The functions here are for computing generators of the vanishing ideal of a set of points (i.e. all polynomials which vanish at all of the points).
The functions expect two parameters: a polynomial ring P, and a set of points pts.
The coordinates of the points must reside in the coefficient ring of P.
The points are represented as a matrix: each point corresponds to a row. Currently the points must be distinct.
The main functions available are:
IdealOfPoints(P,pts) computes the vanishing ideal in P of the points pts.
IdealOfProjectivePoints(P,pts) computes the vanishing ideal in P of the points pts.
The parameter P must be a polyring over a field.
The parameter pts is a matrix where each row corresponds to
one point; the coordinates of the points must belong to the
coefficient field of the polyring P.
Both functions compute an ideal whose generators are the reduced Groebner basis for the ideal.
Impl is simple/clean rather than fast.
There was a minor complication to handle the case where the dim of the space in which the points live is less than the number of indets in the polyring.
2013-01-21 there is only a generic impl (which is simple but inefficient).
There was a fn called BM; it is now commented out (don't know why).
2021
IdealOfProjectivePoints
2017
2013