Everything about Algebraic function
Mathematical function
In mathematics, an algebraic function is a function that satisfies a polynomial equation. Thus an equation of the following form holds: where the are polynomials. Basic examples of algebraic functions are polynomial functions, rational functions, the nth root function, and functions obtained from these by composition and algebraic operations. Thus an example of an algebraic function is the function, whose graph is the top half of the standard unit circle. This function satisfies. Algebraic functions are contrasted with transcendental functions, such as the exponential function, logarithm, and the trigonometric functions. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Algebraic functionA 5-minute orientation
- Skim a recent paper: Algebraic function based Banach space valued ordinary and fractional neural network approximationsInfluential work since 2022
- Pick up a classic book: PrecalculusThe most-reprinted book on the subject
- Read the landmark paper: Algebraic technological function from a simulation modelCited 210 times
- Go sideways: Algebraic numberA closely related topic
- Go sideways: Algebraic equationA closely related topic
📖 Definitions
Noun Informally, any function expressible using (only) the operations of addition, subtraction, multiplication, division and raising to a rational power; more precisely, any continuous function definable as the root of some polynomial equation.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Algebraic technological function from a simulation model
ALGEBRAIC CURVES OVER FUNCTION FIELDS. I
Algebraic convergence of function groups
Excellent Nonlinear Codes From Algebraic Function Fields
Critical points of an algebraic function
Predicting transition with algebraic intermittency function
Algebraic independence of the values of elliptic function at algebraic points
On places of algebraic function fields.
🆕 Influential since 2022
Algebraic function based Banach space valued ordinary and fractional neural network approximations
An implicit function formulation for optimization of discretized index-1 differential algebraic systems
Vojta's abc conjecture for algebraic tori and applications over function fields
Algebraic Construction of the Sigma Function for General Weierstrass Curves
Assessment of an algebraic equilibrium wall-function for supercritical flows
📚 Books worth reading
PrecalculusRon Larson, Roland E. Larson · 1900
CalculusRon Larson · 1988
PrecalculusSheldon Jay Axler · 2007
Precalculus Functions And GraphsRon Larson · 1996
College algebraMichael Joseph Sullivan Jr., Michael Sullivan III · 1987
Precalculus With LimitsRon Larson · 1993
PrecalculusMichael Joseph Sullivan Jr., Michael Sullivan III · 1988
Functions and ChangeBruce Crauder · 1999
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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