CoCoA:GenericPoints

GenericPoints

random projective points

Description

GenericPoints returns a list of NumPoints generic projective points

with integer coordinates; it is not guaranteed that these points are

distinct. RandomRange specifies the largest value any coordinate may take. If the second argument is omitted, the largest value possible is 100 (or P-1 where P is the characteristic of the coefficient ring).

Example

  Use R ::= Q[x,y];GenericPoints(7);
[[1, 0], [0, 1], [1, 1], [12, 59], [6, 63], [12, 80], [17, 63]]
-------------------------------
  GenericPoints(7,500);
[[1, 0], [0, 1], [1, 1], [220, 162], [206, 452], [98, 106], [403, 449]]
-------------------------------
  Use R ::= Z/(5)[x,y,z];
  GenericPoints(7);
[[1, 0, 0], [0, 1, 0], [0, 0, 1], [1, 1, 1], [2, 1, 1], [2, 2, 4], [3, 1, 3]]
-------------------------------
  GenericPoints(7,500);
[[1, 0, 0], [0, 1, 0], [0, 0, 1], [1, 1, 1], [1, 4, 2], [1, 3, 2], [2, 3, 3]]
-------------------------------

Syntax

GenericPoints(NumPoints:INT):LIST
GenericPoints(NumPoints:INT,RandomRange:INT):LIST

   <type>integer</type>
   <type>list</type>
   <type>points</type>