Engineering↗
Reduction of Indefinite Forms and the Cycle Structure
Reduction of indefinite binary forms, the cycle of reduced forms in each class, and how the cycle encodes the regulator.
Every page in the KEVOS library tagged Continued Fraction. 5 pages.
Reduction of indefinite binary forms, the cycle of reduced forms in each class, and how the cycle encodes the regulator.
SQUFOF: factoring by finding a square form in the cycle of an indefinite quadratic form, and why it excels for small inputs.
CFRAC: generating small quadratic residues from the continued fraction expansion, and the congruence-of-squares framework it established.
Computing the fundamental unit of a real quadratic field by continued fractions, its connection to the Pell equation, and its size.
The SQUFOF algorithm: continued fraction expansion of the square root, square forms, the reverse cycle, multipliers, and why it excels in a narrow but important range.