Cellular reductions of the Pommaret-Seiler resolution for Quasi-stable ideals

2021 ◽  
Vol 55 (3) ◽  
pp. 102-106
Author(s):  
Rodrigo Iglesias ◽  
Eduardo Sáenz de Cabezón
Keyword(s):  
Algebraic Geometry ◽  
Commutative Algebra ◽  
Gröbner Bases ◽  
Grobner Bases ◽  
Combinatorial Properties ◽  
Pommaret Bases ◽  
Involutive Bases

Involutive bases were introduced in [6] as a type of Gröbner bases with additional combinatorial properties. Pommaret bases are a particular kind of involutive bases with strong relations to commutative algebra and algebraic geometry[11, 12].

scholarly journals Gröbner Bases and Algebraic Geometry

1998 ◽  
pp. 109-143 ◽  
Author(s):  
Gert-Martin Greuel ◽  
Gerhard Pfister
Keyword(s):  
Algebraic Geometry ◽  
Gröbner Bases ◽  
Grobner Bases

scholarly journals Computing Gröbner and Involutive Bases for Linear Systems of Difference Equations

2018 ◽  
Vol 173 ◽  
pp. 05018
Author(s):  
Denis Yanovich
Keyword(s):  
Linear Systems ◽  
Difference Equations ◽  
Gröbner Bases ◽  
Grobner Bases ◽  
Parallel Version ◽  
Mathematical Problems ◽  
Involutive Bases

The computation of involutive bases and Gröbner bases for linear systems of difference equations is solved and its importance for physical and mathematical problems is discussed. The algorithm and issues concerning its implementation in C are presented and calculation times are compared with the competing programs. The paper ends with consideration on the parallel version of this implementation and its scalability.

scholarly journals An Algebraic Approach to Identifiability

Algorithms ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 255
Author(s):  
Daniel Gerbet ◽  
Klaus Röbenack
Keyword(s):  
Algebraic Geometry ◽  
State Space ◽  
Differential Algebra ◽  
Gröbner Bases ◽  
Algebraic Approach ◽  
Grobner Bases ◽  
Space Systems ◽  
Input Output ◽  
Polynomial Ideals ◽  
State Space Systems

This paper addresses the problem of identifiability of nonlinear polynomial state-space systems. Such systems have already been studied via the input-output equations, a description that, in general, requires differential algebra. The authors use a different algebraic approach, which is based on distinguishability and observability. Employing techniques from algebraic geometry such as polynomial ideals and Gröbner bases, local as well as global results are derived. The methods are illustrated on some example systems.

scholarly journals Gröbner bases and involutive bases

Algebra ◽  
2012 ◽  
Author(s):  
Α. V. Astrelin ◽  
O. D. Golubitsky ◽  
Ε. V. Pankratiev
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases ◽  
Involutive Bases
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