This page is a list of of APL symbol's meanings.

Name | Notation | Meaning |
---|---|---|

Roll | ? | One integer selected randomly from the first B integers |

Ceiling | ⌈ | Least integer greater than or equal to B |

Floor | ⌊ | Greatest integer less than or equal to B |

Shape | ⍴ | Number of components in each dimension of B |

Not | ∼ | Logical: ∼1 is 0, ∼0 is 1 |

Absolute value | ∣ | Magnitude of B |

Index generator | ⍳ | Vector of the first B integers |

Exponential | ⋆ | e to the B power |

Negation | − | Changes sign of B |

Identity | + | No change to B |

Signum | × | ¯1 if B<0; 0 if B=0; 1 if B>0 |

Reciprocal | ÷ | 1 divided by B |

Ravel | , | Reshapes B into a vector |

Matrix inverse | ⌹ | Inverse of matrix B |

Pi times | ○ | Multiply by π |

Logarithm | ⍟ | Natural logarithm of B |

Reversal | ⌽ | Reverse elements of B along last axis |

Reversal | ⊖ | Reverse elements of B along first axis |

Grade up | ⍋ | Indices of B which will arrange B in ascending order |

Grade down | ⍒ | Indices of B which will arrange B in descending order |

Execute | ⍎ | Execute an APL expression |

Monadic format | ⍕ | A character representation of B |

Monadic transpose | ⍉ | Reverse the axes of B |

Factorial | ! | Product of integers 1 to B |

Name | Notation | Meaning |
---|---|---|

Add | + | Sum of A and B |

Subtract | − | A minus B |

Multiply | × | A multiplied by B |

Divide | ÷ | A divided by B |

Exponentiation | ⋆ | A raised to the B power |

Circle | ○ | Trigonometric functions of B selected by A. A=1: sin(B) A=2: cos(B) A=3: tan(B) |

Deal | ? | A distinct integers selected randomly from the first B integers |

Membership | ∈ | 1 for elements of A present in B; 0 where not. |

Maximum | ⌈ | The greater value of A or B |

Minimum | ⌊ | The smaller value of A or B |

Reshape | ⍴ | Array of shape A with data B |

Take | ↑ | Select the first (or last) A elements of B according to ×A |

Drop | ↓ | Remove the first (or last) A elements of B according to ×A |

Decode | ⊥ | Value of a polynomial whose coefficients are B at A |

Encode | ⊤ | Base-A representation of the value of B |

Residue | ∣ | B modulo A |

Catenation | , | Elements of B appended to the elements of A |

Expansion | \ | Insert zeros (or blanks) in B corresponding to zeros in A |

Compression | / | Select elements in B corresponding to ones in A |

Index of | ⍳ | The location (index) of B in A; 1+⌈/⍳⍴A if not found |

Matrix divide | ⌹ | Solution to system of linear equations Ax = B |

Rotation | ⌽ | The elements of B are rotated A positions |

Rotation | ⊖ | The elements of B are rotated A positions along the first axis |

Logarithm | ⍟ | Logarithm of B to base A |

Dyadic format | ⍕ | Format B into a character matrix according to A |

General transpose | ⍉ | The axes of B are ordered by A |

Combinations | ! | Number of combinations of B taken A at a time |

Less than | < | Comparison: 1 if true, 0 if false |

Less than or equal | ≤ | Comparison: 1 if true, 0 if false |

Equal | = | Comparison: 1 if true, 0 if false |

Greater than or equal | ≥ | Comparison: 1 if true, 0 if false |

Greater than | > | Comparison: 1 if true, 0 if false |

Not equal | ≠ | Comparison: 1 if true, 0 if false |

Or | ∨ | Logic: 0 if A and B are 0; 1 otherwise |

And | ∧ | Logic: 1 if A and B are 1; 0 otherwise |

Nor | ⍱ | Logic: 1 if both A and B are 0; otherwise 0 |

Nand | ⍲ | Logic: 0 if both A and B are 1; otherwise 1 |

Name | Symbol | Example | Meaning (of example) |
---|---|---|---|

Reduce (last axis) | / | +/B | Sum across B |

Reduce (first axis) | ⌿ | +⌿B | Sum down B |

Scan (last axis) | \ | +\B | Running sum across B |

Scan (first axis) | ⍀ | +⍀B | Running sum down B |

Inner product | ◇ | A+.×B | Matrix product of A and B |

Outer product | ∘ | A∘.×B | Outer product of A and B |

Sample APL source code: apl_cgi_script.apl

How to Create a APL or Math Symbols Keyboard Layout ⌨

For full detail, see: APL syntax and symbols

- Unicode Support in Ruby, Perl, Python, JavaScript, Java, Emacs Lisp, Mathematica
- Problems of Symbol Congestion in Computer Languages; ASCII Jam vs Unicode
- Vector Normalize Function in Mathematica, APL, Haskell, Ruby, Python, Perl, Lisp, JavaScript, Java, …
- Semantic of Symbols: HTML Entities, Ampersand, Unicode
- Syntax Design: Use of Unicode Matching Brackets as Specialized Delimiters
- Syntax Semantics Design: Use of Unicode Ellipsis Symbol vs Dot Dot Dot
- URL Percent Encoding and Unicode
- Unicode Semantics: the Ɐ in Turn A Gundam