博文
特征标理论，回避了坐标操作矩阵
|||
特征标理论，回避了坐标操作矩阵
点群操作的结果，一是变换了坐标（X,Y,Z），二是变换了函数（f(X,Y,Z)）。前者是涉及坐标操作矩阵，后者涉及特征标。
关于点群特征标的数据，很容易查阅到，而关于坐标操作矩阵的数据，多数是查阅不到的。
推导坐标操作矩阵，就得让大脑转动起来，当然还要进行镜面和反演操作，还要有各种S（转动＋反演）操作。
如果头脑里没有点群操作的物理图像，三转两转就把人给转晕了。
还好，多年转动魔方的经验，让我习惯了这种颠来倒去的转动，同时魔方也给了我一个非常明确的而且很容易把握的点群操作的物理图像。
因此，我推导了32（再加一个C60的Ih点群）点群的全部坐标操作矩阵，根据这些矩阵也可以把32点群的特征标求出来。不过没有这个必要了，因为查找点群的特征标太容易了。
求解坐标操作矩阵本质上只有一条路可走，而求解特征标有很多途径。
1. 根据同构的点群来求特征标
如果两个群同构，它们的乘法表是完全一样的，它们的特征标也是完全一样的。例如C3v和D3就是这种情况，但是它们的坐标操作矩阵是不完全相同的。
2. 根据点群的正则表示求特征标
构造一个点群的正则表示是很容易的，然后再选择一组基函数，把这些基函数正交归一地排列之后，就会得到一个矩阵，用这个矩阵去约化原来的正则表示，就得了这个点群的不可约表示，最后根据不可约矩阵表示求出特征标。
搞群论代数的人，他们有更多方法，但是都不涉及坐标操作矩阵。
应刘俊明老师的要求，给以一个具体的例子。 C3v的乘法表（和D3的排列相同） C3v e C3 C3^2 M1 M2 M3 e e C3 C3^2 M1 M2 M3 C3 C3 C3^2 e M3 M1 M2 C3^2 C3^2 e C3 M2 M3 M1 M1 M1 M2 M3 e C3 C3^2 M2 M2 M3 M1 C3^2 e C3 M3 M3 M1 M2 C3 C3^2 e D3的乘法表（和C3v的排列相同） D3 e C3 C3^2 C2^’ C2^’’ C2^’’’ e e C3 C3^2 C2^’ C2^’’ C2^’’’ C3 C3 C3^2 e C2^’’’ C2^’ C2^’’ C3^2 C3^2 e C3 C2^’’ C2^’’’ C2^’ C2^’ C2^’ C2^’’ C2^’’’ e C3 C3^2 C2^’’ C2^’’ C2^’’’ C2^’ C3^2 e C3 C2^’’’ C2^’’’ C2^’ C2^’’ C3 C3^2 e C3v的特征标（和D3的完全相同） C3v e 2C3 3M A1 +1 +1 +1 A2 +1 +1 -1 E +2 -1 0 D3的特征标（和C3v的完全相同） D3 e 2C3 3C2 A1 +1 +1 +1 A2 +1 +1 -1 E +2 -1 0 C3v的坐标操作矩阵（程序格式） G(nT) = "e" 'Row 1 ni = 1 TRxyz(nT, ni, 1) = 1 TRxyz(nT, ni, 2) = 0 TRxyz(nT, ni, 3) = 0 'Row 2 ni = 2 TRxyz(nT, ni, 1) = 0 TRxyz(nT, ni, 2) = 1 TRxyz(nT, ni, 3) = 0 'Row 3 ni = 3 TRxyz(nT, ni, 1) = 0 TRxyz(nT, ni, 2) = 0 TRxyz(nT, ni, 3) = 1 'TRxyz=C3(z) nT = 2 G(nT) = "C3[z]" 'Row 1 ni = 1 TRxyz(nT, ni, 1) = -1 / 2 TRxyz(nT, ni, 2) = Sqr(3) / 2 TRxyz(nT, ni, 3) = 0 'Row 2 ni = 2 TRxyz(nT, ni, 1) = -Sqr(3) / 2 TRxyz(nT, ni, 2) = -1 / 2 TRxyz(nT, ni, 3) = 0 'Row 3 ni = 3 TRxyz(nT, ni, 1) = 0 TRxyz(nT, ni, 2) = 0 TRxyz(nT, ni, 3) = 1 'TRxyz=C3^2 nT = 3 G(nT) = "C3^2[z]" 'Row 1 ni = 1 TRxyz(nT, ni, 1) = -1 / 2 TRxyz(nT, ni, 2) = -Sqr(3) / 2 TRxyz(nT, ni, 3) = 0 'Row 2 ni = 2 TRxyz(nT, ni, 1) = Sqr(3) / 2 TRxyz(nT, ni, 2) = -1 / 2 TRxyz(nT, ni, 3) = 0 'Row 3 ni = 3 TRxyz(nT, ni, 1) = 0 TRxyz(nT, ni, 2) = 0 TRxyz(nT, ni, 3) = 1 nT = 4 G(nT) = "Qv(zx30)" 'Row 1 ni = 1 TRxyz(nT, ni, 1) = 1 / 2 TRxyz(nT, ni, 2) = Sqr(3) / 2 TRxyz(nT, ni, 3) = 0 'Row 2 ni = 2 TRxyz(nT, ni, 1) = Sqr(3) / 2 TRxyz(nT, ni, 2) = -1 / 2 TRxyz(nT, ni, 3) = 0 'Row 3 ni = 3 TRxyz(nT, ni, 1) = 0 TRxyz(nT, ni, 2) = 0 TRxyz(nT, ni, 3) = 1 nT = 5 G(nT) = "Qv(zx150)" 'Row 1 ni = 1 TRxyz(nT, ni, 1) = 1 / 2 TRxyz(nT, ni, 2) = -Sqr(3) / 2 TRxyz(nT, ni, 3) = 0 'Row 2 ni = 2 TRxyz(nT, ni, 1) = -Sqr(3) / 2 TRxyz(nT, ni, 2) = -1 / 2 TRxyz(nT, ni, 3) = 0 'Row 3 ni = 3 TRxyz(nT, ni, 1) = 0 TRxyz(nT, ni, 2) = 0 TRxyz(nT, ni, 3) = 1 nT = 6 G(nT) = "Qv(zx270)" 'Row 1 ni = 1 TRxyz(nT, ni, 1) = -1 TRxyz(nT, ni, 2) = 0 TRxyz(nT, ni, 3) = 0 'Row 2 ni = 2 TRxyz(nT, ni, 1) = 0 TRxyz(nT, ni, 2) = 1 TRxyz(nT, ni, 3) = 0 'Row 3 ni = 3 TRxyz(nT, ni, 1) = 0 TRxyz(nT, ni, 2) = 0 TRxyz(nT, ni, 3) = 1 D3群的坐标操作矩阵（程序格式） nT = 1 G(nT) = "e" 'Row 1 ni = 1 TRxyz(nT, ni, 1) = 1 TRxyz(nT, ni, 2) = 0 TRxyz(nT, ni, 3) = 0 'Row 2 ni = 2 TRxyz(nT, ni, 1) = 0 TRxyz(nT, ni, 2) = 1 TRxyz(nT, ni, 3) = 0 'Row 3 ni = 3 TRxyz(nT, ni, 1) = 0 TRxyz(nT, ni, 2) = 0 TRxyz(nT, ni, 3) = 1 'TRxyz=C3(z) nT = 2 G(nT) = "C3[z]" 'Row 1 ni = 1 TRxyz(nT, ni, 1) = -1 / 2 TRxyz(nT, ni, 2) = Sqr(3) / 2 TRxyz(nT, ni, 3) = 0 'Row 2 ni = 2 TRxyz(nT, ni, 1) = -Sqr(3) / 2 TRxyz(nT, ni, 2) = -1 / 2 TRxyz(nT, ni, 3) = 0 'Row 3 ni = 3 TRxyz(nT, ni, 1) = 0 TRxyz(nT, ni, 2) = 0 TRxyz(nT, ni, 3) = 1 'TRxyz=C3^2 nT = 3 G(nT) = "C3^2[z]" 'Row 1 ni = 1 TRxyz(nT, ni, 1) = -1 / 2 TRxyz(nT, ni, 2) = -Sqr(3) / 2 TRxyz(nT, ni, 3) = 0 'Row 2 ni = 2 TRxyz(nT, ni, 1) = Sqr(3) / 2 TRxyz(nT, ni, 2) = -1 / 2 TRxyz(nT, ni, 3) = 0 'Row 3 ni = 3 TRxyz(nT, ni, 1) = 0 TRxyz(nT, ni, 2) = 0 TRxyz(nT, ni, 3) = 1 nT = 4 G(nT) = "C2(zx30)" 'Row 1 ni = 1 TRxyz(nT, ni, 1) = 1 / 2 TRxyz(nT, ni, 2) = Sqr(3) / 2 TRxyz(nT, ni, 3) = 0 'Row 2 ni = 2 TRxyz(nT, ni, 1) = Sqr(3) / 2 TRxyz(nT, ni, 2) = -1 / 2 TRxyz(nT, ni, 3) = 0 'Row 3 ni = 3 TRxyz(nT, ni, 1) = 0 TRxyz(nT, ni, 2) = 0 TRxyz(nT, ni, 3) = -1 nT = 5 G(nT) = "C2(zx150)" 'Row 1 ni = 1 TRxyz(nT, ni, 1) = 1 / 2 TRxyz(nT, ni, 2) = -Sqr(3) / 2 TRxyz(nT, ni, 3) = 0 'Row 2 ni = 2 TRxyz(nT, ni, 1) = -Sqr(3) / 2 TRxyz(nT, ni, 2) = -1 / 2 TRxyz(nT, ni, 3) = 0 'Row 3 ni = 3 TRxyz(nT, ni, 1) = 0 TRxyz(nT, ni, 2) = 0 TRxyz(nT, ni, 3) = -1 nT = 6 G(nT) = "C2(zx270)" 'Row 1 ni = 1 TRxyz(nT, ni, 1) = -1 TRxyz(nT, ni, 2) = 0 TRxyz(nT, ni, 3) = 0 'Row 2 ni = 2 TRxyz(nT, ni, 1) = 0 TRxyz(nT, ni, 2) = 1 TRxyz(nT, ni, 3) = 0 'Row 3 ni = 3 TRxyz(nT, ni, 1) = 0 TRxyz(nT, ni, 2) = 0 TRxyz(nT, ni, 3) = -1 两个点群的操作矩阵（最后3个不同） 一个根据正则表示求不可约表示例子： （选自俺自己的《坐标变换和函数变换》） D3（C3v）群的“排列组合”（置换表示）表示。 如果取一组6维基矢量，“横向”有48种满足正交条件的排列，3组（符号排列不同）的基矢量，有3×48＝144种。 基矢量排列： 'Row 1 MA(nX, kk(1), 1) = 1 / Sqr(6) MA(nX, kk(1), 2) = 1 / Sqr(6) MA(nX, kk(1), 3) = 1 / Sqr(6) MA(nX, kk(1), 4) = 1 / Sqr(6) MA(nX, kk(1), 5) = 1 / Sqr(6) MA(nX, kk(1), 6) = 1 / Sqr(6) 'Row 2 MA(nX, kk(2), 1) = 1 / Sqr(6) MA(nX, kk(2), 2) = 1 / Sqr(6) MA(nX, kk(2), 3) = 1 / Sqr(6) MA(nX, kk(2), 4) = -1 / Sqr(6) MA(nX, kk(2), 5) = -1 / Sqr(6) MA(nX, kk(2), 6) = -1 / Sqr(6) 'Row 3 MA(nX, kk(3), 1) = 2 / Sqr(12) MA(nX, kk(3), 2) = -1 / Sqr(12) MA(nX, kk(3), 3) = -1 / Sqr(12) MA(nX, kk(3), 4) = 2 / Sqr(12) MA(nX, kk(3), 5) = -1 / Sqr(12) MA(nX, kk(3), 6) = -1 / Sqr(12) 'Row 4 MA(nX, kk(4), 1) = 2 / Sqr(12) MA(nX, kk(4), 2) = -1 / Sqr(12) MA(nX, kk(4), 3) = -1 / Sqr(12) MA(nX, kk(4), 4) = -2 / Sqr(12) MA(nX, kk(4), 5) = 1 / Sqr(12) MA(nX, kk(4), 6) = 1 / Sqr(12) 'Row 5 MA(nX, kk(5), 1) = 0 MA(nX, kk(5), 2) = 1 / 2 MA(nX, kk(5), 3) = -1 / 2 MA(nX, kk(5), 4) = 0 MA(nX, kk(5), 5) = -1 / 2 MA(nX, kk(5), 6) = 1 / 2 'Row 6 MA(nX, kk(6), 1) = 0 MA(nX, kk(6), 2) = 1 / 2 MA(nX, kk(6), 3) = -1 / 2 MA(nX, kk(6), 4) = 0 MA(nX, kk(6), 5) = 1 / 2 MA(nX, kk(6), 6) = -1 / 2 以上基矢量，没有满足约化条件的排列。 'Row 1 MA(nX, kk(1), 1) = 1 / Sqr(6) MA(nX, kk(1), 2) = 1 / Sqr(6) MA(nX, kk(1), 3) = 1 / Sqr(6) MA(nX, kk(1), 4) = 1 / Sqr(6) MA(nX, kk(1), 5) = 1 / Sqr(6) MA(nX, kk(1), 6) = 1 / Sqr(6) 'Row 2 MA(nX, kk(2), 1) = 1 / Sqr(6) MA(nX, kk(2), 2) = 1 / Sqr(6) MA(nX, kk(2), 3) = 1 / Sqr(6) MA(nX, kk(2), 4) = -1 / Sqr(6) MA(nX, kk(2), 5) = -1 / Sqr(6) MA(nX, kk(2), 6) = -1 / Sqr(6) 'Row 3 MA(nX, kk(3), 1) = 2 / Sqr(12) MA(nX, kk(3), 2) = -1 / Sqr(12) MA(nX, kk(3), 3) = -1 / Sqr(12) MA(nX, kk(3), 4) = -2 / Sqr(12) MA(nX, kk(3), 5) = 1 / Sqr(12) MA(nX, kk(3), 6) = 1 / Sqr(12) 'Row 4 MA(nX, kk(4), 1) = -2 / Sqr(12) MA(nX, kk(4), 2) = 1 / Sqr(12) MA(nX, kk(4), 3) = 1 / Sqr(12) MA(nX, kk(4), 4) = -2 / Sqr(12) MA(nX, kk(4), 5) = 1 / Sqr(12) MA(nX, kk(4), 6) = 1 / Sqr(12) 'Row 5 MA(nX, kk(5), 1) = 0 MA(nX, kk(5), 2) = 1 / 2 MA(nX, kk(5), 3) = -1 / 2 MA(nX, kk(5), 4) = 0 MA(nX, kk(5), 5) = -1 / 2 MA(nX, kk(5), 6) = 1 / 2 'Row 6 MA(nX, kk(6), 1) = 0 MA(nX, kk(6), 2) = 1 / 2 MA(nX, kk(6), 3) = -1 / 2 MA(nX, kk(6), 4) = 0 MA(nX, kk(6), 5) = 1 / 2 MA(nX, kk(6), 6) = -1 / 2 "TC(","nX=",58 "X(1)=",1,"X(2)=",2,"X(3)=",4,"X(4)=",5,"X(5)=",6,"X(6)=",3 "TC(","nX=",58,"nT=",1,")=" 1,0,0,0,0,0, 0,1,0,0,0,0, 0,0,1,0,0,0, 0,0,0,1,0,0, 0,0,0,0,1,0, 0,0,0,0,0,1, "TC(","nX=",58,"nT=",2,")=" 1,0,0,0,0,0, 0,1,0,0,0,0, 0,0,-.5,.866,0,0, 0,0,-.866,-.5,0,0, 0,0,0,0,-.5,.866, 0,0,0,0,-.866,-.5, "TC(","nX=",58,"nT=",3,")=" 1,0,0,0,0,0, 0,1,0,0,0,0, 0,0,-.5,-.866,0,0, 0,0,.866,-.5,0,0, 0,0,0,0,-.5,-.866, 0,0,0,0,.866,-.5, "TC(","nX=",58,"nT=",4,")=" 1,0,0,0,0,0, 0,-1,0,0,0,0, 0,0,1,0,0,0, 0,0,0,-1,0,0, 0,0,0,0,1,0, 0,0,0,0,0,-1, "TC(","nX=",58,"nT=",5,")=" 1,0,0,0,0,0, 0,-1,0,0,0,0, 0,0,-.5,.866,0,0, 0,0,.866,.5,0,0, 0,0,0,0,-.5,.866, 0,0,0,0,.866,.5, "TC(","nX=",58,"nT=",6,")=" 1,0,0,0,0,0, 0,-1,0,0,0,0, 0,0,-.5,-.866,0,0, 0,0,-.866,.5,0,0, 0,0,0,0,-.5,-.866, 0,0,0,0,-.866,.5, "TC(","nX=",67 "X(1)=",1,"X(2)=",2,"X(3)=",6,"X(4)=",3,"X(5)=",4,"X(6)=",5 "TC(","nX=",67,"nT=",1,")=" 1,0,0,0,0,0, 0,1,0,0,0,0, 0,0,1,0,0,0, 0,0,0,1,0,0, 0,0,0,0,1,0, 0,0,0,0,0,1, "TC(","nX=",67,"nT=",2,")=" 1,0,0,0,0,0, 0,1,0,0,0,0, 0,0,-.5,.866,0,0, 0,0,-.866,-.5,0,0, 0,0,0,0,-.5,.866, 0,0,0,0,-.866,-.5, "TC(","nX=",67,"nT=",3,")=" 1,0,0,0,0,0, 0,1,0,0,0,0, 0,0,-.5,-.866,0,0, 0,0,.866,-.5,0,0, 0,0,0,0,-.5,-.866, 0,0,0,0,.866,-.5, "TC(","nX=",67,"nT=",4,")=" 1,0,0,0,0,0, 0,-1,0,0,0,0, 0,0,1,0,0,0, 0,0,0,-1,0,0, 0,0,0,0,1,0, 0,0,0,0,0,-1, "TC(","nX=",67,"nT=",5,")=" 1,0,0,0,0,0, 0,-1,0,0,0,0, 0,0,-.5,.866,0,0, 0,0,.866,.5,0,0, 0,0,0,0,-.5,.866, 0,0,0,0,.866,.5, "TC(","nX=",67,"nT=",6,")=" 1,0,0,0,0,0, 0,-1,0,0,0,0, 0,0,-.5,-.866,0,0, 0,0,-.866,.5,0,0, 0,0,0,0,-.5,-.866, 0,0,0,0,-.866,.5, 'Row 1 MA(nX, kk(1), 1) = 1 / Sqr(6) MA(nX, kk(1), 2) = 1 / Sqr(6) MA(nX, kk(1), 3) = 1 / Sqr(6) MA(nX, kk(1), 4) = 1 / Sqr(6) MA(nX, kk(1), 5) = 1 / Sqr(6) MA(nX, kk(1), 6) = 1 / Sqr(6) 'Row 2 MA(nX, kk(2), 1) = 1 / Sqr(6) MA(nX, kk(2), 2) = 1 / Sqr(6) MA(nX, kk(2), 3) = 1 / Sqr(6) MA(nX, kk(2), 4) = -1 / Sqr(6) MA(nX, kk(2), 5) = -1 / Sqr(6) MA(nX, kk(2), 6) = -1 / Sqr(6) 'Row 3 MA(nX, kk(3), 1) = 2 / Sqr(12) MA(nX, kk(3), 2) = -1 / Sqr(12) MA(nX, kk(3), 3) = -1 / Sqr(12) MA(nX, kk(3), 4) = 2 / Sqr(12) MA(nX, kk(3), 5) = -1 / Sqr(12) MA(nX, kk(3), 6) = -1 / Sqr(12) 'Row 4 MA(nX, kk(4), 1) = 0 MA(nX, kk(4), 2) = 1 / 2 MA(nX, kk(4), 3) = -1 / 2 MA(nX, kk(4), 4) = 0 MA(nX, kk(4), 5) = -1 / 2 MA(nX, kk(4), 6) = 1 / 2 'Row 5 MA(nX, kk(5), 1) = 0 MA(nX, kk(5), 2) = -1 / 2 MA(nX, kk(5), 3) = 1 / 2 MA(nX, kk(5), 4) = 0 MA(nX, kk(5), 5) = -1 / 2 MA(nX, kk(5), 6) = 1 / 2 'Row 6 MA(nX, kk(6), 1) = 2 / Sqr(12) MA(nX, kk(6), 2) = -1 / Sqr(12) MA(nX, kk(6), 3) = -1 / Sqr(12) MA(nX, kk(6), 4) = -2 / Sqr(12) MA(nX, kk(6), 5) = 1 / Sqr(12) MA(nX, kk(6), 6) = 1 / Sqr(12) "TC(","nX=",97 "X(1)=",1,"X(2)=",2,"X(3)=",3,"X(4)=",4,"X(5)=",5,"X(6)=",6 "TC(","nX=",97,"nT=",1,")=" 1,0,0,0,0,0, 0,1,0,0,0,0, 0,0,1,0,0,0, 0,0,0,1,0,0, 0,0,0,0,1,0, 0,0,0,0,0,1, "TC(","nX=",97,"nT=",2,")=" 1,0,0,0,0,0, 0,1,0,0,0,0, 0,0,-.5,-.866,0,0, 0,0,.866,-.5,0,0, 0,0,0,0,-.5,-.866, 0,0,0,0,.866,-.5, "TC(","nX=",97,"nT=",3,")=" 1,0,0,0,0,0, 0,1,0,0,0,0, 0,0,-.5,.866,0,0, 0,0,-.866,-.5,0,0, 0,0,0,0,-.5,.866, 0,0,0,0,-.866,-.5, "TC(","nX=",97,"nT=",4,")=" 1,0,0,0,0,0, 0,-1,0,0,0,0, 0,0,1,0,0,0, 0,0,0,-1,0,0, 0,0,0,0,1,0, 0,0,0,0,0,-1, "TC(","nX=",97,"nT=",5,")=" 1,0,0,0,0,0, 0,-1,0,0,0,0, 0,0,-.5,-.866,0,0, 0,0,-.866,.5,0,0, 0,0,0,0,-.5,-.866, 0,0,0,0,-.866,.5, "TC(","nX=",97,"nT=",6,")=" 1,0,0,0,0,0, 0,-1,0,0,0,0, 0,0,-.5,.866,0,0, 0,0,.866,.5,0,0, 0,0,0,0,-.5,.866, 0,0,0,0,.866,.5, "TC(","nX=",113 "X(1)=",1,"X(2)=",2,"X(3)=",5,"X(4)=",6,"X(5)=",3,"X(6)=",4 "TC(","nX=",113,"nT=",1,")=" 1,0,0,0,0,0, 0,1,0,0,0,0, 0,0,1,0,0,0, 0,0,0,1,0,0, 0,0,0,0,1,0, 0,0,0,0,0,1, "TC(","nX=",113,"nT=",2,")=" 1,0,0,0,0,0, 0,1,0,0,0,0, 0,0,-.5,-.866,0,0, 0,0,.866,-.5,0,0, 0,0,0,0,-.5,-.866, 0,0,0,0,.866,-.5, "TC(","nX=",113,"nT=",3,")=" 1,0,0,0,0,0, 0,1,0,0,0,0, 0,0,-.5,.866,0,0, 0,0,-.866,-.5,0,0, 0,0,0,0,-.5,.866, 0,0,0,0,-.866,-.5, "TC(","nX=",113,"nT=",4,")=" 1,0,0,0,0,0, 0,-1,0,0,0,0, 0,0,1,0,0,0, 0,0,0,-1,0,0, 0,0,0,0,1,0, 0,0,0,0,0,-1, "TC(","nX=",113,"nT=",5,")=" 1,0,0,0,0,0, 0,-1,0,0,0,0, 0,0,-.5,-.866,0,0, 0,0,-.866,.5,0,0, 0,0,0,0,-.5,-.866, 0,0,0,0,-.866,.5, "TC(","nX=",113,"nT=",6,")=" 1,0,0,0,0,0, 0,-1,0,0,0,0, 0,0,-.5,.866,0,0, 0,0,.866,.5,0,0, 0,0,0,0,-.5,.866, 0,0,0,0,.866,.5, "TC(","nX=",113 "X(1)=",1,"X(2)=",2,"X(3)=",5,"X(4)=",6,"X(5)=",3,"X(6)=",4 "TC(","nX=",113,"nT=",1,")=" 1,0,0,0,0,0, 0,1,0,0,0,0, 0,0,1,0,0,0, 0,0,0,1,0,0, 0,0,0,0,1,0, 0,0,0,0,0,1, "TC(","nX=",113,"nT=",2,")=" 1,0,0,0,0,0, 0,1,0,0,0,0, 0,0,-.5,-.866,0,0, 0,0,.866,-.5,0,0, 0,0,0,0,-.5,-.866, 0,0,0,0,.866,-.5, "TC(","nX=",113,"nT=",3,")=" 1,0,0,0,0,0, 0,1,0,0,0,0, 0,0,-.5,.866,0,0, 0,0,-.866,-.5,0,0, 0,0,0,0,-.5,.866, 0,0,0,0,-.866,-.5, "TC(","nX=",113,"nT=",4,")=" 1,0,0,0,0,0, 0,-1,0,0,0,0, 0,0,1,0,0,0, 0,0,0,-1,0,0, 0,0,0,0,1,0, 0,0,0,0,0,-1, "TC(","nX=",113,"nT=",5,")=" 1,0,0,0,0,0, 0,-1,0,0,0,0, 0,0,-.5,-.866,0,0, 0,0,-.866,.5,0,0, 0,0,0,0,-.5,-.866, 0,0,0,0,-.866,.5, "TC(","nX=",113,"nT=",6,")=" 1,0,0,0,0,0, 0,-1,0,0,0,0, 0,0,-.5,.866,0,0, 0,0,.866,.5,0,0, 0,0,0,0,-.5,.866, 0,0,0,0,.866,.5,
https://blog.sciencenet.cn/blog-2321-227272.html
上一篇：如果是天真无邪，先学做事；如果是市侩庸俗，先学做人
下一篇：热门也罢，冷门也罢：没有基础，就是别人藤上的花
