|
In mathematics, the Pythagoras number or reduced height of a field describes the structure of the set of squares in the field. The Pythagoras number ''p''(''K'') of a field ''K'' is the smallest positive integer ''p'' such that every sum of squares in ''K'' is a sum of ''p'' squares. A ''Pythagorean field'' is one with Pythagoras number 1: that is, every sum of squares is already a square. ==Examples== * Every positive real is a square, so ''p''(R) = 1. * For a finite field of odd characteristic, not every element is a square, but all are the sum of two squares,〔Lam (2005) p. 36〕 so ''p'' = 2. * By Lagrange's four-square theorem, every positive rational number is a sum of four squares, and not all are sums of three squares, so ''p''(Q) = 4. 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「Pythagoras number」の詳細全文を読む スポンサード リンク
|