Syntax:
FunctionName(argument1, argument2, ...)
Example:
Factorial(5)
cos(2*pi)
gcd(921,317)
To evaluate a function, enter the name of the function, followed by the arguments (if any) to the function in parentheses. This will return the result of applying the function to its arguments. The number of arguments to the function is, of course, different for each function.
There are many built-in functions, such as sin
, cos
and tan
. You can use the help
built-in command to get a list of available functions, or see Chapter 11, Liste des fonctions GEL for a full listing.
Vous pouvez utiliser la fonction de complétion à l'aide de la touche Tab pour que Genius complète les noms de fonction pour vous. Essayez de saisir les quelques premières lettres du nom et appuyez sur Tab
.
Les noms des fonctions sont sensibles à la casse. Cela signifie que les fonctions appelées fairecela
, FAIRECELA
et Fairecela
sont toutes différentes.
Syntax:
function <identifier>(<comma separated arguments>) = <function body>
<identifier> = (`() = <function body>)
The `
is the backquote character, and signifies an anonymous function. By setting it to a variable name you effectively define a function.
A function takes zero or more comma separated arguments, and returns the result of the function body. Defining your own functions is primarily a matter of convenience; one possible use is to have sets of functions defined in GEL files that Genius can load in order to make them available. Example:
function addup(a,b,c) = a+b+c
then addup(1,4,9)
yields 14
If you include ...
after the last argument name in the function declaration, then Genius will allow any number of arguments to be passed in place of that argument. If no arguments were passed then that argument will be set to null
. Otherwise, it will be a horizontal vector containing all the arguments. For example:
function f(a,b...) = b
Then f(1,2,3)
yields [2,3]
, while f(1)
yields a null
.
Dans Genius, il est possible de transmettre une fonction comme argument d'une autre fonction. Cela peut être fait en utilisant soit des « nœuds de fonction », soit des fonctions anonymes.
If you do not enter the parentheses after a function name, instead of being evaluated, the function will instead be returned as a ‘function node’. The function node can then be passed to another function. Example:
function f(a,b) = a(b)+1;
function b(x) = x*x;
f(b,2)
To pass functions that are not defined, you can use an anonymous function (see the section called “Définition de fonctions”). That is, you want to pass a function without giving it a name. Syntax:
function(<comma separated arguments>) = <function body>
`(<comma separated arguments>) = <function body>
Example:
function f(a,b) = a(b)+1;
f(`(x) = x*x,2)
This will return 5.
Some functions allow arithmetic operations, and some single argument functions such as exp
or ln
, to operate on the function. For example,
exp(sin*cos+4)
will return a function that takes x
and returns exp(sin(x)*cos(x)+4)
. It is functionally equivalent
to typing
`(x) = exp(sin(x)*cos(x)+4)
This operation can be useful when quickly defining functions. For example to create a function called f
to perform the above operation, you can just type:
f = exp(sin*cos+4)
It can also be used in plotting. For example, to plot sin squared you can enter:
LinePlot(sin^2)
Toutes les fonctions ne peuvent pas être utilisées de cette façon. Par exemple, lorsque vous utilisez une opération binaire, les fonctions doivent prendre le même nombre d'arguments.