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In mathematics, an algebraic expression is an expression built up from constants (usually, rational or algebraic numbers) variables, and the basic algebraic operations: addition (+), subtraction (-), multiplication (×), division (÷), whole number powers, and roots (fractional powers).
Rational function. In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K.
Algebraic fraction. In algebra, an algebraic fraction is a fraction whose numerator and denominator are algebraic expressions. Two examples of algebraic fractions are and . Algebraic fractions are subject to the same laws as arithmetic fractions . A rational fraction is an algebraic fraction whose numerator and denominator are both polynomials.
Algebraic equation. In mathematics, an algebraic equation or polynomial equation is an equation of the form , where P is a polynomial with coefficients in some field, often the field of the rational numbers. For example, is an algebraic equation with integer coefficients and. is a multivariate polynomial equation over the rationals.
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 following is a list of integrals ( antiderivative functions) of rational functions. Any rational function can be integrated by partial fraction decomposition of the function into a sum of functions of the form: , and. which can then be integrated term by term. For other types of functions, see lists of integrals . Miscellaneous integrands.
An algebraic expression is an expression built up from algebraic constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by a rational number). [10] For example, 3x 2 − 2xy + c is an algebraic expression.
In calculus and mathematical analysis, algebraic operation is also used for the operations that may be defined by purely algebraic methods. For example, exponentiation with an integer or rational exponent is an algebraic operation, but not the general exponentiation with a real or complex exponent. Also, the derivative is an operation that is ...
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