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In geometry, a circular algebraic curve is a type of plane algebraic curve determined by an equation ''F''(''x'', ''y'') = 0, where ''F'' is a polynomial with real coefficients and the highest-order terms of ''F'' form a polynomial divisible by ''x''2 + ''y''2. More precisely, if ''F'' = ''F''''n'' + ''F''''n''−1 + ... + ''F''1 + ''F''0, where each ''F''''i'' is homogeneous of degree ''i'', then the curve ''F''(''x'', ''y'') = 0 is circular if and only if ''F''''n'' is divisible by ''x''2 + ''y''2. Equivalently, if the curve is determined in homogeneous coordinates by ''G''(''x'', ''y'', ''z'') = 0, where ''G'' is a homogeneous polynomial, then the curve is circular if and only if ''G''(1, ''i'',0) = ''G''(1, −''i'',0) = 0. In other words, the curve is circular if it contains the circular points at infinity, (1, ''i'' ,0) and (1, −''i'', 0), when considered as a curve in the complex projective plane. ==Multicircular algebraic curves== An algebraic curve is called ''p''-circular if it contains the points (1, ''i'', 0) and (1, −''i'', 0) when considered as a curve in the complex projective plane, and these points are singularities of order at least ''p''. The terms ''bicircular'', ''tricircular'', etc. apply when ''p'' = 2, 3, etc. In terms of the polynomial ''F'' given above, the curve ''F''(''x'', ''y'') = 0 is ''p''-circular if ''F''''n''−''i'' is divisible by (''x''2 + ''y''2)''p''−''i'' when ''i'' < ''p''. When ''p'' = 1 this reduces to the definition of a circular curve. The set of ''p''-circular curves is invariant under Euclidean transformations. Note that a ''p''-circular curve must have degree at least 2''p''. The set of ''p''-circular curves of degree ''p'' + ''k'', where ''p'' may vary but ''k'' is a fixed positive integer, is invariant under inversion. When ''k'' is 1 this says that the set of lines (0-circular curves of degree 1) together with the set of circles (1-circular curves of degree 2) form a set which is invariant under inversion. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「circular algebraic curve」の詳細全文を読む スポンサード リンク
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