# BuchbergerMoeller

© 2013 John Abbott
GNU Free Documentation License, Version 1.2

- Examples
- User documentation
  - Operations
- Maintainer documentation
- Bugs, shortcomings and other ideas
- Main changes

CoCoALib Documentation Index

## Examples

- ex-empty.C

## 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`.
- `BM(P,pts)` computes the reduced Groebner basis of the vanishing ideal in `P` of the points `pts`;

## 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).

The name `BM` is too short?

## Main changes

2013

- January (v0.9953): first release