Below is the complete list of Windows ALT Codes for Math Symbols: APL Symbols, their corresponding HTML entity numeric character references, and when available, their corresponding HTML entity named character references, and Unicode code points.
The programming language APL is distinctive in being symbolic rather than lexical: its primitives are denoted by symbols, not words. These symbols were originally devised as a mathematical notation 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 (from Wikipedia).
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.
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 | ⌶ | ⌶ | ⌶ | U+2336 | I-beam | |||
⌷ | ALT 9015 | 2337 ALT X | APL functional symbol squish quad | ⌷ | ⌷ | U+2337 | Materialise | Index | |||
⌸ | ALT 9016 | 2338 ALT X | APL functional symbol quad equal | ⌸ | ⌸ | 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 | ⌹ | ⌹ | 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 | ⌺ | ⌺ | U+233A | |||||
⌻ | ALT 9019 | 233B ALT X | APL functional symbol quad jot | ⌻ | ⌻ | U+233B | |||||
⌼ | ALT 9020 | 233C ALT X | APL functional symbol quad circle | ⌼ | ⌼ | U+233C | |||||
⌽ | ALT 9021 | 233D ALT X | APL functional symbol circle stile | ⌽ | ⌽ | ⌽ | 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 | ⌾ | ⌾ | U+233E | |||||
⌿ | ALT 9023 | 233F ALT X | APL functional symbol slash bar | ⌿ | ⌿ | ⌿ | U+233F | Reduce (first axis) | Sum down B | Replicate first | |
⍀ | ALT 9024 | 2340 ALT X | APL functional symbol backslash bar | ⍀ | ⍀ | U+2340 | Scan (first axis) | Running sum down B | Expand first | ||
⍁ | ALT 9025 | 2341 ALT X | APL functional symbol quad slash | ⍁ | ⍁ | U+2341 | |||||
⍂ | ALT 9026 | 2342 ALT X | APL functional symbol quad backslash | ⍂ | ⍂ | U+2342 | |||||
⍃ | ALT 9027 | 2343 ALT X | APL functional symbol quad less-than | ⍃ | ⍃ | U+2343 | |||||
⍄ | ALT 9028 | 2344 ALT X | APL functional symbol quad greater-than | ⍄ | ⍄ | U+2344 | |||||
⍅ | ALT 9029 | 2345 ALT X | APL functional symbol leftwards vane | ⍅ | ⍅ | U+2345 | |||||
⍆ | ALT 9030 | 2346 ALT X | APL functional symbol rightwards vane | ⍆ | ⍆ | U+2346 | |||||
⍇ | ALT 9031 | 2347 ALT X | APL functional symbol quad leftwards arrow | ⍇ | ⍇ | U+2347 | |||||
⍈ | ALT 9032 | 2348 ALT X | APL functional symbol quad rightwards arrow | ⍈ | ⍈ | U+2348 | |||||
⍉ | ALT 9033 | 2349 ALT X | APL functional symbol circle backslash | ⍉ | ⍉ | 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 | ⍊ | ⍊ | U+234A | |||||
⍋ | ALT 9035 | 234B ALT X | APL functional symbol delta stile | ⍋ | ⍋ | 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 | ⍌ | ⍌ | U+234C | |||||
⍍ | ALT 9037 | 234D ALT X | APL functional symbol quad delta | ⍍ | ⍍ | U+234D | |||||
⍎ | ALT 9038 | 234E ALT X | APL functional symbol down tack jot | ⍎ | ⍎ | U+234E | Execute | Execute an APL expression | Execute | ||
⍏ | ALT 9039 | 234F ALT X | APL functional symbol upwards vane | ⍏ | ⍏ | U+234F | |||||
⍐ | ALT 9040 | 2350 ALT X | APL functional symbol quad upwards arrow | ⍐ | ⍐ | U+2350 | |||||
⍑ | ALT 9041 | 2351 ALT X | APL functional symbol up tack overbar | ⍑ | ⍑ | U+2351 | |||||
⍒ | ALT 9042 | 2352 ALT X | APL functional symbol del stile | ⍒ | ⍒ | 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 | ⍓ | ⍓ | U+2353 | |||||
⍔ | ALT 9044 | 2354 ALT X | APL functional symbol quad del | ⍔ | ⍔ | U+2354 | |||||
⍕ | ALT 9045 | 2355 ALT X | APL functional symbol up tack jot | ⍕ | ⍕ | 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 | ⍖ | ⍖ | U+2356 | |||||
⍗ | ALT 9047 | 2357 ALT X | APL functional symbol quad downwards arrow | ⍗ | ⍗ | U+2357 | |||||
⍘ | ALT 9048 | 2358 ALT X | APL functional symbol quote underbar | ⍘ | ⍘ | U+2358 | |||||
⍙ | ALT 9049 | 2359 ALT X | APL functional symbol delta underbar | ⍙ | ⍙ | U+2359 | |||||
⍚ | ALT 9050 | 235A ALT X | APL functional symbol diamond underbar | ⍚ | ⍚ | U+235A | |||||
⍛ | ALT 9051 | 235B ALT X | APL functional symbol jot underbar | ⍛ | ⍛ | U+235B | |||||
⍜ | ALT 9052 | 235C ALT X | APL functional symbol circle underbar | ⍜ | ⍜ | U+235C | |||||
⍝ | ALT 9053 | 235D ALT X | APL functional symbol up shoe jot | ⍝ | ⍝ | U+235D | Comment | Everything to the right of ⍝ denotes a comment | |||
⍞ | ALT 9054 | 235E ALT X | APL functional symbol quote quad | ⍞ | ⍞ | 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 | ⍟ | ⍟ | 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 | ⍠ | ⍠ | U+2360 | Variant | ||||
⍡ | ALT 9057 | 2361 ALT X | APL functional symbol up tack diaeresis | ⍡ | ⍡ | U+2361 | |||||
⍢ | ALT 9058 | 2362 ALT X | APL functional symbol del diaeresis | ⍢ | ⍢ | U+2362 | |||||
⍣ | ALT 9059 | 2363 ALT X | APL functional symbol star diaeresis | ⍣ | ⍣ | U+2363 | Reapply | The function A is applied B times | |||
⍤ | ALT 9060 | 2364 ALT X | APL functional symbol jot diaeresis | ⍤ | ⍤ | 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 | ⍥ | ⍥ | U+2365 | Coax | ||||
⍦ | ALT 9062 | 2366 ALT X | APL functional symbol down shoe stile | ⍦ | ⍦ | U+2366 | |||||
⍧ | ALT 9063 | 2367 ALT X | APL functional symbol left shoe stile | ⍧ | ⍧ | U+2367 | |||||
⍨ | ALT 9064 | 2368 ALT X | APL functional symbol tilde diaeresis | ⍨ | ⍨ | 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 | ⍩ | ⍩ | U+2369 | |||||
⍪ | ALT 9066 | 236A ALT X | APL functional symbol comma bar | ⍪ | ⍪ | U+236A | Catenate first | Catenate across the first axis | |||
⍫ | ALT 9067 | 236B ALT X | APL functional symbol del tilde | ⍫ | ⍫ | U+236B | Lock | Edit a function which cannot be edited or displayed | |||
⍬ | ALT 9068 | 236C ALT X | APL functional symbol zilde | ⍬ | ⍬ | U+236C | Zilde | Empty numeric vector, equivalent to ⍳0 or 0⍴0 | |||
⍭ | ALT 9069 | 236D ALT X | APL functional symbol stile tilde | ⍭ | ⍭ | U+236D | |||||
⍮ | ALT 9070 | 236E ALT X | APL functional symbol semicolon underbar | ⍮ | ⍮ | U+236E | |||||
⍯ | ALT 9071 | 236F ALT X | APL functional symbol quad not equal | ⍯ | ⍯ | U+236F | |||||
⍰ | ALT 9072 | 2370 ALT X | APL functional symbol quad question | ⍰ | ⍰ | U+2370 | |||||
⍱ | ALT 9073 | 2371 ALT X | APL functional symbol down caret tilde | ⍱ | ⍱ | 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 | ⍲ | ⍲ | U+2372 | Nand | Logic: 0 if both A and B are 1; otherwise 1 | |||
⍳ | ALT 9075 | 2373 ALT X | APL functional symbol iota | ⍳ | ⍳ | 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 | ⍴ | ⍴ | 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 | ⍵ | ⍵ | U+2375 | Omega | ||||
⍶ | ALT 9078 | 2376 ALT X | APL functional symbol alpha underbar | ⍶ | ⍶ | U+2376 | |||||
⍷ | ALT 9079 | 2377 ALT X | APL functional symbol epsilon underbar | ⍷ | ⍷ | 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 | ⍸ | ⍸ | U+2378 | String index | The index of B in A using ⍷ as primary function | |||
⍹ | ALT 9081 | 2379 ALT X | APL functional symbol omega underbar | ⍹ | ⍹ | U+2379 | |||||
⍺ | ALT 9082 | 237A ALT X | APL functional symbol alpha | ⍺ | ⍺ | 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 | ⎕ | ⎕ | 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 | ! | ! | ! | 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 | & | & | & | U+0026 | Spawn | |||
' | ALT 39 | 0027 ALT X | Apostrophe, APL quote | ' | ' | ' | U+0027 | ||||
) | ALT 41 | 0029 ALT X | Right parenthesis, closing parenthesis | ) | ) | ) | U+0029 | Hook | |||
+ | ALT 43 | 002B ALT X | Plus sign | + | + | + | U+002B | Conjugate/Identity | No change to B | Add | Sum of A and B |
, | ALT 44 | 002C ALT X | Comma, decimal separator | , | , | , | 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 | . | . | . | U+002E | Inner product | Matrix product of A and B | ||
/ | ALT 47 | 002F ALT X | Solidus, slash, virgule | / | / | / | 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 | < | < | < | U+003C | Less than | Comparison: 1 if true, 0 if false | ||
= | ALT 61 | 003D ALT X | Equals sign | = | = | = | U+003D | Equal | Comparison: 1 if true, 0 if false | ||
> | ALT 62 | 003E ALT X | Greater-than sign | > | > | > | U+003E | Greater than | Comparison: 1 if true, 0 if false | ||
? | ALT 63 | 003F ALT X | Question mark | ? | ? | ? | 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 | \ | \ | \ | 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 | _ | _ | _ | U+005F | ||||
¨ | ALT 168 | 00A8 ALT X | Diaeresis, spacing diaeresis | ¨ | ¨ | ¨ | 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 | ¯ | ¯ | ¯ | U+00AF | Negative | Denotes a negative number | ||
× | ALT 215 | 00D7 ALT X | Multiplication sign, Z notation Cartesian product | × | × | × | U+00D7 | Sign/signum | ¯1 if B0 | Multiply | A multiplied by B |
÷ | ALT 246 or ALT 0247 | 00F7 ALT X | Division sign, obelus | ÷ | ÷ | ÷ | U+00F7 | Reciprocal | 1 divided by B | Divide | A divided by B |
← | ALT 27 or ALT 8592 | 2190 ALT X | Leftwards arrow | ← | ← | ← | U+2190 | Assign | B←A sets values and shape of B to match A | ||
↑ | ALT 24 or ALT 8593 | 2191 ALT X | Upwards arrow | ↑ | ↑ | ↑ | 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 | → | → | → | U+2192 | Goto | →This_Label sends APL execution to This_Label: | ||
↓ | ALT 25 or ALT 8595 | 2193 ALT X | Downwards arrow | ↓ | ↓ | ↓ | 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) | ∆ | ∆ | U+2206 | Derivative | Difference | |||
∇ | ALT 8711 | 2207 ALT X | Nabla, backward difference, gradient, del | ∇ | ∇ | ∇ | U+2207 | Edit | Toggle function definition mode | ||
∈ | ALT 8712 | 2208 ALT X | Element of | ∈ | ∈ | ∈ | 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 | − | − | − | U+2212 | Negate/negation | Changes sign of B | Subtract | A minus B |
∘ | ALT 8728 | 2218 ALT X | Ring operator, composite function, APL jot | ∘ | ∘ | ∘ | U+2218 | Compose | |||
∝ | ALT 8733 | 221D ALT X | Proportional to | ∝ | ∝ | ∝ | U+221D | ||||
∣ | ALT 8739 | 2223 ALT X | Divides, such that, APL stile | ∣ | ∣ | ∣ | U+2223 | Magnitude/Absolute value | Magnitude of B | Residue | B modulo A |
∧ | ALT 8743 | 2227 ALT X | Logical and, wedge, conjunction | ∧ | ∧ | ∧ | U+2227 | And | Logic: 1 if A and B are 1; 0 otherwise | ||
∨ | ALT 8744 | 2228 ALT X | Logical or, vee, disjunction | ∨ | ∨ | ∨ | U+2228 | Or | Logic: 0 if A and B are 0; 1 otherwise | ||
∩ | ALT 239 or ALT 8745 | 2229 ALT X | Intersection | ∩ | ∩ | ∩ | U+2229 | Intersection | Elements of A that are in B: (A∈B)/A | ||
∪ | ALT 8746 | 222A ALT X | Union | ∪ | ∪ | ∪ | 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 | ∼ | ∼ | ∼ | 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 | ≠ | ≠ | ≠ | U+2260 | Not equal | Comparison: 1 if true, 0 if false | ||
≡ | ALT 240 or ALT 8801 | 2261 ALT X | Identical to | ≡ | ≡ | ≡ | 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 | ≢ | ≢ | ≢ | 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 | ≤ | ≤ | ≤ | 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 | ≥ | ≥ | ≥ | U+2265 | Greater than or equal | Comparison: 1 if true, 0 if false | ||
⊂ | ALT 8834 | 2282 ALT X | Subset of, included in set | ⊂ | ⊂ | ⊂ | 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 | ⊃ | ⊃ | ⊃ | 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 | ⊆ | ⊆ | ⊆ | U+2286 | Subset | Elements in both A and B: (∧/A∈B)∧(∧/B∈A) | ||
⊖ | ALT 8854 | 2296 ALT X | Circled minus, symmetric difference | ⊖ | ⊖ | ⊖ | 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 | ⊢ | ⊢ | ⊢ | 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 | ⊣ | ⊣ | ⊣ | U+22A3 | Stop | Discard argument and return empty matrix | Left | Discard B and pass A unchanged |
⊤ | ALT 8868 | 22A4 ALT X | Down tack, top | ⊤ | ⊤ | ⊤ | U+22A4 | Encode | Base-A representation of the value of B | ||
⊥ | ALT 8869 | 22A5 ALT X | Up tack, base, bottom | ⊥ | ⊥ | ⊥ | U+22A5 | Decode | Value of a polynomial whose coefficients are B at A | ||
⋄ | ALT 8900 | 22C4 ALT X | Diamond operator | ⋄ | ⋄ | ⋄ | U+22C4 | Statement separator | Separates multiple statements on a single line | ||
⋆ | ALT 8902 | 22C6 ALT X | Star operator | ⋆ | ⋆ | ⋆ | 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 | ⌈ | ⌈ | ⌈ | 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 | ⌉ | ⌉ | ⌉ | U+2309 | ||||
⌊ | ALT 8970 | 230A ALT X | Left floor, APL downstile | ⌊ | ⌊ | ⌊ | 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 | ⌋ | ⌋ | ⌋ | U+230B | ||||
◇ | ALT 9671 | 25C7 ALT X | White diamond | ◇ | ◇ | U+25C7 | |||||
○ | ALT 9675 | 25CB ALT X | White circle | ○ | ○ | ○ | 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) |
For more sets of math 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.