Construction of Janet Bases I. Monomial Bases
Algorithms for computation of Janet bases for monomial ideals and implementation of these algorithms are presented and an algorithm for construction of a Janet basis for the ideal generated by a finite monomial set is described.
Fast Search for the Janet Divisor
An algorithm for fast search for the involutive monomial Janet divisor is suggested. Such search is an important part of the construction of monomial and polynomial Janet bases. For a data structure…
Construction of Janet Bases II. Polynomial Bases
Effectiveness of involutive criteria in computation of polynomial Janet bases
The results of this study are that the role of the criteria in an involutive algorithm is not as important as in the Buchberger algorithm, and also that these criteria affect the growth of intermediate coefficients.
Computation of Involutive and Gröbner Bases Using the Tableau Representation of Polynomials
- D. Yanovich
- Computer Science, MathematicsProgramming and computer software
- 1 March 2020
An attempt to give a new look on the representation of polynomials for computing involutive and Gröbner bases of systems of nonlinear polynomial equations is made.
Experimental Analysis of Involutive Criteria
The experimental study shows that the role of criteria in the involutive approach is definitely weaker than that in Buchberger’s algorithm.
Parallel computation of Janet and Gröbner bases over rational numbers
The algorithm discussed is an improved version of an earlier suggested parallel algorithm for computation of polynomial Janet bases that is illustrated by way of the standard test examples that are often used for comparing various algorithms and codes for computing Gröbner bases.
Parallelization of an Algorithm for Computation of Involutive Janet Bases
- D. Yanovich
- Computer ScienceProgramming and computer software
- 1 March 2002
Results of parallelization of modular computations on a two-processor computer are presented and an involutive algorithm for computation of Janet bases for polynomial ideals is considered.
Parallel modular computation of Gröbner and involutive bases
- D. Yanovich
- MathematicsProgramming and computer software
- 1 March 2013
An overview of an algorithm and an efficient implementation of parallel computing of involutive and Gröbner bases with the help of modular operations is presented. Difficulties arising in modulo…
New exact solutions for polynomial oscillators in large dimensions
A new type of exact solvability is reported. The Schrodinger equation is considered in a very large spatial dimension D 1 and its central polynomial potential is allowed to depend on 'many' ( = 2q)…