论文标题
Clifford代数的多场在3D中的平方根：带有标志的游戏
Square root of a multivector of Clifford algebras in 3D: A game with signs
论文作者
论文摘要
提出了一种算法，用于从真实Clifford代数Cl（P，Q）中从多骑（MV）中提取平方根的算法，以n = p+q <= 3。我们表明，在最通用（通用）MV的情况下，在代数CL（3,0），Cl（1,2）和Cl（0,3）中最多有四个孤立的根。代数CL（2,1）构成例外，此处的MV最多可以具有16个孤立的根。除了孤立的根外，除p+q = 1以外，所有代数还可以出现一个根的连续体。提供了许多示例来说明n = 3 Clifford代数中可能出现的各种根的属性。
An algorithm to extract the square root in radicals from a multivector (MV) in real Clifford algebras Cl(p,q) for n=p+q <=3 is presented. We show that in the algebras Cl(3,0), Cl(1,2) and Cl(0,3) there are up to four isolated roots in a case of the most general (generic) MV. The algebra Cl(2,1) makes up an exception and the MV here can have up to 16 isolated roots. In addition to isolated roots, a continuum of roots can appear in all algebras except p+q=1. A number of examples are provided to illustrate properties of various roots that may appear in n=3 Clifford algebras.
