IdealOfPoints

© 2013,2017 John Abbott, Anna M. Bigatti

GNU Free Documentation License, Version 1.2

CoCoALib Documentation Index

Examples

User documentation

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.

Operations

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.

Maintainer documentation

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.

Bugs, shortcomings and other ideas

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).

Main changes

2021

  • November (v0.99718): added doc for IdealOfProjectivePoints

2017

  • February (v0.99543): added an example

2013

  • January (v0.9953): first release