Numbers

To compute usual arithmetical operations, use the symbols: (, ), +, -, *, /, ^ (for exponentiation).

There's a C-like ternary test operator using the symbols ? and |. To perform a test one may use the following comparison and logical operators: ==, !=, <=, >=, <, >, and, or, not.

The available numerical functions are: abs(x), min(x), max(x), clamp(x, y, z) (which returns x if y<=x<=z, y if x<y, z if x>z), sign(x), (which returns -1 if x<0, 0 if x=0, 1 if x>0), ceil(x), floor(x), round(x), sqrt(x), exp(x), ln(x), sin(x), cos(x), tan(x), asin(x), acos(x), atan(x), deg(x) (to convert radians in degrees), rad(x) (to convert degrees in radians).

There is one constant: pi.

Next, the following number valued functions are also available:

• abscissa(A) or abscissa(u)
• ordinate(A) or ordinate(u)
• distance(A, B) or distance(A, l)
• length(u) or length(s)
• radius(c)
• major(cc)
  Half of the major axis if cc is an ellipse; half of the real axis if cc is an hyperbola; semifocal chord if cc is a parabola.
• minor(cc)
  Half of the minor axis if cc is an ellipse; half of the imaginary axis if cc is an hyperbola; zero if cc is a parabola.
• eccentricity(cc)
• arg(c, A)
  Argument of point A in respect of circle c. If A isn't on c, arg returns the argument of the image of A by a projection on c in the direction of its center.
• arg(cc, A)
  Argument of point A in respect of the internal parametric representation of cc. If A isn't on cc, arg returns the argument of the image of A by a projection on cc. The direction of the projection is the one of the principal axis if cc is a parabola, of the center if cc is an ellipse, of the major axis if cc is an hyperbola.
• height(A, B, C)
  Distance between point B and line AC.

Last, there are all the angle measure functions. The result is in degrees. Eukleides handles directed angles, hence angle returns a signed number greater than -180° and smaller than or equal to 180°.

• angle(u) or angle(l) or angle(s)
  Polar angle of the object.
• angle(cc)
  Polar angle of the principal axis of conic curve cc.
• angle(u, v)
  Measure of the angle between vector u and vector v.
• angle(A, B, C)
  Measure of the angle under ABC. (The angle under ABC is the angular sector in which one can draw counterclockwise an arc of center B from point A to line BC. Therefore the angle under ABC is different from the angle under CBA.)