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Trigonometric functions of npi/13 for n an integer cannot be expressed in terms of sums, products, and finite root extractions on real rational numbers because 13 is not a ...

A root-finding algorithm which converges to a complex root from any starting position. To motivate the formula, consider an nth order polynomial and its derivatives, P_n(x) = ...

A field K is said to be algebraically closed if every polynomial with coefficients in K has a root in K.

A Lie algebra over an algebraically closed field is called exceptional if it is constructed from one of the root systems E_6, E_7, E_8, F_4, and G_2 by the Chevalley ...

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

R^- denotes the real negative numbers.

R^+ denotes the real positive numbers.

The operator I^~ which takes a real number to the same real number I^~r=r.

An extension F of a field K is said to be algebraic if every element of F is algebraic over K (i.e., is the root of a nonzero polynomial with coefficients in K).

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