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单词 DecomposableCurve
释义

decomposable curve


An algebraic curve

f(x,y)= 0

is decomposablePlanetmathPlanetmath, if the polynomialMathworldPlanetmathf(x,y)  is in  [x,y]; that is, if there are polynomials  g(x,y)  and  h(x,y)  with positive degree in  [x,y]  such that

f(x,y)=g(x,y)h(x,y).

Example.  The quadratic curve

x2a2-y2b2= 0(1)

is decomposable, since the equation may be written

(xa+yb)(xa-yb)= 0

or equivalently

xa+yb= 0xa-yb= 0.

Thus the curve (1) consists of two intersecting lines.

Analogically, one can say that an algebraic surface

g(x,y,z)= 0

is decomposable, e.g.  (x+y+z)2-1=0  which consists of two parallel planesMathworldPlanetmath.

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更新时间:2025/5/4 22:27:25