## Variable definitions

A **variable** is a sequence of symbols. Allowed symbols are letters, digits, and the underscore. The first symbol must be a letter.

You can create a definition using the symbol **:=**.

my_variable:= 2x^2-3x+4

Note that the definition does not have to be a number, but can be any mathematical expression.

## Operators

The following table lists the basic math operators

Symbol | Operation |
---|---|

* | Multiplication. See remark 1) |

/ | Division |

+ | Addition |

– | Subtraction |

^ | Power |

=, >, <, >=, <=, <> | Relational symbols (not evaluated) |

==, >>, <<, >>=, <<=, <<>> | Relational symbols (evaluated, see remark 2) |

- The multiplication symbol is optional. So 3x is interpreted as 3*x. However, ab is interpreted as the variable ‘ab’ and not as a*b. You should add a times symbol or an extra space if you intend the multiplication.
- The relational symbols =, >, <, <=, and >= are used to construct mathematical relations without evaluating them. E.g. x^2=2x is an equation, whereas 2==3 is an expression that will be evaluated as False.

## Constants

Constant | Description |
---|---|

True, False | Boolean constants |

Pi | The number π |

EulerE | Euler’s constant e |

NaN | Not-a-number |

{} | The empty set |

## Constructions

The scripting language of AlgebraKiT defines the following constructions to build expressions:

Construction | Description |
---|---|

( ) | Parenthesis |

[ ] | Function arguments |

{ } | List |

` ` | Toggle between text (HTML) and math |

[[ ]] | List index |

Some examples:

Expression | Description |
---|---|

Sin[2 x] | The sine of 2x |

v:= {1, 2a, x^y} | Define variable v as a list of 3 items |

v[[2]] | Take the 2nd element of the list (which is 2a in this case). Note that the first element has index 1, not 0. |

Text[`this is a text`] | A command that contains text |

## Some essential commands

The complete list of commands can be found in the Syntax guide. The following table lists the commands that are used most often.

Command | Description | Example |
---|---|---|

Simplify | Apply mathematical rules to simplify the expression as much as possible. | Simplify[1*x*x] gives x^2 |

RandomInt | Generate a random integer number within a range. | RandomInt[2,10] gives an integer number in the range 2 to 10. |

RandSelect | Select a random element from the list | RandSelect[{1,x,2y}] gives one of the three items in the list. |

Strict | Evaluate a boolean expression. An undetermined expression will result in False | Strict[3>>2] gives True Strict[x>>y] gives False |

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