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Given a general quadratic curve Ax^2+Bxy+Cy^2+Dx+Ey+F=0, (1) the quantity X is known as the discriminant, where X=B^2-4AC, (2) and is invariant under rotation. Using the ...

The determinant of a binary quadratic form Au^2+2Buv+Cv^2 is defined as D=AC-B^2. It is equal to 1/4 of the corresponding binary quadratic form discriminant. Unfortunately, ...

The discriminant of a binary quadratic form au^2+buv+cv^2 is defined by d=4ac-b^2. It is equal to four times the corresponding binary quadratic form determinant. ...

The use of three prior points in a root-finding algorithm to estimate the zero crossing.

A transformation of a hypergeometric function,

A quadratic form Q(x) is said to be positive semidefinite if it is never <0. However, unlike a positive definite quadratic form, there may exist a x!=0 such that the form is ...

Let pi_(m,n)(x) denote the number of primes <=x which are congruent to n modulo m (i.e., the modular prime counting function). Then one might expect that ...

The function f(beta,z)|->z^((1+cosbeta+isinbeta)/2), illustrated above for beta=0.4.

If f:(X,A)->(Y,B) is homotopic to g:(X,A)->(Y,B), then f_*:H_n(X,A)->H_n(Y,B) and g_*:H_n(X,A)->H_n(Y,B) are said to be the induced maps.

The binary quadratic form F=<a,b,c> is said to be reduced if the following conditions hold. Let D=b^2-4ac be the discriminant, then 1. If D is negative, F is reduced if ...