This note presents an algorithm which composes two reduced properly primitive binary quadratic forms of the same nonquadratic determinant D in ...
This note presents an algorithm which composes two reduced properly primitive binary quadratic forms of the same nonquadratic determinant D.
Analysis of an Algorithm for Composition of Binary Quadratic Forms · C. Iliopoulos · Published in J. Algorithms 1 June 1982 · Computer Science, Mathematics · J.
In 2004, Bhargava introduced a new way to understand the composition law of integral binary quadratic forms through what he calls the 'cubes of integers'.
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This book studies the theory of binary quadratic forms following an algorithmic approach. Applications of binary quadratic forms to cryptography are also ...
We will now discuss representations of integers by binary quadratic forms, which are expressions of the form ax2 + bxy + cy2 for fixed integers a,b,c.
As we shall show in j4, it is essentially enough to have a fast algorithm for size reduction of positive forms. (i.e.,. [a, b, c] with a, b, c > O) by means of.
One of the most famous results in elementary number theory is Fermat's theorem on sums of two squares. It states that an odd prime is the sum of two squares ...
The idea is to apply an invertible linear transformation simultaneously to a pair of opposite sides. For example, if one applies an invertible linear ...
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This paper provides an introduction to binary quadratic forms and to their properties relevant to application in the Chia VDF, and an efficient algorithm for ...