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D.5.19 JMBTest_lib
- Library:
- JMBTest.lib
- Purpose:
- A library for Singular which performs JM basis test.
- Author:
- Michela Ceria, email: michela.ceria@unito.it
- 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 rp.
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:
See also:
JMSConst_lib.
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