Feature #644: Buchberger-Moeller: add option to stop as soon as 1 poly has been found - CoCoALib - CoCoA Project

Feature #644

Buchberger-Moeller: add option to stop as soon as 1 poly has been found

Added by John Abbott over 9 years ago. Updated over 6 years ago.

Status:

New

Priority:

Normal

Assignee:

John Abbott

Category:

New Function

Target version:

CoCoALib-1.0

Start date:

29 Oct 2014

Due date:

% Done:

Estimated time:

Spent time:

0.25 h

Description

Add option to compute just the first gen of an ideal of points. This may be useful for computing implicitizations (from random sample points).

History

#1 Updated by John Abbott over 9 years ago

I wonder whether this proposal is actually what we want.

I imagine that the intended use is:

generate (conceptually infinite) sequence of points by picking random values for the parameters
check whether (n+1)-th point satisfies the first poly from the gens of the ideal of the first n points
if so, return that poly as "probably the right answer"

However, it would be inefficient to compute the poly in step (2) from scratch every time; it would seem to be better to have a sort of incremental Buchberger-Moeller where a new point may be added after the computation has begun (but before finding the first generator). I suspect that such an incremental algorithm would be sufficiently different from standard BM that a separate implementation is indicated.