三元六次半正定条件
若设\(d_1=x+y+z,d_2=xy+xz+yz,d_3=xyz\),且\(x\geqslant0,y\geqslant0,z\geqslant0\),试找到：\(f(x,y,z)=k_0 d_1^6+k_1 d_2 d_1^4+k_2 d_3 d_1^3+k_3 d_2^2 d_1^2+k_4 d_1 d_2 d_3 +k_5 d_2^3+k_6 d_3^2 \geqslant0\)
成立的条件，并指出\(f(x,y,z)\)取\(＝\)的条件？
上面的问题来自于：
http://bbs.cnool.net/cthread-105590209.html
数学爱好者xzlbq给出了如下结果：
则有 \(\)
1.\(\)
2.\(\)
3.\(\)
4.\(\)
5.\(\)
6.\(\)
7.\(\)
8.\(\)
9.\(\)
10.\(\)
11.\(\)
12.\(\)
13.\(\)
14.\(\)
15.\(\)
16.\(\)
17.\(\)
18.\(\)
19.\(\)
20.\(\)
21.\(\)
22.\(\)
23.\(\)
24.\(\)
25.\(\)
26.\(\)
27.\(\)
28.\(\)
且\(f(x,y,z)\) 取\(=\)仅当\(x=y,y=kz\)成立
其中第25项中的\(0 \leqslant k _{00}\leqslant 0.03921970753\)
即满足：\(62k^6+204k^5+210k^4+200k^3+30k^2+24k-1\leqslant 0\)
上面是否给出了所有成立条件？
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