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### 2.3 Sets

A set consists in a finite ordered list of points. Thus a set can also be seen as an open path of line segments or as a polygon.

A set of two points is considered as a single line segment. When a parameter is expected to be a segment, any subsequent point is ignored.

#### Set operators

`s.t`

  Concatenates s and t. Each operand can be either a set or a point.

`s[i]`

  Point of index i in variable s, assuming s contains a set. Indices start at 0.

#### Set related functions

`set(P)`

  Singleton containing point P.

`card(s)`

  Number of elements of set s.

`length(s)`

  Length of path s.

`perimeter(s)`

  Perimeter of polygon s.

`area(s)`

  Area enclosed by polygon s, provided s is not self-intersecting.

`arg(s)`

  Polar angle of segment s (in degrees).

`point(s, x)`

  Point of abscissa x on an axis containing segment s. The point is on segment s when x ranges from 0 to 1.

`midpoint(s)`

  Midpoint of segment s.

`bisector(s)`

  Perpendicular bisector of segment s.

`isobarycenter(s)`

  Isobarycenter of set s.

`centroid(s)`

  Centroid of polygon s.

`element(s, i)`

  Point of index i in set s.

`vector(s)`

  Vector going from first to second point of segment s.

`sub(s, i, j)`

  Subset of set s from index i to j.

`polygon(n, O, r, a)`
`pentagon(O, r, a)`
`hexagon(O, r, a)`

  Vertices of a n-sided (or 5-sided or 6-sided) convex regular polygon of center O. The first point has (r, a) as polar coordinates with respect to O. The vertices are ordered anticlockwise.

#### Set constant

`empty`

  Empty set.

#### Set related assignments

Each element of a variable containing a set may be modified individually using its index enclosed in square brackets.

Example: `S[1] = point(2, pi/3)`

When using empty square brackets, the given point is added to the tail of the set.

Example: `S[] = point(0, 0)`

Several elements of a set may be assigned at once to a dot separated list of variables. Exceeding points, if any, are ignored.

Example: `A.B.C.D.E = pentagon(O, 1, 0°)`

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