# RadicalMembership

* © 2017 John Abbott, Anna M. Bigatti*

GNU Free Documentation License, Version 1.2

CoCoALib Documentation Index
## Examples

## User documentation

This file offers functions for testing membership in the radical
of an ideal. This can be done relatively cheaply compared to
actually computing a generating set for the radical.

### Queries and views

Let `I`

be an `ideal`

in a polynomial ring, and let `f`

be
an element of the same polynomial ring.

`IsInRadical(f,I)`

-- `true`

iff `f`

is in the radical of `I`

`MinPowerInIdeal(f,I)`

-- returns the smallest integer `n`

such that `power(f,n)`

is in `I`

; returns -1 if `f`

is not in the radical.

## Maintainer documentation

The implementation is straightforward (once you have learned the theory
about "Rabinowitch's Trick").

We can be slightly clever when the ideal is homogeneous.

## Bugs, shortcomings and other ideas

Can be terribly slow: see in test-RadicalMembership1.C for some commented
out cases.

## Main changes

**2017**

- July (v0.99560): first release