Efficiency estimate for distributed computation of Gröbner bases and involutive bases

D. A. Yanovich

doi:10.1134/s036176880804004x

Efficiency estimate for distributed computation of Gröbner bases and involutive bases

Programming and Computer Software ◽

10.1134/s036176880804004x ◽

2008 ◽

Vol 34 (4) ◽

pp. 210-215 ◽

Cited By ~ 1

Author(s):

D. A. Yanovich

Keyword(s):

Gröbner Bases ◽

Distributed Computation ◽

Grobner Bases ◽

Efficiency Estimate ◽

Involutive Bases

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

ACM Communications in Computer Algebra ◽

10.1145/3511528.3511537 ◽

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].

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Computing Gröbner and Involutive Bases for Linear Systems of Difference Equations

EPJ Web of Conferences ◽

10.1051/epjconf/201817305018 ◽

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.

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