# BuchbergerMoeller

* © 2013 John Abbott*

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`

.
`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