result
4751:array.
4749:nested
4747:and a
4727:Since
4709:nested
4400:Arrays
4375:second
4059:named
4053:iota ⍳
3797:Notes:
3786:.
3783:
3781:U+002E
3770:
3768:U+2218
3733:.
3730:
3728:U+002E
3690:
3688:U+2340
3660:\
3657:
3655:U+005C
3621:
3619:U+233F
3591:/
3588:
3586:U+002F
3529:
3527:U+236A
3502:
3500:U+2261
3479:Match
3467:
3465:U+22A2
3450:Right
3438:
3436:U+22A3
3409:
3407:U+2372
3372:
3370:U+2371
3335:
3333:U+2227
3285:
3283:U+2228
3219:
3217:U+2260
3195:>
3192:
3190:U+003E
3181:A>B
3165:
3163:U+2265
3141:=
3138:
3136:U+003D
3109:
3107:U+2264
3085:<
3082:
3080:U+003C
3071:A<B
3058:¨
3055:
3053:U+00A8
3021:!
3018:
3016:U+0021
3007:taken
2983:
2981:U+2349
2949:
2947:U+2355
2915:
2913:U+235F
2879:
2877:U+2296
2844:
2842:U+233D
2809:
2807:U+2339
2766:
2764:U+2373
2719:/
2716:
2714:U+002F
2685:\
2682:
2680:U+005C
2651:,
2648:
2646:U+002C
2614:
2612:U+2223
2579:
2577:U+22A4
2545:
2543:U+22A5
2511:
2509:U+2193
2473:
2471:U+2191
2435:
2433:U+2374
2398:
2396:U+230A
2361:
2359:U+2308
2324:
2322:U+2377
2289:
2287:U+2208
2257:?
2254:
2252:U+003F
2220:
2218:U+25CB
2133:
2131:U+22C6
2126:power
2100:÷
2097:
2095:U+00F7
2075:Divide
2065:×
2062:
2060:U+00D7
2027:
2025:U+2212
2017:minus
1995:+
1992:
1990:U+002B
1931:
1929:U+236A
1920:Makes
1912:Table
1900:
1898:U+2261
1874:!
1871:
1869:U+0021
1839:
1837:U+2349
1806:
1804:U+2355
1776:
1774:U+234E
1743:
1741:U+2352
1708:
1706:U+234B
1673:
1671:U+2296
1642:
1640:U+233D
1611:
1609:U+235F
1579:
1577:U+25CB
1564:times
1549:
1547:U+2339
1519:,
1516:
1514:U+002C
1488:÷
1485:
1483:U+00F7
1456:×
1453:
1451:U+00D7
1446:>0
1434:¯1 if
1425:Signum
1415:+
1412:
1410:U+002B
1379:
1377:U+2212
1347:
1345:U+22C6
1340:power
1314:
1312:U+2373
1280:
1278:U+2223
1248:
1246:U+223C
1215:
1213:U+2374
1182:
1180:U+230A
1150:
1148:U+2308
1121:?
1118:
1116:U+003F
1029:ABCDE
1011:FindIt
1006:is 5.
958:FindIt
946:FindIt
937:FindIt
928:FindIt
670:equals
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603:repeat
582:atomic
358:delete
346:vector
292:Expand
243:reduce
224:Reduce
200:reduce
192:reduce
159:dyadic
8531:LaTeX
8274:(CMU)
8235:(MCM)
8208:(DEC)
8136:(PPL)
8037:Major
7991:(dfn)
7908:S2CID
7851:S2CID
7695:(PDF)
7671:(PDF)
7618:. IBM
7587:(PDF)
7533:S2CID
7482:(PDF)
7460:S2CID
7415:(PDF)
7404:(PDF)
7399:IBM.
7347:"APL"
7247:S2CID
7043:IOwas
6953:IOwas
6944:IOwas
6853:prime
6817:prime
6742:prime
6712:prime
6685:prime
6679:prime
6673:prime
6649:⎕TCNL
6601:⎕TCNL
6020:Take
6002:ASCII
5937:Fonts
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5913:)VARS
5909:)VARS
5769:X = 1
5483:, an
5268:input
4745:mixed
4582:X = 1
4363:first
4049:rho ⍴
3749:A∘.×B
3709:A+.×B
3487:0 if
3421:Left
3122:Equal
2654:COMMA
2565:Base-
2485:Drop
2447:Take
2232:Deal
2201:)
2185:)
2169:)
1884:Depth
1522:COMMA
1232:Tilde
1163:Floor
1099:Roll
1043:does
916:ABCDE
711:⍳¨3 3
689:⍳¨3 3
662:slash
548:lower
544:floor
403:of a
401:scope
394:scope
366:lists
247:slash
8640:and
8529:and
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8116:kdb+
8060:NARS
8049:APLX
8005:Rank
7932:help
7898:ISBN
7875:help
7841:ISBN
7764:2015
7624:2015
7557:help
7523:ISBN
7494:2015
7423:2015
7386:2015
7359:2015
7332:2015
7305:2015
7278:2015
7185:ISBN
7162:ISBN
7143:ISBN
7124:ISBN
6050:⌽⊃⌽∊
5975:both
5931:hook
5927:)OFF
5899:VARS
5654:hook
5487:and
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5370:AREA
5346:SIGN
5316:SIGN
5286:AREA
5142:AREA
5130:SIGN
5115:AREA
5088:SIGN
5052:SIGN
5022:AREA
4970:AREA
4916:AREA
4883:AREA
4871:AREA
4785:name
4777:user
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4737:text
4653:Text
4316:4+⍳4
4310:Var
4147:(or
4097:and
4051:and
3760:and
3720:and
3634:Scan
3398:and
3385:Nand
3361:and
3313:both
3252:and
3247:both
2799:x =
2730:Iota
1982:and
1294:Iota
1063:Iota
1056:Iota
1041:Iota
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728:and
707:and
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597:The
580:APL
399:The
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182:and
153:. A
8385:Jr.
8218:IBM
8098:ELI
7888:doi
7831:doi
7513:doi
7450:doi
7237:doi
7103:233
7100:144
7037:⎕IO
7004:Nth
6992:↓↑+
6965:⎕IO
6959:⎕IO
6938:Nth
6920:⎕CR
6418:⎕CR
6388:100
6301:100
6214:⎕CR
5854:⎕WA
5852:or
5840:⎕WA
5810:⎕IO
5784:⎕IO
5761:⎕IO
5734:⎕IO
5650:")"
5620:B←A
5470:.
5406:¯90
5403:270
5400:180
5331:360
5209:¯90
5206:270
5203:180
5185:may
5172:not
5070:360
4955:360
4571:⎕IO
4561:= 7
4532:⎕IO
4379:B,C
4367:B,C
4328:or
4141:","
4107:is
4083:or
3756:of
3745:∘.
3716:of
3676:+⍀B
3643:+\B
3607:+⌿B
3574:+/B
3518:A⍪B
3483:A≡B
3454:A⊢B
3425:A⊣B
3390:A⍲B
3353:A⍱B
3348:Nor
3319:and
3303:A∧B
3298:And
3237:A∨B
3208:A≠B
3154:A≥B
3127:A=B
3098:A≤B
3034:A¨B
2999:A!B
2965:A⍉B
2931:A⍕B
2897:A⍟B
2860:A⊖B
2825:A⌽B
2784:A⌹B
2743:in
2735:A⍳B
2698:A/B
2664:A\B
2630:A,B
2597:A∣B
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2535:at
2527:A⊥B
2489:A↓B
2451:A↑B
2417:A⍴B
2412:Rho
2388:or
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2351:or
2343:A⌈B
2305:A⍷B
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2236:A?B
2149:A○B
2115:A⋆B
2080:A÷B
2045:A×B
2010:A−B
1974:A+B
1969:Add
1767:APL
1228:Not
1196:Rho
1017:in
982:or
868:or
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435:):
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118:APL
92:APL
8914::
8507:,
8123:,
8084:A+
8082:→
7924::
7922:}}
7918:{{
7906:.
7896:.
7867::
7865:}}
7861:{{
7849:.
7839:.
7723:,
7719:,
7715:,
7614:.
7589:.
7549::
7547:}}
7543:{{
7531:.
7521:.
7484:.
7458:.
7444:.
7440:.
7406:.
7376:.
7349:.
7322:.
7295:.
7268:.
7245:.
7097:89
7094:55
7091:34
7088:21
7085:13
7058:14
6880:15
6856:14
6850:13
6820:12
6814:11
6790:10
6664:15
6541:=⍴
6520:))
6391:25
6379:97
6376:89
6373:83
6370:79
6367:73
6364:71
6361:67
6358:61
6355:59
6352:53
6349:47
6346:43
6343:41
6340:37
6337:31
6334:29
6331:23
6328:19
6325:17
6322:13
6319:11
6277:|⍳
6274:∘.
6250:=+
6182:21
6179:35
6176:35
6173:21
6161:15
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