Engineering↗
Applications of the LLL Algorithm
Practical applications of lattice reduction: integer kernel and image computation, integer relation detection, recovering minimal polynomials from numerical approximations, and …
Tag
Linear Algebra & Lattices
Every page in the KEVOS library tagged Linear Algebra & Lattices. 7 pages.
Engineering↗
Gram–Schmidt Orthogonalisation
The Gram-Schmidt procedure, the mu coefficients and their role in reduction conditions, the numerical instability of the classical algorithm, and exact integral alternatives.
Engineering↗
Lattices and Quadratic Forms
Lattices as discrete subgroups, bases and unimodular change of basis, the Gram matrix and determinant, successive minima, and the correspondence with positive definite quadratic…
Engineering↗
Linear Algebra Algorithms over Fields and Rings
Exact Gaussian elimination, fraction-free elimination, determinant and characteristic polynomial algorithms, and kernel and image computation over fields and over ℤ.
Engineering↗
The Hermite Normal Form
Definition and uniqueness of the Hermite normal form, algorithms for computing it, entry explosion and its remedies, and its role as the representation of choice for modules and…
Engineering↗
The LLL Lattice Reduction Algorithm
The LLL algorithm: reduction conditions, the swap-and-reduce loop, the potential function that proves polynomial termination, quality guarantees, and the deep-insertion and floa…
Engineering↗
The Smith Normal Form and Its Applications
The Smith normal form, elementary divisors, the structure theorem for finitely generated abelian groups, and the application to class group structure determination.
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