Chapter 5. Fondamentaux GEL
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# Chapter 5. Fondamentaux GEL

GEL stands for Genius Extension Language. It is the language you use to write programs in Genius. A program in GEL is simply an expression that evaluates to a number, a matrix, or another object in GEL. Genius Mathematics Tool can be used as a simple calculator, or as a powerful theoretical research tool. The syntax is meant to have as shallow of a learning curve as possible, especially for use as a calculator.

## Types de données

Values in GEL can be numbers, Booleans, or strings. GEL also treats matrices as values. Values can be used in calculations, assigned to variables and returned from functions, among other uses.

### Nombres

Integers are the first type of number in GEL. Integers are written in the normal way.

    1234

Hexadecimal and octal numbers can be written using C notation. For example:

    0x123ABC
    01234

Or you can type numbers in an arbitrary base using `<base>\<number>`. Digits higher than 10 use letters in a similar way to hexadecimal. For example, a number in base 23 could be written:

    23\1234ABCD

The second type of GEL number is rationals. Rationals are simply achieved by dividing two integers. So one could write:

    3/4

to get three quarters. Rationals also accept mixed fraction notation. So in order to get one and three tenths you could write:

    1 3/10

The next type of number is floating point. These are entered in a similar fashion to C notation. You can use `E`, `e` or `@` as the exponent delimiter. Note that using the exponent delimiter gives a float even if there is no decimal point in the number. Examples:

    1.315
    7.887e77
    7.887e-77
    .3
    0.3
    77e5

When Genius prints a floating point number it will always append a `.0` even if the number is whole. This is to indicate that floating point numbers are taken as imprecise quantities. When a number is written in the scientific notation, it is always a floating point number and thus Genius does not print the `.0`.

The final type of number in GEL is the complex numbers. You can enter a complex number as a sum of real and imaginary parts. To add an imaginary part, append an `i`. Here are examples of entering complex numbers:

    1+2i
    8.01i
    77*e^(1.3i)

### Important

Lorsque vous saisissez des nombres imaginaires, il doit y avoir un nombre devant le `i`. Si vous utilisez `i` tout seul, Genius l'interprète comme une référence à la variable `i`. Si vous avez besoin de faire référence à `i` tout seul, utilisez `1i` à la place.

Afin de pouvoir utiliser la notation en fraction mixte avec des nombres imaginaires, vous devez mettre la fraction mixte entre parenthèses (par exemple, `(1 2/5)i`).

### Booléens

Genius prend également en charge nativement les données booléennes. Les deux constantes booléennes sont `true` (vrai) et `false` (faux) ; ces identifiants peuvent être utilisés comme n'importe quelle autre variable. Vous pouvez aussi utiliser les identifiants `True`, `TRUE`, `False` et `FALSE` comme alias de ces précédents.

Là où une expression booléenne est attendue, vous pouvez utiliser une grandeur booléenne ou toute expression qui produit soit un nombre soit un booléen. Si Genius a besoin d'évaluer un nombre en tant que booléen, il interprète 0 comme `false` et tout autre nombre comme `true`.

In addition, you can do arithmetic with Boolean values. For example:

    ( (1 + true) - false ) * true

is the same as:

    ( (true or true) or not false ) and true

Only addition, subtraction and multiplication are supported. If you mix numbers with Booleans in an expression then the numbers are converted to Booleans as described above. This means that, for example:

    1 == true

always evaluates to `true` since 1 will be converted to `true` before being compared to `true`.

### Chaînes de caractères

Like numbers and Booleans, strings in GEL can be stored as values inside variables and passed to functions. You can also concatenate a string with another value using the plus operator. For example:

    a=2+3;"The result is: "+a

will create the string:

    The result is: 5

You can also use C-like escape sequences such as `\n`,`\t`,`\b`,`\a` and `\r`. To get a `\` or `"` into the string you can quote it with a `\`. For example:

    "Slash: \\ Quotes: \" Tabs: \t1\t2\t3"

will make a string:

    Slash: \ Quotes: " Tabs: 	1	2	3

Do note however that when a string is returned from a function, escapes are quoted, so that the output can be used as input. If you wish to print the string as it is (without escapes), use the `print` or `printn` functions.

In addition, you can use the library function `string` to convert anything to a string. For example:

    string(22)

will return

    "22"

Strings can also be compared with `==` (equal), `!=` (not equal) and `<=>` (comparison) operators

### Null

There is a special value called `null`. No operations can be performed on it, and nothing is printed when it is returned. Therefore, `null` is useful when you do not want output from an expression. The value `null` can be obtained as an expression when you type `.`, the constant `null` or nothing. By nothing we mean that if you end an expression with a separator `;`, it is equivalent to ending it with a separator followed by a `null`.

Example:

    x=5;.
    x=5;

Certaines fonctions renvoient `null` quand aucune valeur ne peut être renvoyée ou quand une erreur survient. La grandeur `null` est aussi utilisée comme vecteur ou matrice vide ou comme une référence vide.

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