Engineering↗
Continued Fraction Expansions
Simple continued fractions, convergent recurrences and best-approximation properties, Lagrange's periodicity theorem, and the expansion of a square root used for Pell's equation…
Tag
Foundational Algorithms
Every page in the KEVOS library tagged Foundational Algorithms. 9 pages.
Engineering↗
Integer Square Roots and Perfect Power Detection
Computing exact integer square roots by Newton's method, fast rejection of non-squares by modular filters, and detection of perfect powers and prime powers.
Engineering↗
Legendre, Jacobi and Kronecker Symbols
Quadratic residues, Euler's criterion, the Legendre symbol, its Jacobi and Kronecker extensions, and the reciprocity-based algorithm that evaluates them in logarithmic time.
Engineering↗
Modular Exponentiation and Powering Algorithms
Left-to-right and right-to-left binary powering, sliding window exponentiation, addition chains, and the generic monoid formulation that makes one routine serve many algebraic s…
Engineering↗
Multiprecision Integer Arithmetic
Representation of multiprecision integers, schoolbook and fast multiplication, division, modular reduction strategies, and how to choose the right base ring for a computation.
Engineering↗
Solving Polynomial Equations Modulo p
Root-finding modulo a prime: the gcd with x^p − x, equal-degree splitting by random shifts, and the special low-degree cases that admit closed forms.
Engineering↗
Square Roots Modulo a Prime
Computing modular square roots: the p ≡ 3 (mod 4) shortcut, the Tonelli–Shanks algorithm and its 2-adic structure, and Cornacchia's algorithm for x² + dy² = p.
Engineering↗
The Euclidean Algorithm and GCD Computation
Euclid's algorithm and its worst case, the binary GCD, Lehmer's method for multiprecision operands, and how to choose between them by operand size.
Engineering↗
The Extended Euclidean Algorithm and Modular Inverses
The extended Euclidean algorithm, its loop invariants, half-extended variants, modular inversion, and rational reconstruction from a partial remainder sequence.
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mathematics 387
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algebra handbook 85
graduate mathematics 85
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templates and examples 78
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universal algebra 62
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project delivery 60
principles of project management 58
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Fasteners and Joints 53
Civil Engineering 48
CAD 42
Context and scope 42
Machine Elements 40
Threading and Gaging 37
Mechanical Engineering 35
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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