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Inhaltsverzeichnis
Functions
General
+
A binlary operator which calculates the sum of two variables. The following combinations of argument types are allowed:
argument 1 | argument 2 | result |
---|---|---|
integer | integer | integer |
double | double | double |
integer | double | double |
double | integer | double |
integer | complex | complex |
double | complex | complex |
complex | complex | complex |
complex | integer | complex |
complex | double | complex |
3d vector | 3d vector | 3d vector |
3d matrix | 3d matrix | 3d matrix |
Example
A + B
-
This unary operator changes the sign of the given argument. For matrix argument the matrix inverse is determined.
Types:
Argument | Result |
---|---|
integer | integer |
double | double |
complex | complex |
3d vector | 3d vector |
3d matrix | 3d matrix |
Examples
-A
*
/
abs()
This named function calculates the absolute value of the variable give as argument.
Types:
Argument | Result |
---|---|
integer | integer |
double | double |
complex | complex |
Examples
abs(A) abs(-3)
log()
ln()
mod()
sqr()
sqrt()
real()
im()
pow()
Trigometric
acos()
This named function determines the acrcos tangens of the given argument.
Argument | Result |
---|---|
integer | double |
double | double |
complex | double |
Examples
acos(a)
asin()
This named function determines the arcos sinus of the given argument.
Types:
Argument | Result |
---|---|
integer | double |
double | double |
complex | double |
Examples
asin(A)
asinh()
This named function determines the arcos sinus hyperbolicus of the given argument.
Types:
Argument | Result |
---|---|
integer | double |
double | double |
complex | double |
Examples
asinh(A)
acosh()
This named function determines the acrcos tangens hyperbolicos of the given argument.
Types:
Argument | Result |
---|---|
integer | double |
double | double |
complex | complex |
Examples
acosh(a)
asin'
This named function determines the first derivative of the arcos sinus of the given argument: 1d/(sqrt(1d-x*x))
Types:
Argument | result |
---|---|
integer | double |
double | double |
complex | double |
Examples
asin'(A)
asin''
This named function determines the second derivative of the arcos sinus of the given argument: x/pow(1-x*x, 1.5).
Types:
Argument | result |
---|---|
integer | double |
double | double |
complex | double |
Examples
asin''(A)
3d
dot()
Determination of the dot product of two given 3d vectors.
Types:
Argument 1 | Argument 2 | Result |
---|---|---|
3d vector | 3d vector |
Examples
dot(A,B)
length()
Determination of the length of a given 3d vector.
Types:
Argument | Result |
---|---|
3d vector | double |
Examples
length(A)
lengthSqr()
Determination of the length square of a given 3d vector.
Types:
Argument | Result |
---|---|
3d vector | double |
Examples
length(A)
vec()
This named function bundles the three double arguments to a 3d vector result value.
Types:
Argument 1 | Argument 2 | Argument 3 | Result |
---|---|---|---|
double | double | double | 3d vector |
Examples
vec(x,y,z)
angle2()
This named function with three arguments calculates the angle between arrows defined by the first two arguments. The third argument is used to define the sign of the resulting angle. It is interpreted as an arrow which defines the rotation direction to rotate the arrow from the first argument to the arrow of the second argument. If this results in angles more than 180 degrees a negativ angle is given instead.
Types:
Argument 1 | Argument 2 | Argument 3 | Result |
---|---|---|---|
3d vector | 3d vector | 3d vector | double |
Examples
angle2(A,B,t)
angle()
This named function with two arguments calculates the so called atan2(x, y) if the arguments are of the type double. 3d vector arguments are interpreted as arrows and the angle between the two arrows are calculated.
Types:
Argument 1 | Argument 2 | Result |
---|---|---|
double | double | double |
3d vector | 3d vector | double |
Examples
angle(A,B)
align()
If the vectors of both arguments are directed in the same half-space this named function results in a double value of -1, else +1.
Types:
Argument 1 | Argument 2 | Result |
---|---|---|
3d vector | 3d vector | double (-1 or +1) |