In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). For example, 3x 2 − 2xy + c is an algebraic expression. Since taking the square root is the same as raising to the power 1 / 2, …

An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients.For example, the golden ratio, (+) /, is an algebraic number, because it is a root of the polynomial x 2 − x − 1.That is, it is a value for x for which the polynomial evaluates to zero. As another example, the complex number + is algebraic …

Pre-history. Galois' theory originated in the study of symmetric functions – the coefficients of a monic polynomial are (up to sign) the elementary symmetric polynomials in the roots. For instance, (x – a)(x – b) = x 2 – (a + b)x + ab, where 1, a + b and ab are the elementary polynomials of degree 0, 1 and 2 in two variables. This was first formalized by the 16th-century …

A regex processor translates a regular expression in the above syntax into an internal representation that can be executed and matched against a string representing the text being searched in. One possible approach is the Thompson's construction algorithm to construct a nondeterministic finite automaton (NFA), which is then made deterministic and the resulting …

In mathematics, a cubic function is a function of the form () = + + + where the coefficients a, b, c, and d are complex numbers, and the variable x takes real values, and .In other words, it is both a polynomial function of degree three, and a real function.In particular, the domain and the codomain are the set of the real numbers.. Setting f(x) = 0 produces a cubic equation of the form

The Quine–McCluskey algorithm (QMC), also known as the method of prime implicants, is a method used for minimization of Boolean functions that was developed by Willard V. Quine in 1952 and extended by Edward J. McCluskey in 1956. As a general principle this approach had already been demonstrated by the logician Hugh McColl in 1878, was proved by Archie Blake …

If the acute angle θ is given, then any right triangles that have an angle of θ are similar to each other. This means that the ratio of any two side lengths depends only on θ.Thus these six ratios define six functions of θ, which are the trigonometric functions.In the following definitions, the hypotenuse is the length of the side opposite the right angle, opposite represents the side ...

Algebraic expression. The n th roots of unity are, by definition, the roots of the polynomial x n − 1, and are thus algebraic numbers. As this polynomial is not irreducible (except for n = 1), the primitive n th roots of unity are roots of an irreducible polynomial of lower degree, called the n th cyclotomic polynomial, and often denoted Φ n.

Infix notation is a method where unary operations are input into the calculator in the same order as they are written on paper. Different forms of this input scheme exist. In the algebraic entry system with hierarchy (AESH), the precedence of basic mathematical operators is taken into account, whereas calculators with algebraic entry system with parentheses (AESP) support …

Large-signal modelling Shockley diode model. The Shockley diode equation relates the diode current of a p-n junction diode to the diode voltage .This relationship is the diode I-V characteristic: = (), where is the saturation current or scale current of the diode (the magnitude of the current that flows for negative in excess of a few , typically 10 −12 A).