令 a=x1+x2, b=x1-x2, c=x3, d=x4 ,
即 x1=a/2+b/2, x2 = a/2-b/2, x3=c, x4=d.
则 f = ab+bc+cd+da
= (x1+x2)(x1-x2)+(x1-x2)x3+x3x4+x4(x1+x2)
= x1^2 - x2^2 + x1x3 + x1x4 - x2x3 + x2x4 + x3x4
= (x1+x3/2+x4/2)^2 - (x2+x3/2-x4/2)^2
= y1^2-y2^2
y1 1 0 1/2 1/2 x1 1 0 1/2 1/2 1/2 1/2 0 0 a
y2 = 0 1 1/2 -1/2 x2 = 0 1 1/2 -1/2 1/2 -1/2 0 0 b
y3 0 0 1 0 x3 0 0 1 0 0 0 1 0 c
y4 0 0 0 1 x4 0 0 0 1 0 0 0 1 d
1/2 1/2 1/2 1/2 a
= 1/2 -1/2 1/2 -1/2 b
0 0 1 0 c
0 0 0 1 d
满意请采纳^_^