D.5.19 JMBTest_lib

Library:

JMBTest.lib

Purpose:

A library for Singular which performs JM basis test.

Author:

Michela Ceria, email: [email protected]

Overview:

The library performs the J-marked basis test, as described in [CR], [BCLR]. Such a test is performed via the criterion explained in [BCLR], concerning Eliahou-Kervaire polynomials (EK from now on). We point out that all the polynomials are homogeneous and they must be arranged by degree.
The fundamental steps are the following:
-construct the Vm polynomials, via the algorithm VConstructor explained in [CR];
-construct the Eliahou-Kervaire polynomials defined in [BCLR];
-reduce the Eliahou-Kervaire polynomials using the Vm's;
-if it exist an Eliahou-Kervaire polynomial such that its reduction mod Vm is different from zero, the given one is not a J-Marked basis.

The algorithm terminates only if the ordering is ip. Anyway, the number of reduction steps is bounded.

References:

[CR] Francesca Cioffi, Margherita Roggero,Flat Families by Strongly Stable Ideals and a Generalization of Groebner Bases, J. Symbolic Comput. 46, 1070-1084, (2011).
[BCLR] Cristina Bertone, Francesca Cioffi, Paolo Lella, Margherita Roggero, Upgraded methods for the effective computation of marked schemes on a strongly stable ideal, Journal of Symbolic Computation
(2012), http://dx.doi.org/10.1016/j.jsc.2012.07.006

Procedures:

D.5.19.1 Minimus		minimal variable in an ideal
D.5.19.2 Maximus		maximal variable in an ideal
D.5.19.3 StartOrderingV		ordering of polynomials as in [BCLR]
D.5.19.4 TestJMark		tests whether we have a J-marked basis