# ExpressionSyntaxForGenericApplets¶

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

## 1.Expression for math functions¶

In Genericframework these expressions are used to describe the value of a number or function variables.

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

Numbers | 0-9 | 1+2 |

$\pi$ | pi | pi/2 |

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

Standard Operations | +,-,/,*,^,sqrt(x) | 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+2) |

Theta | theta(arg) | theta(x) |

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

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

Floor | floor | floor(x) |

Faculty | fac or ! | fac(2) or 2! |

Nth root | x#n | x#4, 8#3 |

## 2.Expression for conditions¶

This is used to described conditions, such as in \randadjustif or in the GenericVisualizations \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] |

## 3.Special syntax in generic problems¶

## 4.Special syntax in GenericVisualization¶

### Using other variables with var()¶

In GenericVisualization, 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}).

... \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} ...