Table of Contents
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.
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.
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)
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
).
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
.
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
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.