回复 5# kuing
我不是编程大神,我只能半自动生成
n=3时
输入- {{1, 4}, {2, 5}, {3,6}} //. {{t1___, {a_, b_}, t2___, {c_, d_}, t3___} /;
- a < c < b < d -> {{t1, {a, c}, t2, {b, d}, t3}, {t1, {a, d},
- t2, {c, b}, t3}}, {t1___, {a_, b_}, t2___, {c_, d_}, t3___} /;
- c < a < d < b -> {{t1, {c, a}, t2, {d, b}, t3}, {t1, {a, d},
- t2, {c, b}, t3}}}
复制代码 输出
{{{1, 2}, {4, 5}, {3,6}}, {{{{1, 2}, {3, 4}, {5, 6}}, {{1, 4}, {2, 3}, {5, 6}}}, {{{1,
6}, {2, 3}, {4, 5}}, {{1, 6}, {2, 5}, {3, 4}}}}}
输入- Partition[Partition[Flatten[%, 2], 3]
复制代码 输出- {{{1, 2}, {4, 5}, {3, 6}}, {{1, 2}, {3, 4}, {5, 6}},
- {{1, 4}, {2,3}, {5, 6}}, {{1, 6}, {2, 3}, {4, 5}}, {{1, 6}, {2, 5}, {3, 4}}}
复制代码 输入- Plus @@ Times @@@ (%58 /. {c_, d_} -> (Subscript[a, c] - Subscript[a, d]))
复制代码 输出$\left(a_3-a_4\right) \left(a_2-a_5\right) \left(a_1-a_6\right)+\left(a_2-a_3\right) \left(a_4-a_5\right) \left(a_1-a_6\right)+\left(a_1-a_2\right) \left(a_4-a_5\right) \left(a_3-a_6\right)+\left(a_2-a_3\right) \left(a_1-a_4\right) \left(a_5-a_6\right)+\left(a_1-a_2\right) \left(a_3-a_4\right) \left(a_5-a_6\right)$
验证:
输入Factor[%]
输出$-\left(a_4-a_1\right) \left(a_2-a_5\right) \left(a_3-a_6\right)$ |