Bug #1248: MinPolyQuot: guaranteed and ideal without GBasis - CoCoALib - CoCoA Project

Bug #1248

MinPolyQuot: guaranteed and ideal without GBasis

Added by John Abbott about 5 years ago. Updated over 4 years ago.

Status:

Closed

Priority:

High

Assignee:

Anna Maria Bigatti

Category:

Maths Bugs

Target version:

CoCoALib-0.99650 November 2019

Start date:

01 Mar 2019

Due date:

% Done:

100%

Estimated time:

Spent time:

1.60 h

Description

Today we noticed that ex-Verification1 failed. What happened is that MinPolyQuot was called with a (principal) ideal without a G-basis. Comparison was made between the result obtained with VerificationLevel set to 0, set to 2 and set to "guaranteed".

The answer was wrong with "guaranteed".

Fix this!

Related issues

History

#1 Updated by John Abbott about 5 years ago

The cause was an incompatibility:

(A) if the ideal supplied has no G-basis then verification was disabled (since verification would entail computing a G-basis, which might be very costly)
(B) if the VerificationLevel is set to guaranteed then the result should always be correct.

Anna asks what should happen of the caller does not specify what VerificationLevel to use? Previously the heuristic (A) was used.

#2 Updated by John Abbott about 5 years ago

Related to Support #1240: John's visit Feb 2019 added

#3 Updated by John Abbott about 5 years ago

Related to Feature #1103: Pseudo-zero-dim ideals added

#4 Updated by John Abbott about 5 years ago

For min polys it might be possible to work with a sub-ideal in a subring. For example,

use QQ[x,y,z,t];
I := ideal(x^2-2, y^3-3, z^5-5);
f := x+y;
MinPolyQuot(f,I,x);

------ this comment has been converted into Feature #1254 ------

#5 Updated by John Abbott about 5 years ago

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

Two more comments:

(1) my preference is that computations in CoCoALib be guaranteed correct unless the caller explicitly says otherwise (e.g. by specifying a finite VerificationLevel).
(2) I forgot to mention that in the case that a guaranteed answer is desired and the ideal has no GBasis, MinPolyQuot could perhaps map the ideal into another ring with DegRevLex, and compute the min poly there (because computing a GBasis in the original ring might be costly if the term-ordering is inconvenient)

#6 Updated by John Abbott about 5 years ago

The CoCoA-5 test test-ApproxSolve.cocoa5 failed with wrong output: there should have been no output, instead a warning about "no precomputed GBasis" is printed 88 times!

This should be fixed.