GenericPoints

GenericPoints

random projective points

Syntax

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

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 ::= QQ[x,y];  GenericPoints(R,7);
[[1, 0], [0, 1], [1, 1], [12, 59], [6, 63], [12, 80], [17, 63]]

/**/  GenericPoints(R,7,500);
[[1, 0], [0, 1], [1, 1], [220, 162], [206, 452], [98, 106], [403, 449]]

/**/  Use R ::= ZZ/(5)[x,y,z];
/**/  GenericPoints(R,7);
[[1, 0, 0], [0, 1, 0], [0, 0, 1], [1, 1, 1], [2, 1, 1], [2, 2, 4], [3, 1, 3]]

/**/  GenericPoints(R,7,500);
[[1, 0, 0], [0, 1, 0], [0, 0, 1], [1, 1, 1], [1, 4, 2], [1, 3, 2], [2, 3, 3]]