# Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems

@article{Buchberger1970EinAK, title={Ein algorithmisches Kriterium f{\"u}r die L{\"o}sbarkeit eines algebraischen Gleichungssystems}, author={Bruno Buchberger}, journal={aequationes mathematicae}, year={1970}, volume={4}, pages={374-383} }

## 106 Citations

### Application of Gröbner bases to the resolution of systems of norm equations

- Computer ScienceISSAC '91
- 1991

Permission to copy without fee all or part of this material is that copying is by permission of the Association for Computing granted provided that the copies are not made or distributed for…

### Analytic solution of GPS atmospheric sounding refraction angles

- Physics
- 2004

The nonlinear system of equations for solving GPS atmospheric sounding’s bending angles are normally solved using Newton’s method. Because of the nonlinear nature of the equations, Newton’s method…

### Effective computation of the Gelfand-Kirillov dimension

- MathematicsProceedings of the Edinburgh Mathematical Society
- 1997

In this note we propose an effective method based on the computation of a Gröbner basis of a left ideal to calculate the Gelfand-Kirillov dimension of modules.

### Generalized Gröbner Bases: Theory and Applications. A Condensation

- Mathematics, Computer ScienceRTA
- 1989

An abstract rewriting characterization of generalized Grobner bases is developed and used to give new proofs of the Spear-Zacharias and Trinks theorems for testing and constructing generalized GroBner bases.

### Testing Binomiality of Chemical Reaction Networks Using Comprehensive Gröbner System

- MathematicsCASC
- 2021

This work makes automatic computations on n−site phosphorylations and biomodels from the Biomodels repository using the grobcov library of the computer algebra system Singular to approach the binomiality problem using Comprehensive Gröbner systems.

### Wiener path integral most probable path determination: A computational algebraic geometry solution treatment

- MathematicsMechanical Systems and Signal Processing
- 2021

### A Gröbner-Shirshov basis over a special type of braid monoids

- Mathematics
- 2020

The aim of this paper is to present a Grobner-Shirshov basis for a special type of braid monoids, namely the symmetric inverse monoid In, in terms of the dex-leg ordering on the related elements of…

### Why you cannot even hope to use Gröbner bases in cryptography: an eternal golden braid of failures

- Computer Science, MathematicsApplicable Algebra in Engineering, Communication and Computing
- 2020

A further generalization is proposed and it is shown that such protocols can be broken simply via polynomial division and Buchberger reduction.