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Expression syntax are used to describe mathematical operations, functions and conditions in applets.

In the generic framework, there are predefined expressions for constants of functions that are used to describe the value of a number or function variable. Be aware that you shouldn't use these expressions as names of your variables, as this will cause problems.

Category | Syntax | Examples |
---|---|---|

Numbers | 0-9 | 1+2 |

Number Constants | pi, e | pi/2, e (~2.718...) |

Parentheses | () | (-x+1)*(x+2) |

Standard Operations | +,-,/,*,^ | 1+2, pi/2 |

Absolute value | abs(arg) or |arg| | abs(x), |

Trigonometric functions | sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, asinh, acosh, atanh | sin(2*pi), (cos(x))^2 |

Signum | sign(arg) | sign(x) = 1, x>0; sign(0)=0; sign(x)=-1,x<0 |

Theta | theta(arg) | theta(x) = 1,x>=0; theata(x)=0, x<0 |

Dirac delta function (1 for x = 0, 0 otherwise) | dirac(arg) | dirac(x) |

Exponential function | exp(x) or e^x | exp(2*x) |

If the number field is chosen to be *complex* or *complex-rational*, the imaginary unit is `i`

, and there are the functions `re`

and `im`

for the real and imaginary part, e.g. `re(1+2*i)`

and `im (1-i)`

.

This is used to described conditions, such as in \randadjustif or in generic visualization's \IFELSE command

It is basically a relation between the values of two Operations or function from the 1st category

Category | Syntax | Examples | Note |
---|---|---|---|

Equal | left=right | x=0, x=y, |(x)|=1 | is true if the value of the left side equals the value of the right side |

Not equal | left!=right | x!=0, x!=y | |

Greater than | left>right | x > y | |

Less than | left < right | x < y | |

Greater than or equal | left >=right | x >= y | |

Less than or equal | left <=right | x <= y, abs(x)<3, sin(x)<0.5 | |

Grouping brackets | [left>=right] | [abs(x)>3] AND [abs(x)<5] | use to group a relation |

Negation | NOT [left > right] | NOT [x = y] | negate the relation in the brackets, returns true if x != y |

AND | [cond1] AND [cond2] | [x>0] AND [x<3] | |

OR | [cond1] OR [cond2] | [x<0] OR [x>3] |

In a generic visualization, `var(arg)`

can be used in operations or conditions and it will be replaced by the value of

the variable with the name arg. Remember to write var as a function `var(x)`

and *not* as a Tex-command \var{x}.

12345 `\begin{variables}`

` `

`\randint{x}{-5}{5} %create two random integers`

` `

`\randint{y}{-5}{5} `

` `

`\point{p1}{real}{var(x),var(y)} %creates a point on (x,y) depending on the values of x and y.`

`\end{variables}`

Updated by **Ruedi Seiler**, **6 months ago **– a83d0e8