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A number which can be specified implicitly or explicitly by exponential, logarithmic, and algebraic operations.

One of the operations of addition, subtraction, multiplication, division, and integer (or rational) root extraction.

The parallel curves for (outward) offset k of an ellipse with semi-axis lengths a and b are given by x_p = (a+(bk)/(sqrt(a^2sin^2t+b^2cos^2t)))cost (1) y_p = ...

An even Mathieu function ce_r(z,q) with characteristic value a_r.

An odd Mathieu function se_r(z,q) with characteristic value a_r.

Schubert's application of the conservation of number principle.

A bounded operator U on a Hilbert space H is called essentially unitary if U^*U-I and UU^*-I are compact operators.

A more common way to describe a Euclidean ring.

For any real alpha and beta such that beta>alpha, let p(alpha)!=0 and p(beta)!=0 be real polynomials of degree n, and v(x) denote the number of sign changes in the sequence ...

A finite extension K=Q(z)(w) of the field Q(z) of rational functions in the indeterminate z, i.e., w is a root of a polynomial a_0+a_1alpha+a_2alpha^2+...+a_nalpha^n, where ...