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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. ...

A Tschirnhausen transformation can be used to algebraically transform a general quintic equation to the form z^5+c_1z+c_0=0. (1) In practice, the general quintic is first ...

A homogeneous polynomial in two or more variables.

A clear-cut way of describing every object in a class in a one-to-one manner.

A one-dimensional geometric object such as a pencil or line segment range.

A 1-form omega=sum_(i=1)^na_i(x)dx_i such that omega=0.

An expression built up from statements letters by appropriate application of connectives (Mendelson 1997, p. 13).

A 1-form w is said to be exact in a region R if there is a function f that is defined and of class C^1 (i.e., is once continuously differentiable in R) and such that df=w.

Consider the forms Q for which the generic characters chi_i(Q) are equal to some preassigned array of signs e_i=1 or -1, e_1,e_2,...,e_r, subject to product_(i=1)^(r)e_i=1. ...

All elementary functions can be extended to the complex plane. Such definitions agree with the real definitions on the x-axis and constitute an analytic continuation.