Syntax to define a mathematical function

In a mathematical function, used for example in field definition, it’s possible to use the predifined function (an object parser is used to evaluate the functions) :

ABS	absolute value function
COS	cosine function
SIN	sine function
TAN	tangent function
ATAN	arctangent function
EXP	exponential function
LN	natural logarithm function
SQRT	square root function
INT	integer function
ERF	error function
RND(x)	random function (values between 0 and x)
COSH	hyperbolic cosine function
SINH	hyperbolic sine function
TANH	hyperbolic tangent function
ACOS	inverse cosine function
ASIN	inverse sine function
ATANH	inverse hyperbolic tangent function
NOT(x)	NOT x (returns 1 if x is false, 0 otherwise)
SGN(x)	SGN x (returns 1 if x is positive, -1 if negative, 0 if zero)
x_AND_y	boolean logical operation AND (returns 1 if both x and y are true, else 0)
x_OR_y	boolean logical operation OR (returns 1 if x or y is true, else 0)
x_GT_y	greater than (returns 1 if \(x>y\), else 0)
x_GE_y	greater than or equal to
x_LT_y	less than (returns 1 if x<y, else 0)
x_LE_y	less than or equal to
x_MIN_y	returns the smallest of x and y
x_MAX_y	returns the largest of x and y
x_MOD_y	modular division of x per y
x_EQ_y	equal to (returns 1 if x==y, else 0)
x_NEQ_y	not equal to (returns 1 if x!=y, else 0)

You can also use the following operations:

+	addition
-	subtraction
/	division
*	multiplication
%	modulo
$	max
^	power
<	less than
>	greater than
[	less than or equal to
]	greater than or equal to

You can also use the following constants:

Pi	pi value (3,1415…)

The variables which can be used are:

x,y,z	coordinates
t	time

Examples:

Champ_front_fonc_txyz 2 cos(y+x^2) t+ln(y)

Champ_fonc_xyz dom 2 tanh(4*y)*(0.95+0.1*rnd(1)) 0.

Possible errors:

Error 1:

Champ_fonc_txyz 1 cos(10*t)*(1<x<2)*(1<y<2)

Previous line is wrong. It should be written as:

Champ_fonc_txyz 1 cos(10*t)*(1<x)*(x<2)*(1<y)*(y<2)

Error 2:

Champ_front_fonc_xyz 1 20*(x<-2)+10*(y]-5)+3*(z>0)

Previous line is wrong because negative values are not written between parentheses. It should be written as:

Champ_front_fonc_xyz 1 20*(x<(-2))+10*(y](-5))+3*(z>0)