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 | β | Least integer greater than or equal to B |

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

Shape | β΄ | Number of components in each dimension of B |

Not | βΌ | Logical: βΌ1 is 0, βΌ0 is 1 |

Absolute value | β£ | Magnitude of B |

Index generator | β³ | Vector of the first B integers |

Exponential | β | e to the B power |

Negation | β | Changes sign of B |

Identity | + | No change to B |

Signum | Γ | Β―1 if B<0; 0 if B=0; 1 if B>0 |

Reciprocal | Γ· | 1 divided by B |

Ravel | , | Reshapes B into a vector |

Matrix inverse | βΉ | Inverse of matrix B |

Pi times | β | Multiply by Ο |

Logarithm | β | Natural logarithm of B |

Reversal | β½ | Reverse elements of B along last axis |

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

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

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

Execute | β | Execute an APL expression |

Monadic format | β | A character representation of B |

Monadic transpose | β | Reverse the axes of B |

Factorial | ! | Product of integers 1 to B |

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

Add | + | Sum of A and B |

Subtract | β | A minus B |

Multiply | Γ | A multiplied by B |

Divide | Γ· | A divided by B |

Exponentiation | β | A raised to the B power |

Circle | β | 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 | β | 1 for elements of A present in B; 0 where not. |

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

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

Reshape | β΄ | Array of shape A with data B |

Take | β | Select the first (or last) A elements of B according to ΓA |

Drop | β | Remove the first (or last) A elements of B according to ΓA |

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

Encode | β€ | Base-A representation of the value of B |

Residue | β£ | 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 | β³ | The location (index) of B in A; 1+β/β³β΄A if not found |

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

Rotation | β½ | The elements of B are rotated A positions |

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

Logarithm | β | Logarithm of B to base A |

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

General transpose | β | 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 | β€ | Comparison: 1 if true, 0 if false |

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

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

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

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

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

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

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

Nand | β² | 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) | βΏ | +βΏB | Sum down B |

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

Scan (first axis) | β | +βB | Running sum down B |

Inner product | β | A+.ΓB | Matrix product of A and B |

Outer product | β | Aβ.ΓB | Outer product of A and B |

Sample APL source code: apl_cgi_script.apl

How to Create a APL or Math Symbols Keyboard Layout β¨

For full detail, see: APL syntax and symbols

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