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Algebraic function. In mathematics, an algebraic function is a function that can be defined as the root of an irreducible polynomial equation. Algebraic functions are often algebraic expressions using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional ...
The integral of the Dirac delta function. Saw-tooth wave. Square wave. Triangle wave. Rectangular function. Floor function: Largest integer less than or equal to a given number. Ceiling function: Smallest integer larger than or equal to a given number. Sign function: Returns only the sign of a number, as +1 or −1.
Lambda calculus is Turing complete, that is, it is a universal model of computation that can be used to simulate any Turing machine. [ 3 ] Its namesake, the Greek letter lambda (λ), is used in lambda expressions and lambda terms to denote binding a variable in a function. Lambda calculus may be untyped or typed.
An expression like 1/2x is interpreted as 1/(2x) by TI-82, [3] as well as many modern Casio calculators [36] (configurable on some like the fx-9750GIII), but as (1/2)x by TI-83 and every other TI calculator released since 1996, [37] [3] as well as by all Hewlett-Packard calculators with algebraic notation.
Fundamental theorem of algebra. The fundamental theorem of algebra, also called d'Alembert's theorem[1] or the d'Alembert–Gauss theorem, [2] states that every non- constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex ...
An algebraic number is a number that is a root of a non-zero polynomial (of finite degree) 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 x2 − x − 1. That is, it is a value for x for which the polynomial evaluates to zero.
Computational complexity of mathematical operations. Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations. Here, complexity refers to the time ...
Rational functions are quotients of two polynomial functions, and their domain is the real numbers with a finite number of them removed to avoid division by zero. The simplest rational function is the function x ↦ 1 x , {\displaystyle x\mapsto {\frac {1}{x}},} whose graph is a hyperbola , and whose domain is the whole real line except for 0.
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