# 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. Currently the **points must be distinct.**

### 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