Question

mathematica问题求解

NSum[(-1)^(a+b+c)/Sqrt[(a+b-c)^2+(-a+b+c)^2+(a-b+c)^2],{a,-200,200},{b,-200,200},{c,-200,200}]

用mathematica算这个累次求和的时候，需要把(0,0,0)这点去掉，求问用什么语句?
怎么写？

Answer 1

{a,-200,-1},{b,-200,200},{c,-200,200} + {a,1,200},{b,-200,200},{c,-200,200}

+ {a=0},{b,-200,-1},{c,-200,200} + {a=0},{b,1,200},{c,-200,200}
+ {a=0},{b=0},{c,-200,-1} + {a=0},{b=0},{c,1,200}
__________________________________________________________________ or you can
NSum[(-1)^(a+b+c)/(Sqrt[(a+b-c)^2+(-a+b+c)^2+(a-b+c)^2] + Boole[a==0&&b==0&&c==0]),{a,-200,200},{b,-200,200},{c,-200,200}] -1

Answer 2

这个用逻辑判断就行了：
NSum[If[a == 0 && b == 0 && c == 0, 0, (-1)^(a + b + c)/Sqrt[(a + b - c)^2 + (-a + b + c)^2 + (a - b + c)^2]], {a, -5, 5}, {b, -5, 5}, {c, -5, 5}]

试了一下，比用Boole的解法要快一些。