结论是将所有$x_1,x_2,...,x_n$各乘n后的问题
t=1对应两个数:0,2 贡献乘积-8（最多使用两次??）
t=2情况1对应三个数:0,0.4514162296451364698327947488,2.548583770354863530167205252，贡献乘积3.786781856645392948227249015(最多使用一次）
t=2情况2对应三个数:0,2.215250437021530196833871917,0.7847495629784698031661280788，贡献乘积-12.67567074553428183711613785(可以任意多次使用）
t=3对应4个数:0,2.307017519236618480036245864,2×0.5419168336818726459757413173,4×0.1522872033499090570030678703，贡献乘积-15.46378268292782988622147943(最多使用一次？也许可以两个？）
t=4对应5个数:0,2.349928651318642985553754527,1.218297519424779455160694324,0.8828682331717251216906905210,0.5489055960848524375948605796，贡献乘积-16.98091409574632203491364107(最多使用一次）
利用它们合并构成n个数即可
其中t=2的情况1可以用来改变总乘积的符号，所以最多使用1次
前面分析应该有点问题，但是最大t=4不会有问题。但是最终结论估计还是t=1的可以任意多个（因为其效率最高），而t=2的也应该有限个，而t=3的最多两个。
具体可用组合可以通过数字计算得出
为方便起见可将t=1,2,3,4等乘积记为A2,A3,A4,A5,而t=3还有个正乘积B3,于是A5显然不如A2B3.所以t=4情况不需要。
而n=4最大值必然为A2^2,最小值A4.n=5最大值必然A2A3最小值A2B3
A4^2<A2^4 A4A3<B3A2^2 -A4B3<-A3A2^2 由此得出A4只能出现一次而且不会同其他模式同时使用。所以只有n=4才会用A4.
又因为B3^2<A3^2-A3B3<-A2^3 A3^4<A2^6 所以对于n>4余下模式只有 A2^x A2^xA3^y(2<=y<=3)A2^3B3
又因为-A2^3B3<-A3^3,所以用模式B3时A2最多两个，也就是只有n=3,5,7才会用B3
所以n=6时最小A2^3最大A3^2. n =7时最小A2^2A3,最大A2^2B3.而对于n>=8,偶数时最值在为A2^(n/2),A2^(n/2-3)A3^2.而n为奇数时最值为A2^((n-3)/2)A3和A2^((n-9)/2)A3^3
http://bbs.emath.ac.cn/forum.php?mod=redirect&goto=findpost&ptid=5642&pid=54312&fromuid=8888
7#的三角形的三个顶点也是要验算的,这样更准确一些!
可以尝试把三角形区域转化成球面区域.
同样是拉格朗日乘子法,转化后只需要一次拉格朗日乘子法就可以了,
但是计算结果多了很多,不过精确解的计算还是可能的.
Clear["Global`*"];(*Clear all variables*)
(*把三维空间中的三角形转化成球面a^2+b^2+c^2==1*)
fun=(2*a^2-b^2)(2*b^2-c^2)(2*c^2-a^2)+x*(a^2+b^2+c^2-1)
fa=D
fb=D
fc=D
fx=D
sol1=Solve[{fa==0,fb==0,fc==0,fx==0},{a,b,c,x}]
Print["显示三角形内部的最值"]
sol11=fun/.sol1
Print["数值化"]
N@sol1
N@sol11
运算结果有些长,但是也算把问题解决了!
Out= (2 a^2 - b^2) (2 b^2 - c^2) (-a^2 + 2 c^2) + (-1 + a^2 +
b^2 + c^2) x
Out= -2 a (2 a^2 - b^2) (2 b^2 - c^2) +
4 a (2 b^2 - c^2) (-a^2 + 2 c^2) + 2 a x
Out= 4 b (2 a^2 - b^2) (-a^2 + 2 c^2) -
2 b (2 b^2 - c^2) (-a^2 + 2 c^2) + 2 b x
Out= 4 (2 a^2 - b^2) c (2 b^2 - c^2) -
2 (2 a^2 - b^2) c (-a^2 + 2 c^2) + 2 c x
Out= -1 + a^2 + b^2 + c^2
Out= {{x -> -(1/9), b -> -(1/Sqrt), c -> -(1/Sqrt),
a -> -(1/Sqrt)}, {x -> -(1/9), b -> -(1/Sqrt),
c -> -(1/Sqrt), a -> 1/Sqrt}, {x -> -(1/9), b -> -(1/Sqrt),
c -> 1/Sqrt, a -> -(1/Sqrt)}, {x -> -(1/9),
b -> -(1/Sqrt), c -> 1/Sqrt, a -> 1/Sqrt}, {x -> -(1/9),
b -> 1/Sqrt, c -> -(1/Sqrt), a -> -(1/Sqrt)}, {x -> -(1/9),
b -> 1/Sqrt, c -> -(1/Sqrt), a -> 1/Sqrt}, {x -> -(1/9),
b -> 1/Sqrt, c -> 1/Sqrt, a -> -(1/Sqrt)}, {x -> -(1/9),
b -> 1/Sqrt, c -> 1/Sqrt, a -> 1/Sqrt}, {x -> 0, a -> -1,
c -> 0, b -> 0}, {x -> 0, a -> 1, c -> 0, b -> 0}, {x -> 0, b -> -1,
c -> 0, a -> 0}, {x -> 0, b -> 1, c -> 0, a -> 0}, {x -> 0,
b -> -Sqrt[(2/7)], c -> -(2/Sqrt), a -> -(1/Sqrt)}, {x -> 0,
b -> -Sqrt[(2/7)], c -> -(2/Sqrt), a -> 1/Sqrt}, {x -> 0,
b -> -Sqrt[(2/7)], c -> 2/Sqrt, a -> -(1/Sqrt)}, {x -> 0,
b -> -Sqrt[(2/7)], c -> 2/Sqrt, a -> 1/Sqrt}, {x -> 0,
b -> Sqrt, c -> -(2/Sqrt), a -> -(1/Sqrt)}, {x -> 0,
b -> Sqrt, c -> -(2/Sqrt), a -> 1/Sqrt}, {x -> 0,
b -> Sqrt, c -> 2/Sqrt, a -> -(1/Sqrt)}, {x -> 0,
b -> Sqrt, c -> 2/Sqrt, a -> 1/Sqrt}, {x -> 0,
b -> -(2/Sqrt), c -> -(1/Sqrt), a -> -Sqrt[(2/7)]}, {x -> 0,
b -> -(2/Sqrt), c -> -(1/Sqrt), a -> Sqrt}, {x -> 0,
b -> -(2/Sqrt), c -> 1/Sqrt, a -> -Sqrt[(2/7)]}, {x -> 0,
b -> -(2/Sqrt), c -> 1/Sqrt, a -> Sqrt}, {x -> 0,
b -> -(1/Sqrt), c -> -Sqrt[(2/7)], a -> -(2/Sqrt)}, {x -> 0,
b -> -(1/Sqrt), c -> -Sqrt[(2/7)], a -> 2/Sqrt}, {x -> 0,
b -> -(1/Sqrt), c -> Sqrt, a -> -(2/Sqrt)}, {x -> 0,
b -> -(1/Sqrt), c -> Sqrt, a -> 2/Sqrt}, {x -> 0,
b -> 1/Sqrt, c -> -Sqrt[(2/7)], a -> -(2/Sqrt)}, {x -> 0,
b -> 1/Sqrt, c -> -Sqrt[(2/7)], a -> 2/Sqrt}, {x -> 0,
b -> 1/Sqrt, c -> Sqrt, a -> -(2/Sqrt)}, {x -> 0,
b -> 1/Sqrt, c -> Sqrt, a -> 2/Sqrt}, {x -> 0,
b -> 2/Sqrt, c -> -(1/Sqrt), a -> -Sqrt[(2/7)]}, {x -> 0,
b -> 2/Sqrt, c -> -(1/Sqrt), a -> Sqrt}, {x -> 0,
b -> 2/Sqrt, c -> 1/Sqrt, a -> -Sqrt[(2/7)]}, {x -> 0,
b -> 2/Sqrt, c -> 1/Sqrt, a -> Sqrt}, {x -> 0, c -> -1,
a -> 0, b -> 0}, {x -> 0, c -> 1, a -> 0,
b -> 0}, {x -> 4/81 (10 - 7 Sqrt), a -> -(1/3) Sqrt],
c -> -(1/3) Sqrt],
b -> 0}, {x -> 4/81 (10 - 7 Sqrt), a -> -(1/3) Sqrt],
c -> Sqrt]/3, b -> 0}, {x -> 4/81 (10 - 7 Sqrt),
a -> Sqrt]/3, c -> -(1/3) Sqrt],
b -> 0}, {x -> 4/81 (10 - 7 Sqrt), a -> Sqrt]/3,
c -> Sqrt]/3, b -> 0}, {x -> 4/81 (10 - 7 Sqrt),
b -> -(1/3) Sqrt], c -> -Sqrt/9],
a -> 0}, {x -> 4/81 (10 - 7 Sqrt), b -> -(1/3) Sqrt],
c -> Sqrt/9], a -> 0}, {x -> 4/81 (10 - 7 Sqrt),
b -> Sqrt]/3, c -> -Sqrt/9],
a -> 0}, {x -> 4/81 (10 - 7 Sqrt), b -> Sqrt]/3,
c -> Sqrt/9], a -> 0}, {x -> 4/81 (10 - 7 Sqrt),
b -> -(1/3) Sqrt], a -> -(1/3) Sqrt],
c -> 0}, {x -> 4/81 (10 - 7 Sqrt), b -> -(1/3) Sqrt],
a -> Sqrt]/3, c -> 0}, {x -> 4/81 (10 - 7 Sqrt),
b -> Sqrt]/3, a -> -(1/3) Sqrt],
c -> 0}, {x -> 4/81 (10 - 7 Sqrt), b -> Sqrt]/3,
a -> Sqrt]/3, c -> 0}, {x -> 4/81 (10 + 7 Sqrt),
a -> -(1/3) Sqrt], c -> -Sqrt/9],
b -> 0}, {x -> 4/81 (10 + 7 Sqrt), a -> -(1/3) Sqrt],
c -> Sqrt/9], b -> 0}, {x -> 4/81 (10 + 7 Sqrt),
a -> Sqrt]/3, c -> -Sqrt/9],
b -> 0}, {x -> 4/81 (10 + 7 Sqrt), a -> Sqrt]/3,
c -> Sqrt/9], b -> 0}, {x -> 4/81 (10 + 7 Sqrt),
b -> -(1/3) Sqrt], a -> -Sqrt/9], c -> 0},
{x -> 4/81 (10 + 7 Sqrt), b -> -(1/3) Sqrt],
a -> Sqrt/9], c -> 0}, {x -> 4/81 (10 + 7 Sqrt),
b -> Sqrt]/3, a -> -Sqrt/9],
c -> 0}, {x -> 4/81 (10 + 7 Sqrt), b -> Sqrt]/3,
a -> Sqrt/9], c -> 0}, {x -> 4/81 (10 + 7 Sqrt),
b -> -(1/3) Sqrt], c -> -(1/3) Sqrt],
a -> 0}, {x -> 4/81 (10 + 7 Sqrt), b -> -(1/3) Sqrt],
c -> Sqrt]/3, a -> 0}, {x -> 4/81 (10 + 7 Sqrt),
b -> Sqrt]/3, c -> -(1/3) Sqrt],
a -> 0}, {x -> 4/81 (10 + 7 Sqrt), b -> Sqrt]/3,
c -> Sqrt]/3, a -> 0}}
During evaluation of In:= 显示三角形内部的最值
Out= {1/27, 1/27, 1/27, 1/27, 1/27, 1/27, 1/27, 1/27, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 2/
81 (-4 + Sqrt) (5 + Sqrt) (1/9 (-5 - Sqrt) +
2/9 (4 - Sqrt)) +
4/81 (10 - 7 Sqrt) (-1 + 1/9 (4 - Sqrt) + 1/9 (5 + Sqrt)),
2/81 (-4 + Sqrt) (5 + Sqrt) (1/9 (-5 - Sqrt) +
2/9 (4 - Sqrt)) +
4/81 (10 - 7 Sqrt) (-1 + 1/9 (4 - Sqrt) + 1/9 (5 + Sqrt)),
2/81 (-4 + Sqrt) (5 + Sqrt) (1/9 (-5 - Sqrt) +
2/9 (4 - Sqrt)) +
4/81 (10 - 7 Sqrt) (-1 + 1/9 (4 - Sqrt) + 1/9 (5 + Sqrt)),
2/81 (-4 + Sqrt) (5 + Sqrt) (1/9 (-5 - Sqrt) +
2/9 (4 - Sqrt)) +
4/81 (10 - 7 Sqrt) (-1 + 1/9 (4 - Sqrt) + 1/9 (5 + Sqrt)),
4/81 (10 - 7 Sqrt) (-(4/9) + Sqrt/9 + 1/9 (4 - Sqrt)) +
2/9 (5/9 + Sqrt/9) (-4 + Sqrt) (-(5/9) - Sqrt/9 +
2/9 (4 - Sqrt)),
4/81 (10 - 7 Sqrt) (-(4/9) + Sqrt/9 + 1/9 (4 - Sqrt)) +
2/9 (5/9 + Sqrt/9) (-4 + Sqrt) (-(5/9) - Sqrt/9 +
2/9 (4 - Sqrt)),
4/81 (10 - 7 Sqrt) (-(4/9) + Sqrt/9 + 1/9 (4 - Sqrt)) +
2/9 (5/9 + Sqrt/9) (-4 + Sqrt) (-(5/9) - Sqrt/9 +
2/9 (4 - Sqrt)),
4/81 (10 - 7 Sqrt) (-(4/9) + Sqrt/9 + 1/9 (4 - Sqrt)) +
2/9 (5/9 + Sqrt/9) (-4 + Sqrt) (-(5/9) - Sqrt/9 +
2/9 (4 - Sqrt)),
2/81 (-4 + Sqrt) (5 + Sqrt) (1/9 (-5 - Sqrt) +
2/9 (4 - Sqrt)) +
4/81 (10 - 7 Sqrt) (-1 + 1/9 (4 - Sqrt) + 1/9 (5 + Sqrt)),
2/81 (-4 + Sqrt) (5 + Sqrt) (1/9 (-5 - Sqrt) +
2/9 (4 - Sqrt)) +
4/81 (10 - 7 Sqrt) (-1 + 1/9 (4 - Sqrt) + 1/9 (5 + Sqrt)),
2/81 (-4 + Sqrt) (5 + Sqrt) (1/9 (-5 - Sqrt) +
2/9 (4 - Sqrt)) +
4/81 (10 - 7 Sqrt) (-1 + 1/9 (4 - Sqrt) + 1/9 (5 + Sqrt)),
2/81 (-4 + Sqrt) (5 + Sqrt) (1/9 (-5 - Sqrt) +
2/9 (4 - Sqrt)) +
4/81 (10 - 7 Sqrt) (-1 + 1/9 (4 - Sqrt) + 1/9 (5 + Sqrt)),
4/81 (10 + 7 Sqrt) (-(5/9) + Sqrt/9 + 1/9 (5 - Sqrt)) +
2/9 (5 - Sqrt) (-(4/9) - Sqrt/9) (2 (4/9 + Sqrt/9) +
1/9 (-5 + Sqrt)),
4/81 (10 + 7 Sqrt) (-(5/9) + Sqrt/9 + 1/9 (5 - Sqrt)) +
2/9 (5 - Sqrt) (-(4/9) - Sqrt/9) (2 (4/9 + Sqrt/9) +
1/9 (-5 + Sqrt)),
4/81 (10 + 7 Sqrt) (-(5/9) + Sqrt/9 + 1/9 (5 - Sqrt)) +
2/9 (5 - Sqrt) (-(4/9) - Sqrt/9) (2 (4/9 + Sqrt/9) +
1/9 (-5 + Sqrt)),
4/81 (10 + 7 Sqrt) (-(5/9) + Sqrt/9 + 1/9 (5 - Sqrt)) +
2/9 (5 - Sqrt) (-(4/9) - Sqrt/9) (2 (4/9 + Sqrt/9) +
1/9 (-5 + Sqrt)),
4/81 (10 + 7 Sqrt) (-(5/9) + Sqrt/9 + 1/9 (5 - Sqrt)) +
2/9 (5 - Sqrt) (-(4/9) - Sqrt/9) (2 (4/9 + Sqrt/9) +
1/9 (-5 + Sqrt)),
4/81 (10 + 7 Sqrt) (-(5/9) + Sqrt/9 + 1/9 (5 - Sqrt)) +
2/9 (5 - Sqrt) (-(4/9) - Sqrt/9) (2 (4/9 + Sqrt/9) +
1/9 (-5 + Sqrt)),
4/81 (10 + 7 Sqrt) (-(5/9) + Sqrt/9 + 1/9 (5 - Sqrt)) +
2/9 (5 - Sqrt) (-(4/9) - Sqrt/9) (2 (4/9 + Sqrt/9) +
1/9 (-5 + Sqrt)),
4/81 (10 + 7 Sqrt) (-(5/9) + Sqrt/9 + 1/9 (5 - Sqrt)) +
2/9 (5 - Sqrt) (-(4/9) - Sqrt/9) (2 (4/9 + Sqrt/9) +
1/9 (-5 + Sqrt)),
4/81 (10 + 7 Sqrt) (-1 + 1/9 (5 - Sqrt) + 1/9 (4 + Sqrt)) +
2/81 (-4 - Sqrt) (5 - Sqrt) (1/9 (-5 + Sqrt) +
2/9 (4 + Sqrt)),
4/81 (10 + 7 Sqrt) (-1 + 1/9 (5 - Sqrt) + 1/9 (4 + Sqrt)) +
2/81 (-4 - Sqrt) (5 - Sqrt) (1/9 (-5 + Sqrt) +
2/9 (4 + Sqrt)),
4/81 (10 + 7 Sqrt) (-1 + 1/9 (5 - Sqrt) + 1/9 (4 + Sqrt)) +
2/81 (-4 - Sqrt) (5 - Sqrt) (1/9 (-5 + Sqrt) +
2/9 (4 + Sqrt)),
4/81 (10 + 7 Sqrt) (-1 + 1/9 (5 - Sqrt) + 1/9 (4 + Sqrt)) +
2/81 (-4 - Sqrt) (5 - Sqrt) (1/9 (-5 + Sqrt) +
2/9 (4 + Sqrt))}
During evaluation of In:= 数值化
Out= {{x -> -0.111111, b -> -0.57735, c -> -0.57735,
a -> -0.57735}, {x -> -0.111111, b -> -0.57735, c -> -0.57735,
a -> 0.57735}, {x -> -0.111111, b -> -0.57735, c -> 0.57735,
a -> -0.57735}, {x -> -0.111111, b -> -0.57735, c -> 0.57735,
a -> 0.57735}, {x -> -0.111111, b -> 0.57735, c -> -0.57735,
a -> -0.57735}, {x -> -0.111111, b -> 0.57735, c -> -0.57735,
a -> 0.57735}, {x -> -0.111111, b -> 0.57735, c -> 0.57735,
a -> -0.57735}, {x -> -0.111111, b -> 0.57735, c -> 0.57735,
a -> 0.57735}, {x -> 0., a -> -1., c -> 0., b -> 0.}, {x -> 0.,
a -> 1., c -> 0., b -> 0.}, {x -> 0., b -> -1., c -> 0.,
a -> 0.}, {x -> 0., b -> 1., c -> 0., a -> 0.}, {x -> 0.,
b -> -0.534522, c -> -0.755929, a -> -0.377964}, {x -> 0.,
b -> -0.534522, c -> -0.755929, a -> 0.377964}, {x -> 0.,
b -> -0.534522, c -> 0.755929, a -> -0.377964}, {x -> 0.,
b -> -0.534522, c -> 0.755929, a -> 0.377964}, {x -> 0.,
b -> 0.534522, c -> -0.755929, a -> -0.377964}, {x -> 0.,
b -> 0.534522, c -> -0.755929, a -> 0.377964}, {x -> 0.,
b -> 0.534522, c -> 0.755929, a -> -0.377964}, {x -> 0.,
b -> 0.534522, c -> 0.755929, a -> 0.377964}, {x -> 0.,
b -> -0.755929, c -> -0.377964, a -> -0.534522}, {x -> 0.,
b -> -0.755929, c -> -0.377964, a -> 0.534522}, {x -> 0.,
b -> -0.755929, c -> 0.377964, a -> -0.534522}, {x -> 0.,
b -> -0.755929, c -> 0.377964, a -> 0.534522}, {x -> 0.,
b -> -0.377964, c -> -0.534522, a -> -0.755929}, {x -> 0.,
b -> -0.377964, c -> -0.534522, a -> 0.755929}, {x -> 0.,
b -> -0.377964, c -> 0.534522, a -> -0.755929}, {x -> 0.,
b -> -0.377964, c -> 0.534522, a -> 0.755929}, {x -> 0.,
b -> 0.377964, c -> -0.534522, a -> -0.755929}, {x -> 0.,
b -> 0.377964, c -> -0.534522, a -> 0.755929}, {x -> 0.,
b -> 0.377964, c -> 0.534522, a -> -0.755929}, {x -> 0.,
b -> 0.377964, c -> 0.534522, a -> 0.755929}, {x -> 0.,
b -> 0.755929, c -> -0.377964, a -> -0.534522}, {x -> 0.,
b -> 0.755929, c -> -0.377964, a -> 0.534522}, {x -> 0.,
b -> 0.755929, c -> 0.377964, a -> -0.534522}, {x -> 0.,
b -> 0.755929, c -> 0.377964, a -> 0.534522}, {x -> 0., c -> -1.,
a -> 0., b -> 0.}, {x -> 0., c -> 1., a -> 0.,
b -> 0.}, {x -> -0.420754, a -> -0.921698, c -> -0.387907,
b -> 0.}, {x -> -0.420754, a -> -0.921698, c -> 0.387907,
b -> 0.}, {x -> -0.420754, a -> 0.921698, c -> -0.387907,
b -> 0.}, {x -> -0.420754, a -> 0.921698, c -> 0.387907,
b -> 0.}, {x -> -0.420754, b -> -0.387907, c -> -0.921698,
a -> 0.}, {x -> -0.420754, b -> -0.387907, c -> 0.921698,
a -> 0.}, {x -> -0.420754, b -> 0.387907, c -> -0.921698,
a -> 0.}, {x -> -0.420754, b -> 0.387907, c -> 0.921698,
a -> 0.}, {x -> -0.420754, b -> -0.921698, a -> -0.387907,
c -> 0.}, {x -> -0.420754, b -> -0.921698, a -> 0.387907,
c -> 0.}, {x -> -0.420754, b -> 0.921698, a -> -0.387907,
c -> 0.}, {x -> -0.420754, b -> 0.921698, a -> 0.387907,
c -> 0.}, {x -> 1.40841, a -> -0.511452, c -> -0.859312,
b -> 0.}, {x -> 1.40841, a -> -0.511452, c -> 0.859312,
b -> 0.}, {x -> 1.40841, a -> 0.511452, c -> -0.859312,
b -> 0.}, {x -> 1.40841, a -> 0.511452, c -> 0.859312,
b -> 0.}, {x -> 1.40841, b -> -0.511452, a -> -0.859312,
c -> 0.}, {x -> 1.40841, b -> -0.511452, a -> 0.859312,
c -> 0.}, {x -> 1.40841, b -> 0.511452, a -> -0.859312,
c -> 0.}, {x -> 1.40841, b -> 0.511452, a -> 0.859312,
c -> 0.}, {x -> 1.40841, b -> -0.859312, c -> -0.511452,
a -> 0.}, {x -> 1.40841, b -> -0.859312, c -> 0.511452,
a -> 0.}, {x -> 1.40841, b -> 0.859312, c -> -0.511452,
a -> 0.}, {x -> 1.40841, b -> 0.859312, c -> 0.511452, a -> 0.}}
Out= {0.037037, 0.037037, 0.037037, 0.037037, 0.037037, 0.037037, \
0.037037, 0.037037, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., \
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., \
0., 0.140251, 0.140251, 0.140251, 0.140251, 0.140251, 0.140251, \
0.140251, 0.140251, 0.140251, 0.140251, 0.140251, 0.140251, \
-0.469469, -0.469469, -0.469469, -0.469469, -0.469469, -0.469469, \
-0.469469, -0.469469, -0.469469, -0.469469, -0.469469, -0.469469}
Clear["Global`*"];(*Clear all variables*)
(*把三维空间中的三角形转化成球面a^2+b^2+c^2+d^2==1*)
fun=(2*a^2-b^2)(2*b^2-c^2)(2*c^2-d^2)(2*d^2-a^2)+x*(a^2+b^2+c^2+d^2-1)
fa=D
fb=D
fc=D
fd=D
fx=D
sol1=Solve[{fa==0.0,fb==0.0,fc==0.0,fd==0.0,fx==0.0},{a,b,c,d,x}]
Print["显示三角形内部的最值"]
sol11=fun/.sol1
四维的mathematica直接干不动了,也许是因为变量的次数太高了.
算了很长时间没有结果.