A5028867902- Polynomial and algebraic computation
- Coding theory and cryptography
- Algebraic Geometry and Number Theory
- Cryptography and Residue Arithmetic
- Commutative Algebra and Its Applications
- Finite Group Theory Research
- Advanced Topics in Algebra
- Matrix Theory and Algorithms
- Algebraic structures and combinatorial models
- Earthquake Detection and Analysis
- Geometric and Algebraic Topology
- Historical and Archaeological Studies
- Photonic and Optical Devices
- Synthesis and properties of polymers
- Seismology and Earthquake Studies
- Advanced Combinatorial Mathematics
- Seismic Waves and Analysis
- Advanced Algebra and Geometry
- Melanoma and MAPK Pathways
The University of Sydney
1997-2019
We prove that van Hoeij's original algorithm to factor univariate polynomials over the rationals runs in polynomial time, as well natural variants. In particular, our approach also yields time complexity results for bivariate a finite field.
Let K be a global field and f in K[X] polynomial. We present an efficient algorithm which factors polynomial time.
We show how some very large multivariate polynomial systems over finite fields can be solved by Gröbner basis techniques coupled with the Block Wiedemann algorithm, thus extending Wiedemann-based 'Sparse FGLM' approach of Faugère and Mou. The main components our are a dense variant F4 algorithm which have been implemented within Magma Computer Algebra System (released in version V2.20 late 2014). A major feature algorithms is that they map much computation to matrix multiplication, this...