Sentence examples for binary quadratic form from inspiring English sources

A simple calculation with these matrices resulted in a binary quadratic form.

The archetypal example of an invariant is the discriminant B2 − 4AC of a binary quadratic form Ax2 + Bxy + Cy2.

Write a quadratic partial fraction and equate it to a variable, say z Then by straight forward manipulation show that this partial fraction can be transformed into a binary quadratic form.

From the three ways of slicing the cube, three binary quadratic forms emerged.

Gauss was interested in binary quadratic forms, which are polynomials ax2+bxy+cy2, where a, b, and c are integers.

In the Disquisitiones, Gauss developed his ingenious composition law, which gives a method for composing two binary quadratic forms to obtain a third one.

Up until this time, mathematicians had looked upon Gauss's composition law as a curiosity that happened only with binary quadratic forms.

Euclid's algorithm, fundamental theorems on divisibility; prime numbers; congruence of numbers; theorems of Fermat, Euler, Wilson; congruences of first and higher degrees; quadratic residues; introduction to the theory of binary quadratic forms; quadratic reciprocity; partitions.

Usually includes most of the following topics: the Euclidean algorithm, continued fractions, Pythagorean triples, Diophantine equations such as Pell's equation, congruences, quadratic reciprocity, binary quadratic forms, Gaussian integers, and factorization in quadratic number fields.

A classical fact in number theory states that the narrow class group of a quadratic number field of discriminant D is in bijection with the SL_2(Z) equivalence classes of integral binary quadratic forms of discriminant D. In this talk, I will explain a generalization of this presented in Bhargava's dissertation.

Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer invented ideals and the theory of cyclotomic fields in his attempt to prove Fermat's Last Theorem.