What does algebraic function mean?
Definitions for algebraic function
al·ge·bra·ic func·tion
This dictionary definitions page includes all the possible meanings, example usage and translations of the word algebraic function.
Wiktionary
algebraic functionnoun
Any function that only uses the operations of addition, subtraction, multiplication, division and raising to a rational power
Wikidata
Algebraic function
In mathematics, an algebraic function is a function that can be expressed using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power. An algebraic function in one variable x is a function that satisfies a polynomial equation where the coefficients ai(x) are polynomial functions of x. A function that is not algebraic is called a transcendental function. In more precise terms, an algebraic function may not be a function at all, at least not in the conventional sense. Consider for example the equation of the unit circle: This determines y, except only up to an overall sign: However, both branches are thought of as belonging to the "function" determined by the polynomial equation. Thus an algebraic function is most naturally considered as a multiple valued function. An algebraic function in n variables is similarly defined as a function y which solves a polynomial equation in n + 1 variables: It is normally assumed that p should be an irreducible polynomial. The existence of an algebraic function is then guaranteed by the implicit function theorem. Formally, an algebraic function in n variables over the field K is an element of the algebraic closure of the field of rational functions K. In order to understand algebraic functions as functions, it becomes necessary to introduce ideas relating to Riemann surfaces or more generally algebraic varieties, and sheaf theory.
Numerology
Chaldean Numerology
The numerical value of algebraic function in Chaldean Numerology is: 6
Pythagorean Numerology
The numerical value of algebraic function in Pythagorean Numerology is: 7
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"algebraic function." Definitions.net. STANDS4 LLC, 2024. Web. 26 Apr. 2024. <https://www.definitions.net/definition/algebraic+function>.
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