## 8 Citations

### New order bounds in di ff erential elimination algorithms I

- Mathematics, Computer Science
- 2017

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.

### On the algorithmic linearizability of nonlinear ordinary differential equations

- Mathematics, Computer ScienceJ. Symb. Comput.
- 2020

### Computer-assisted proofs of congruences for multipartitions and divisor function convolutions, based on methods of differential algebra

- MathematicsThe Ramanujan Journal
- 2021

This paper provides elementary proofs for several types of congruences involving multipartitions and self-convolutions of the divisor function. Our computations use differential algebra and Gröbner…

### Computer-assisted proofs of congruences for multipartitions and divisor function convolutions, based on methods of differential algebra

- Materials ScienceThe Ramanujan Journal
- 2021

This paper provides elementary proofs for several types of congruences involving multipartitions and self-convolutions of the divisor function. Our computations use differential algebra and Gröbner…

### Some Classical Models of Particles and Quantum Gauge Theories

- PhysicsQuantum Reports
- 2022

The article contains a review and new results of some mathematical models relevant to the interpretation of quantum mechanics and emulating well-known quantum gauge theories, such as scalar…

### Welding studs detection based on line structured light

- PhysicsInternational Conference on Optical Instruments and Technology
- 2018

A welding stud detection method based on line structured light is proposed and experimental results demonstrate that the error rate of proposed method is lower than 0.1%, which is applied for automobile manufacturing.

### Differential Elimination and Algebraic Invariants of Polynomial Dynamical Systems

- Mathematics, Computer Science
- 2023

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

## References

SHOWING 1-10 OF 26 REFERENCES

### Bounds for Orders of Derivatives in Differential Elimination Algorithms

- Mathematics, Computer ScienceISSAC
- 2016

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.

### Computing representations for radicals of finitely generated differential ideals

- MathematicsApplicable Algebra in Engineering, Communication and Computing
- 2009

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…

### Involutive Algorithms for Computing Groebner Bases

- Computer Science
- 2005

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

- MathematicsISSAC '95
- 1995

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.

### Symbolic and Numerical Scientific Computation

- Mathematics, Computer ScienceLecture Notes in Computer Science
- 2003

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.