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# Algebraic curve

## Explanation

Algebraic curve: In mathematics, an algebraic curve or plane algebraic curve is the set of points on the Euclidean plane whose coordinates are zeros of some polynomial in two variables.

• also known as 代數曲線

## Printed dictionaries and other books with definitions for Algebraic curve

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### Elementary Geometry of Algebraic Curves (1998)

An Undergraduate Introduction by C. G. Gibson

A real algebraic curve is a non-zero real polynomial /, up to multiplication by a non-zero scalar.

### Linear Algebraic Groups (2012)

by Armand Borel

An algebraic curve is an algebraic variety of dimension 1. In the discussion to follow we shall assume that all algebraic varieties are irreducible. (a) An algebraic curve is smooth if and only if it is normal. (b) Let L be a finitely generated field ...

### Geometry of Curves (2000)

by J.W. Rutter

An algebraic curve is a curve which is determined by some polynomial equation lxy =0 in x and y. The degree of the curve is the degree of the polynomial used to define it. In Chapter 2 we gave a complete classification, up to rotation and ...

### Moduli of Riemann Surfaces, Real Algebraic Curves, and Their Superanalogs

by S. M. Natanzon

According to standard definitions, a real algebraic curve is a complex algebraic curve (that is, a compact ...

### Geometry, Topology, and Mathematical Physics (2008)

S.P. Novikov's Seminar, 2006-2007 by V. M. Buchstaber, I. M. Krichever

A real algebraic curve is a pair (P, r), where A. V. ALEXEEVSKI AND S. M. NATANZON.

### Encyclopaedia of Mathematics (2012)

by Michiel Hazewinkel

An algebraic curve is the most frequently studied object in algebraic geometry. In the sequel, an algebraic curve means an irreducible algebraic curve over an algebraically closed field. The simplest and clearest concept is that of a plane affine ...

### Encyclopaedia of Mathematics (set) (1994)

by Michiel Hazewinkel

An algebraic curve is the most frequently studied object in algebraic geometry. In the sequel, an algebraic curve means an irreducible algebraic curve over an algebraically closed field. The simplest and clearest concept is that of a plane affine ...

### CRC Concise Encyclopedia of Mathematics, Second Edition (2002)

by Eric W. Weisstein

Algebraic Curve An algebraic curve over a FIELD K is an equation f(X; ...

### Encyclopedia of Computer Science and Technology (2001)

by Allen Kent, James G. Williams

an algebraic curve of degree m intersects an algebraic surface of degree n in at most mn points (assuming no part of the curve is common with the ...

### Encyclopedic Dictionary of Mathematics (1993)

by Kiyosi Itô

Algebraic Curves A. General Remarks An *algebraic variety of dimension 1 is called an algebraic curve (for analytic theory —- 11 Algebraic Functions). The theory of algebraic curves has two aspects, the geometry of 1dimensional ...

### The Penguin Dictionary of Mathematics (2008)

Fourth edition by David Nelson

algebraic curve A curve defined by a set of *polynomial equations and an example of an *algebraic variety. For example, in the plane with coordinates x, y, ax+by+c=0isaline, x 2 +y 2 ...

### Academic Press Dictionary of Science and Technology (1992)

by Christopher G. Morris, Academic Press

algebraic curve Mathematics, a set of points in «- dimensional Euclidean space satisfying a polynomial in the n coordinate functions.

### Van Nostrand’s Scientific Encyclopedia (2013)

by Douglas M. Considine, Glenn D. Considine

An algebraic curve of order one is thus a straight line; of order two, a conic section, or one of its degenerate cases, such as a circle. (For algebraic curves of order greater than two and transcendental curves see Curve (Higher Plane).) Analytic ...

### MCGRAW-HILL DICTIONARY OF MATHEMATICS, 2/E (2002)

by McGraw-Hill Education

{ :al~jalbra-ik 'klo-zhar av a 'feld } algebraic curve 1. The set of points in the plane satisfying a polynomial equation in two variables. 2. More generally, the set of points in n-space satisfying a polynomial equation in n variables. { :al-ja:bra-ik ' karv } ...

## Online dictionaries and encyclopedias with entries for Algebraic curve

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