Feature #885: IsIrred3: fast 3-way irred test (returning bool3) - CoCoALib - CoCoA Project

Feature #885

IsIrred3: fast 3-way irred test (returning bool3)

Added by John Abbott about 8 years ago. Updated about 5 years ago.

Status:

In Progress

Priority:

Normal

Assignee:

Category:

New Function

Target version:

CoCoALib-1.0

Start date:

24 May 2016

Due date:

% Done:

10%

Estimated time:

Spent time:

0.75 h

Description

Implement an irreducibility test IsIrred3 which is guaranteed to be fast, but returns a bool3.

Related issues

History

#1 Updated by John Abbott about 8 years ago

Related to Design #846: IsIrred: correct design? added

#2 Updated by John Abbott about 8 years ago

Related to Slug #874: factor: too slow on largish multivariate poly added

#3 Updated by John Abbott about 8 years ago

Status changed from New to In Progress
% Done changed from 0 to 10

Some questions:

(A) what should the function be called? Is IsIrred3 a reasonable name?
(B) what should the function return? Just a bool3, or something more if a factor has been found?

Regarding (B) I am inclined to return just a bool3 as that seems to fit best the KISS philosophy.

Regarding (A) there are a number of other functions returning bool3 whose names have simply the suffix 3: for instance, IsMaximal3 and IsIntegralDomain3. So I think that IsIrred3 is a reasonable choice (but I'm willing to listen to other suggestions).

Presumably the normal IsIrred function should call IsIrred3 as a first step.

#4 Updated by John Abbott about 8 years ago

The idea of IsIrred3 was created because of some computations Mario needed to do with multivariate polynomials, so the idea is mostly oriented toward that application. In some other contexts there may be no obvious distinction between IsIrred and IsIrred3.

Since I see no universal impl of IsIrred3, I presume the impl will be via mem fns of rings (presumably called myIsIrred3). A valid implementation is to make myIsIrred3 return uncertain3 always; this could be a reasonable default impl.