# Algebraic curve

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## 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,

*. The simplest and clearest concept is that of a plane affine ...*

**an algebraic curve**means**an irreducible algebraic curve**over an algebraically closed field### Encyclopaedia of Mathematics (set) (1994)

by Michiel Hazewinkel

* An algebraic curve is the most frequently studied object in algebraic geometry*. In
the sequel,

*. The simplest and clearest concept is that of a plane affine ...*

**an algebraic curve**means**an irreducible algebraic curve**over an algebraically closed field### 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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