Engineering↗
Detecting Algebraic and Linear Dependence with LLL
Recovering exact integer relations from numerical approximations using LLL, and the precision requirements that make the method reliable.
Tag
LLL
Every page in the KEVOS library tagged LLL. 10 pages.
Engineering↗
Factoring Polynomials over the Integers
The modular-lift-recombine pipeline, the exponential recombination problem, and the LLL-based algorithm that makes factorisation polynomial time.
Engineering↗
Ideal Reduction in Number Fields
Finding a small ideal in a given ideal class by lattice reduction, and why reduction is the enabling step for relation collection.
Engineering↗
Integer Kernel and Image via LLL
Computing a reduced basis of the integer kernel and image of a matrix, and why this is not the same as clearing denominators from a rational kernel.
Engineering↗
LLL for Linearly Dependent Generating Sets
Extending LLL to generating sets that are not independent, and using the resulting zero vectors to extract relations.
Engineering↗
LLL-Based Hermite Normal Form Computation
Using lattice reduction to control entry growth during Hermite normal form computation, and when this beats the modular approach.
Engineering↗
The LLL Lattice Basis Reduction Algorithm
The LLL algorithm: size reduction interleaved with swaps under the Lovasz condition, and the guarantees it provides in polynomial time.
Engineering↗
The LLL Lattice Basis Reduction Algorithm
The LLL algorithm: size reduction interleaved with swaps under the Lovasz condition, and the guarantees it provides in polynomial time.
Engineering↗
The Polynomial Reduction Algorithm
Finding a small defining polynomial for a number field using lattice reduction on the maximal order, and why this pays for itself.
Engineering↗
The Subfield Problem
Finding the subfields of a number field, by lattice methods and by linear algebra over the complex numbers.
Related
Other tags in the library.
mathematics 387
abstract algebra 252
Machine Design 184
business 179
project management 158
Computational Number Theory 123
algebra handbook 85
graduate mathematics 85
handbook 79
templates and examples 78
History of Engineering 77
Manufacturing 76
algebra and trigonometry 74
universal algebra 62
algebra 60
project delivery 60
principles of project management 58
advanced algebra 53
Fasteners and Joints 53
Civil Engineering 48
CAD 42
Context and scope 42
Machine Elements 40
Threading and Gaging 37
Mechanical Engineering 35
Power Transmission 34
template 34
Operational Excellence 32
example 31
project leadership 31
project teams 31
strategy 31
Business Expansion 29
Metrology 29
project management research 29
Sales & Marketing 29
personal development 27
behaviour change 26
habits 26
systems 26