ALT Codes for Math APL Symbols (⌸ ⌾ ⍋)

Below is the complete list of Windows ALT Codes for Math APL Symbols, their corresponding HTML entity numeric character references, and when available, their corresponding HTML entity named character references, and Unicode code points. If you are new to ALT codes and need detailed instructions on how to use ALT codes in your Microsoft Office documents such as Word, Excel & PowerPoint or applicable Microsoft Windows programs & applications, please read How to Use ALT Codes to Enter Special Characters. If you want, instead of using ALT codes, you can also just quickly tap or click any APL symbol in the list below to copy and paste it into your document. (Note: Some symbols might not display correctly due to device or platform limitations in character/text representation.)

Symbol	ALT Code	ALT X Code	Symbol Name	HTML Entity DEC	HTML Entity HEX	HTML Entity Named	Unicode Code Point	Monadic Name	Monadic Meaning	Dyadic Name	Dyadic Meaning
⌶	ALT 9014	2336 ALT X	APL functional symbol i-beam	&#9014	&#x2336	&topbot;	U+2336	I-beam
⌷	ALT 9015	2337 ALT X	APL functional symbol squish quad	&#9015	&#x2337		U+2337	Materialise		Index
⌸	ALT 9016	2338 ALT X	APL functional symbol quad equal	&#9016	&#x2338		U+2338	Key	Apply function A to each unique key in B and elements of ⍳≢B having that key	Key	Apply function to each unique key in A and major cells of B having that key
⌹	ALT 9017	2339 ALT X	APL functional symbol quad divide	&#9017	&#x2339		U+2339	Matrix inverse	Inverse of matrix B	Matrix divide	Solution to system of linear equations Ax = B
⌺	ALT 9018	233A ALT X	APL functional symbol quad diamond	&#9018	&#x233A		U+233A
⌻	ALT 9019	233B ALT X	APL functional symbol quad jot	&#9019	&#x233B		U+233B
⌼	ALT 9020	233C ALT X	APL functional symbol quad circle	&#9020	&#x233C		U+233C
⌽	ALT 9021	233D ALT X	APL functional symbol circle stile	&#9021	&#x233D	&ovbar;	U+233D	Reverse first	Reverse elements of B along last axis	Rotate first	The elements of B are rotated A positions
⌾	ALT 9022	233E ALT X	APL functional symbol circle jot	&#9022	&#x233E		U+233E
⌿	ALT 9023	233F ALT X	APL functional symbol slash bar	&#9023	&#x233F	&solbar;	U+233F	Reduce (first axis)	Sum down B	Replicate first
⍀	ALT 9024	2340 ALT X	APL functional symbol backslash bar	&#9024	&#x2340		U+2340	Scan (first axis)	Running sum down B	Expand first
⍁	ALT 9025	2341 ALT X	APL functional symbol quad slash	&#9025	&#x2341		U+2341
⍂	ALT 9026	2342 ALT X	APL functional symbol quad backslash	&#9026	&#x2342		U+2342
⍃	ALT 9027	2343 ALT X	APL functional symbol quad less-than	&#9027	&#x2343		U+2343
⍄	ALT 9028	2344 ALT X	APL functional symbol quad greater-than	&#9028	&#x2344		U+2344
⍅	ALT 9029	2345 ALT X	APL functional symbol leftwards vane	&#9029	&#x2345		U+2345
⍆	ALT 9030	2346 ALT X	APL functional symbol rightwards vane	&#9030	&#x2346		U+2346
⍇	ALT 9031	2347 ALT X	APL functional symbol quad leftwards arrow	&#9031	&#x2347		U+2347
⍈	ALT 9032	2348 ALT X	APL functional symbol quad rightwards arrow	&#9032	&#x2348		U+2348
⍉	ALT 9033	2349 ALT X	APL functional symbol circle backslash	&#9033	&#x2349		U+2349	Monadic transpose	Reverse the axes of B	General transpose	The axes of B are ordered by A
⍊	ALT 9034	234A ALT X	APL functional symbol down tack underbar	&#9034	&#x234A		U+234A
⍋	ALT 9035	234B ALT X	APL functional symbol delta stile	&#9035	&#x234B		U+234B	Grade up	Indices of B which will arrange B in ascending order	Grade up	Arrange B according to collating sequence specified by A
⍌	ALT 9036	234C ALT X	APL functional symbol quad down caret	&#9036	&#x234C		U+234C
⍍	ALT 9037	234D ALT X	APL functional symbol quad delta	&#9037	&#x234D		U+234D
⍎	ALT 9038	234E ALT X	APL functional symbol down tack jot	&#9038	&#x234E		U+234E	Execute	Execute an APL expression	Execute
⍏	ALT 9039	234F ALT X	APL functional symbol upwards vane	&#9039	&#x234F		U+234F
⍐	ALT 9040	2350 ALT X	APL functional symbol quad upwards arrow	&#9040	&#x2350		U+2350
⍑	ALT 9041	2351 ALT X	APL functional symbol up tack overbar	&#9041	&#x2351		U+2351
⍒	ALT 9042	2352 ALT X	APL functional symbol del stile	&#9042	&#x2352		U+2352	Grade down	Indices of B which will arrange B in descending order	Grade down	Arrange B according to inverse collating sequence specified by A
⍓	ALT 9043	2353 ALT X	APL functional symbol quad up caret	&#9043	&#x2353		U+2353
⍔	ALT 9044	2354 ALT X	APL functional symbol quad del	&#9044	&#x2354		U+2354
⍕	ALT 9045	2355 ALT X	APL functional symbol up tack jot	&#9045	&#x2355		U+2355	Monadic format / format	A character representation of B	Dyadic format / specified format	Format B into a character matrix according to A
⍖	ALT 9046	2356 ALT X	APL functional symbol downwards vane	&#9046	&#x2356		U+2356
⍗	ALT 9047	2357 ALT X	APL functional symbol quad downwards arrow	&#9047	&#x2357		U+2357
⍘	ALT 9048	2358 ALT X	APL functional symbol quote underbar	&#9048	&#x2358		U+2358
⍙	ALT 9049	2359 ALT X	APL functional symbol delta underbar	&#9049	&#x2359		U+2359
⍚	ALT 9050	235A ALT X	APL functional symbol diamond underbar	&#9050	&#x235A		U+235A
⍛	ALT 9051	235B ALT X	APL functional symbol jot underbar	&#9051	&#x235B		U+235B
⍜	ALT 9052	235C ALT X	APL functional symbol circle underbar	&#9052	&#x235C		U+235C
⍝	ALT 9053	235D ALT X	APL functional symbol up shoe jot	&#9053	&#x235D		U+235D	Comment	Everything to the right of ⍝ denotes a comment
⍞	ALT 9054	235E ALT X	APL functional symbol quote quad	&#9054	&#x235E		U+235E	Bare I/O	Read data typed on the keyboard as characters or display without terminating newline
⍟	ALT 9055	235F ALT X	APL functional symbol circle star	&#9055	&#x235F		U+235F	Natural logarithm	Natural logarithm of B	Logarithm	Logarithm of B to base A
⍠	ALT 9056	2360 ALT X	APL functional symbol quad colon	&#9056	&#x2360		U+2360			Variant
⍡	ALT 9057	2361 ALT X	APL functional symbol up tack diaeresis	&#9057	&#x2361		U+2361
⍢	ALT 9058	2362 ALT X	APL functional symbol del diaeresis	&#9058	&#x2362		U+2362
⍣	ALT 9059	2363 ALT X	APL functional symbol star diaeresis	&#9059	&#x2363		U+2363			Reapply	The function A is applied B times
⍤	ALT 9060	2364 ALT X	APL functional symbol jot diaeresis	&#9060	&#x2364		U+2364			Rank	Apply function successively to the sub-arrays in B specified by k
⍥	ALT 9061	2365 ALT X	APL functional symbol circle diaeresis	&#9061	&#x2365		U+2365			Coax
⍦	ALT 9062	2366 ALT X	APL functional symbol down shoe stile	&#9062	&#x2366		U+2366
⍧	ALT 9063	2367 ALT X	APL functional symbol left shoe stile	&#9063	&#x2367		U+2367
⍨	ALT 9064	2368 ALT X	APL functional symbol tilde diaeresis	&#9064	&#x2368		U+2368			Commute	Exchanges the arguments of a dyadic function: A+⍨B ↔ B+A
⍩	ALT 9065	2369 ALT X	APL functional symbol greater-than diaeresis	&#9065	&#x2369		U+2369
⍪	ALT 9066	236A ALT X	APL functional symbol comma bar	&#9066	&#x236A		U+236A			Catenate first	Catenate across the first axis
⍫	ALT 9067	236B ALT X	APL functional symbol del tilde	&#9067	&#x236B		U+236B	Lock	Edit a function which cannot be edited or displayed
⍬	ALT 9068	236C ALT X	APL functional symbol zilde	&#9068	&#x236C		U+236C	Zilde	Empty numeric vector, equivalent to ⍳0 or 0⍴0
⍭	ALT 9069	236D ALT X	APL functional symbol stile tilde	&#9069	&#x236D		U+236D
⍮	ALT 9070	236E ALT X	APL functional symbol semicolon underbar	&#9070	&#x236E		U+236E
⍯	ALT 9071	236F ALT X	APL functional symbol quad not equal	&#9071	&#x236F		U+236F
⍰	ALT 9072	2370 ALT X	APL functional symbol quad question	&#9072	&#x2370		U+2370
⍱	ALT 9073	2371 ALT X	APL functional symbol down caret tilde	&#9073	&#x2371		U+2371			Nor	Logic: 1 if both A and B are 0; otherwise 0
⍲	ALT 9074	2372 ALT X	APL functional symbol up caret tilde	&#9074	&#x2372		U+2372			Nand	Logic: 0 if both A and B are 1; otherwise 1
⍳	ALT 9075	2373 ALT X	APL functional symbol iota	&#9075	&#x2373		U+2373	Count / Index generator	Vector of the first B integers	Index of	The location (index) of B in A; 1+⌈/⍳⍴A if not found
⍴	ALT 9076	2374 ALT X	APL functional symbol rho	&#9076	&#x2374		U+2374	Shape	Number of components in each dimension of B	Reshape	Array of shape A with data B
⍵	ALT 9077	2375 ALT X	APL functional symbol omega	&#9077	&#x2375		U+2375			Omega
⍶	ALT 9078	2376 ALT X	APL functional symbol alpha underbar	&#9078	&#x2376		U+2376
⍷	ALT 9079	2377 ALT X	APL functional symbol epsilon underbar	&#9079	&#x2377		U+2377			Find	Elements of A within B, returning 1 if the start of A is found in B
⍸	ALT 9080	2378 ALT X	APL functional symbol iota underbar	&#9080	&#x2378		U+2378			String index	The index of B in A using ⍷ as primary function
⍹	ALT 9081	2379 ALT X	APL functional symbol omega underbar	&#9081	&#x2379		U+2379
⍺	ALT 9082	237A ALT X	APL functional symbol alpha	&#9082	&#x237A		U+237A	Alpha		Picture format	Displays the numbers in B according to the instructions in A
⎕	ALT 9109	2395 ALT X	APL functional symbol quad	&#9109	&#x2395		U+2395	Evaluated I/O	Read number or expression typed on the keyboard or display result with newline
!	ALT 33	0021 ALT X	Exclamation mark, factorial, bang	&#33	&#x0021	&excl;	U+0021	Factorial	Product of integers 1 to B	Binomial/Combinations	Number of combinations of B taken A at a time
&	ALT 38	0026 ALT X	Ampersand	&#38	&#x0026	&	U+0026	Spawn
'	ALT 39	0027 ALT X	Apostrophe, APL quote	&#39	&#x0027	'	U+0027
)	ALT 41	0029 ALT X	Right parenthesis, closing parenthesis	&#41	&#x0029	)	U+0029	Hook
+	ALT 43	002B ALT X	Plus sign	&#43	&#x002B	+	U+002B	Conjugate/Identity	No change to B	Add	Sum of A and B
,	ALT 44	002C ALT X	Comma, decimal separator	&#44	&#x002C	,	U+002C	Ravel	Reshapes B into a vector	Catenation	Elements of B appended to the elements of A
.	ALT 46	002E ALT X	Full stop, period, dot, decimal point	&#46	&#x002E	&period;	U+002E			Inner product	Matrix product of A and B
/	ALT 47	002F ALT X	Solidus, slash, virgule	&#47	&#x002F	/	U+002F	Reduce (last axis)	Sum across B	Replicate	Select elements in B corresponding to ones in A
<	ALT 60	003C ALT X	Less-than sign	&#60	&#x003C	<	U+003C			Less than	Comparison: 1 if true, 0 if false
=	ALT 61	003D ALT X	Equals sign	&#61	&#x003D	=	U+003D			Equal	Comparison: 1 if true, 0 if false
>	ALT 62	003E ALT X	Greater-than sign	&#62	&#x003E	>	U+003E			Greater than	Comparison: 1 if true, 0 if false
?	ALT 63	003F ALT X	Question mark	&#63	&#x003F	&quest;	U+003F	Roll	One integer selected randomly from the first B integers	Deal	A distinct integers selected randomly from the first B integers
\	ALT 92	005C ALT X	Reverse solidus, backslash	&#92	&#x005C	\	U+005C	Scan (last axis)	Running sum across B	Expand	Insert zeros (or blanks) in B corresponding to zeros in A
_	ALT 95	005F ALT X	Low line, spacing underscore	&#95	&#x005F	&lowbar;	U+005F
¨	ALT 168	00A8 ALT X	Diaeresis, spacing diaeresis	&#168	&#x00A8	&die;	U+00A8			Each	Over each, or perform each separately; B = on these; A = operation to perform or using (e.g. iota)
¯	ALT 175	00AF ALT X	Macron, spacing macron, overline, APL overbar	&#175	&#x00AF	¯	U+00AF	Negative	Denotes a negative number
×	ALT 215	00D7 ALT X	Multiplication sign, Z notation Cartesian product	&#215	&#x00D7	×	U+00D7	Sign/signum	¯1 if B0	Multiply	A multiplied by B
÷	ALT 246 or ALT 0247	00F7 ALT X	Division sign, obelus	&#247	&#x00F7	&div;	U+00F7	Reciprocal	1 divided by B	Divide	A divided by B
←	ALT 27 or ALT 8592	2190 ALT X	Leftwards arrow	&#8592	&#x2190	←	U+2190	Assign	B←A sets values and shape of B to match A
↑	ALT 24 or ALT 8593	2191 ALT X	Upwards arrow	&#8593	&#x2191	&ShortUpArrow;	U+2191	Nub		Take	Select the first (or last) A elements of B according to ×A
→	ALT 26 or ALT 8594	2192 ALT X	Rightwards arrow, z notation total function	&#8594	&#x2192	→	U+2192	Goto	→This_Label sends APL execution to This_Label:
↓	ALT 25 or ALT 8595	2193 ALT X	Downwards arrow	&#8595	&#x2193	↓	U+2193	Split		Drop	Remove the first (or last) A elements of B according to ×A
∆	ALT 8710	2206 ALT X	Increment, Laplace operator, forward difference, symmetric difference (in set theory)	&#8710	&#x2206		U+2206	Derivative		Difference
∇	ALT 8711	2207 ALT X	Nabla, backward difference, gradient, del	&#8711	&#x2207	&Del;	U+2207	Edit	Toggle function definition mode
∈	ALT 8712	2208 ALT X	Element of	&#8712	&#x2208	&Element;	U+2208	Enlist	Every element in B as simple vector	Membership	1 for elements of A present in B; 0 where not.
−	ALT 8722	2212 ALT X	Minus sign	&#8722	&#x2212	−	U+2212	Negate/negation	Changes sign of B	Subtract	A minus B
∘	ALT 8728	2218 ALT X	Ring operator, composite function, APL jot	&#8728	&#x2218	&compfn;	U+2218			Compose
∝	ALT 8733	221D ALT X	Proportional to	&#8733	&#x221D	&prop;	U+221D
∣	ALT 8739	2223 ALT X	Divides, such that, APL stile	&#8739	&#x2223	&mid;	U+2223	Magnitude/Absolute value	Magnitude of B	Residue	B modulo A
∧	ALT 8743	2227 ALT X	Logical and, wedge, conjunction	&#8743	&#x2227	&and;	U+2227			And	Logic: 1 if A and B are 1; 0 otherwise
∨	ALT 8744	2228 ALT X	Logical or, vee, disjunction	&#8744	&#x2228	&or;	U+2228			Or	Logic: 0 if A and B are 0; 1 otherwise
∩	ALT 239 or ALT 8745	2229 ALT X	Intersection	&#8745	&#x2229	∩	U+2229			Intersection	Elements of A that are in B: (A∈B)/A
∪	ALT 8746	222A ALT X	Union	&#8746	&#x222A	∪	U+222A	Unique		Union	Catenate A and B determined by combining ranks: A,(∼A∈B)/A
∼	ALT 8764	223C ALT X	Tilde operator, varies with (proportional to), difference between, similar to, not, cycle, APL tilde	&#8764	&#x223C	&sim;	U+223C	Not	Logical: ∼1 is 0, ∼0 is 1	Difference	Items found in B are removed from A
≠	ALT 8800	2260 ALT X	Not equal to	&#8800	&#x2260	≠	U+2260			Not equal	Comparison: 1 if true, 0 if false
≡	ALT 240 or ALT 8801	2261 ALT X	Identical to	&#8801	&#x2261	&Congruent;	U+2261	Depth	Level of nesting: 1 + maximum array depth or 0 if scalar	Match	1 if arguments are the same in every respect, 0 if not
≢	ALT 8802	2262 ALT X	Not identical to	&#8802	&#x2262	&nequiv;	U+2262	Tally	Number of major cells in B, equivalent to {⍬⍴ (⍴⍵),1}	Not match	1 if arguments are different if any respect, 0 if not
≤	ALT 243 or ALT 8804	2264 ALT X	Less-than or equal to	&#8804	&#x2264	≤	U+2264			Less than or equal	Comparison: 1 if true, 0 if false
≥	ALT 242 or ALT 8805	2265 ALT X	Greater-than or equal to	&#8805	&#x2265	≥	U+2265			Greater than or equal	Comparison: 1 if true, 0 if false
⊂	ALT 8834	2282 ALT X	Subset of, included in set	&#8834	&#x2282	⊂	U+2282	Enclose	Produce a scalar of vector B	Partition	Divide B into an array of vectors according to specification in A
⊃	ALT 8835	2283 ALT X	Superset of, includes in set	&#8835	&#x2283	⊃	U+2283	Disclose	Produce an array made up of the items in B	Pick	Select item A from vector B
⊆	ALT 8838	2286 ALT X	Subset of or equal to	&#8838	&#x2286	&sube;	U+2286			Subset	Elements in both A and B: (∧/A∈B)∧(∧/B∈A)
⊖	ALT 8854	2296 ALT X	Circled minus, symmetric difference	&#8854	&#x2296	&CircleMinus;	U+2296	Reversal	Reverse elements of B along first axis	Rotation	The elements of B are rotated A positions along the first axis
⊢	ALT 8866	22A2 ALT X	Right tack, turnstile, proves, implies, yields, reducible	&#8866	&#x22A2	&RightTee;	U+22A2	Pass	Passes argument unchanged, useful to force display of non-printing result	Right	Discard A and pass B unchanged
⊣	ALT 8867	22A3 ALT X	Left tack, reverse turnstile, non-theorem, does not yield	&#8867	&#x22A3	&dashv;	U+22A3	Stop	Discard argument and return empty matrix	Left	Discard B and pass A unchanged
⊤	ALT 8868	22A4 ALT X	Down tack, top	&#8868	&#x22A4	&DownTee;	U+22A4			Encode	Base-A representation of the value of B
⊥	ALT 8869	22A5 ALT X	Up tack, base, bottom	&#8869	&#x22A5	&bot;	U+22A5			Decode	Value of a polynomial whose coefficients are B at A
⋄	ALT 8900	22C4 ALT X	Diamond operator	&#8900	&#x22C4	&diam;	U+22C4			Statement separator	Separates multiple statements on a single line
⋆	ALT 8902	22C6 ALT X	Star operator	&#8902	&#x22C6	&sstarf;	U+22C6	Exponential	e to the B power	Power/Exponentiation	A raised to the B power
⌈	ALT 8968	2308 ALT X	Left ceiling, APL upstile	&#8968	&#x2308	&lceil;	U+2308	Ceiling	Least integer greater than or equal to B	Maximum	The greater value of A or B
⌉	ALT 8969	2309 ALT X	Right ceiling	&#8969	&#x2309	&rceil;	U+2309
⌊	ALT 8970	230A ALT X	Left floor, APL downstile	&#8970	&#x230A	&LeftFloor;	U+230A	Floor	Greatest integer less than or equal to B	Minimum	The smaller value of A or B
⌋	ALT 8971	230B ALT X	Right floor	&#8971	&#x230B	&rfloor;	U+230B
◇	ALT 9671	25C7 ALT X	White diamond	&#9671	&#x25C7		U+25C7
○	ALT 9675	25CB ALT X	White circle	&#9675	&#x25CB	&cir;	U+25CB	Pi times	Multiply by π	Circle	Trigonometric functions of B selected by A. A=1: sin(B) A=2: cos(B) A=3: tan(B)

APL (A Programming Language) is a high-level, array-oriented programming language known for its concise and expressive syntax. It was developed in the 1960s by Kenneth E. Iverson and later refined with the help of Adin D. Falkoff. APL is particularly notable for its unique set of symbols and operators used for mathematical and array operations.

Key features and characteristics of APL include:

Array-Centric: APL is designed primarily for array processing. Arrays are fundamental data structures in APL, and many operations can be performed on entire arrays in a single statement.
Symbolic Notation: APL uses a rich set of symbolic characters and operators, often represented by special symbols like ⍺, ⍵, and ⌿. This allows for highly compact and expressive code.
Interactive: APL is well-suited for interactive programming. Programmers can enter and test code directly in an interactive environment, making it suitable for exploratory data analysis and mathematical modeling.
Functional Programming: APL incorporates elements of functional programming, allowing for the composition of functions and operations on data.
Cross-Platform: APL has been implemented on various computer systems and is available on different platforms.
Conciseness: APL code is often much shorter and more expressive than equivalent code in other programming languages, which can make it efficient for certain types of tasks.
Mathematical and Scientific Applications: APL is commonly used in fields such as mathematics, scientific computing, and data analysis, particularly for tasks involving numerical arrays.

Although APL has a unique and powerful notation, it can also be challenging to learn due to its unconventional symbols and operators. Despite this, it has a dedicated user base and continues to be used in specialized domains, especially for mathematical and array-intensive computations. Various modern programming languages have drawn inspiration from APL’s array-oriented approach, such as J and NumPy in Python.

For more math signs and symbols, see ALT Codes for Math Symbols. For the the complete list of the first 256 Windows ALT Codes, visit Windows ALT Codes for Special Characters & Symbols.