New order bounds in differential elimination algorithms

@article{Gustavson2016NewOB,
  title={New order bounds in differential elimination algorithms},
  author={Richard Gustavson and Alexey Ovchinnikov and Gleb Pogudin},
  journal={J. Symb. Comput.},
  year={2016},
  volume={85},
  pages={128-147}
}
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8 Citations
Background Citations
4
Methods Citations
3
Results Citations
1

8 Citations

New order bounds in di ff erential elimination algorithms I

A new upper bound for the orders of derivatives in the Rosenfeld-Gröbner algorithm under weighted rankings is presented, achieved by associating to the algorithm antichain sequences whose lengths can be bounded using the results of León Sánchez and Ovchinnikov.

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Differential Elimination and Algebraic Invariants of Polynomial Dynamical Systems

The eliminationtheoretic Rosenfeld-Gröbner algorithm is adapted to systematically obtain algebraic invariants of polynomial dynamical systems without using GröBner bases or quantifier elimination.

Elimination for Systems of Algebraic Differential Equations

References

SHOWING 1-10 OF 26 REFERENCES

Bounds for Orders of Derivatives in Differential Elimination Algorithms

An upper bound for the orders of derivatives in the Rosenfeld-Grobner algorithm is computed by associating to the algorithm antichain sequences whose lengths can be bounded using the results of Leon Sanchez and Ovchinnikov.

A bound for the Rosenfeld-Gröbner algorithm

New effective differential Nullstellensatz

Computing representations for radicals of finitely generated differential ideals

This paper deals with systems of polynomial differential equations, ordinary or with partial derivatives. The embedding theory is the differential algebra of Ritt and Kolchin. We describe an…

A bound for orders in differential Nullstellensatz

Effective uniform bounding in partial differential fields

Involutive Algorithms for Computing Groebner Bases

An involutive algorithm for construct- ing Gröbner bases of polynomial ideals based on the concept of involutive monomial division which restricts the conventional division in a certain way is described.

Representation for the radical of a finitely generated differential ideal

An algorithm is given which represents the radical J of a finitely generated differential ideal as an intersection of radical differential ideals and provides an algorithm for testing membership in J.

On bounds for the effective differential Nullstellensatz

Symbolic and Numerical Scientific Computation

This is the first in a series of two tutorial articles devoted to triangulation-decomposition algorithms, addressing here polynomial systems and some of the material here will be used in the second part, devoted to differential systems.