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An algebraic equation is an equation involving polynomials, for which algebraic expressions may be solutions. If you restrict your set of constants to be numbers, any algebraic expression can be called an arithmetic expression. However, algebraic expressions can be used on more abstract objects such as in Abstract algebra.
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). [41] For example, 3x 2 − 2xy + c is an algebraic expression.
A rational fraction is the quotient (algebraic fraction) of two polynomials. Any algebraic expression that can be rewritten as a rational fraction is a rational function. While polynomial functions are defined for all values of the variables, a rational function is defined only for the values of the variables for which the denominator is not zero.
Algebraic notation describes the rules and conventions for writing mathematical expressions, as well as the terminology used for talking about parts of expressions. For example, the expression + has the following components: Algebraic expression notation: 1 – power (exponent) 2 – coefficient 3 – term
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.
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 ...
A function that is not transcendental is algebraic. Simple examples of algebraic functions are the rational functions and the square root function, but in general, algebraic functions cannot be defined as finite formulas of the elementary functions, as shown by the example above with () + = (see Abel–Ruffini theorem).
An algebraic integer is an algebraic number that is a root of a polynomial with integer coefficients with leading coefficient 1 (a monic polynomial). Examples of algebraic integers are 5 + 13 2 , {\displaystyle 5+13{\sqrt {2}},} 2 − 6 i , {\displaystyle 2-6i,} and 1 2 ( 1 + i 3 ) . {\textstyle {\frac {1}{2}}(1+i{\sqrt {3}}).}