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例子
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带有条目T(n,m)的不规则三角形T开始于:(增加k>=1的值之间用;隔开;)
n\m 1 2 3 4 5 6 7 8 9 10 11 12 13。。。
1: [1, 0]
2: [1, 1]
3: [2, 1], [1, 2]; [1, 0, 1]
4: [3, 1], [1, 3]; [2, 0, 1], [1, 0, 2], [1, 1, 1]
...
n=5:[4,1],[1,4],[3,2],[2,3];[3, 0, 1], [1, 0, 3], [2, 1, 1], [1, 2, 1], [1, 1, 2]; [2, 0, 0, 1], [1, 0, 0, 2], [1, 1, 0, 1], [1, 0, 1, 1]; [1, 0, 0, 0, 1]
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n=6:[5,1],[1,5];[4, 0, 1], [1, 0, 4], [3, 0, 2], [2, 0, 3], [3, 1, 1], [1, 3, 1], [1, 1, 3], [2, 2, 1], [2, 1, 2], [1, 2, 2]; [3, 0, 0, 1], [1, 0, 0, 3], [2, 1, 0, 1], [2, 0, 1, 1], [1, 2, 0, 1], [1, 0, 2, 1], [1, 1, 0, 2], [1, 0, 1, 2], [1, 1, 1, 1]; [2, 0, 0, 0, 1], [1, 0, 0, 0, 2], [1, 1, 0, 0, 1], [1, 0, 1, 0, 1], [1, 0, 0, 1, 1]
---------
n=7:[6,1],[1,6],[5,2],[2,5],[4,3],[3,4];[5, 0, 1], [1, 0, 5], [4, 1, 1], [1, 4, 1], [1, 1, 4], [3, 2, 1], [3, 1, 2], [2, 3, 1], [2, 1, 3], [1, 3, 2], [1, 2, 3]; [4, 0, 0, 1], [1, 0, 0, 4], [3, 0, 0, 2], [2, 0, 0, 3], [3, 1, 0, 1], [3, 0, 1, 1], [1, 3, 0, 1], [1, 0, 3, 1], [1, 1, 0, 3], [1, 0, 1, 3], [2, 2, 0, 1], [2, 0, 2, 1], [2, 1, 0, 2], [2, 0, 1, 2], [1, 2, 0, 2], [1, 0, 2, 2], [2, 1, 1, 1], [1, 2, 1, 1], [1, 1, 2, 1], [1, 1, 1, 2]; [3, 0, 0, 0, 1], [1, 0, 0, 0, 3], [2, 1, 0, 0, 1], [2, 0, 1, 0, 1], [2, 0, 0, 1, 1], [1, 2, 0, 0, 1], [1, 0, 2, 0, 1], [1, 0, 0, 2, 1], [1, 1, 0, 0, 2], [1, 0, 1, 0, 2], [1, 0, 0, 1, 2], [1, 1, 1, 0, 1], [1, 1, 0, 1, 1], [1, 0, 1, 1, 1]; [2, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 2], [1, 1, 0, 0, 0, 1], [1, 0, 1, 0, 0, 1], [1, 0, 0, 1, 0, 1], [1, 0, 0, 0, 1, 1]
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x^6+1=(x^2+1)*(x^4-x^2+1]),因此没有记录[1,0,0,0,0,0,1],因为x^6-1也分解。
...
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多项式:n=4,度k=1:3*x+1,x+3;k=2:2*x^2+1,x^2+2,x^2+x+1;k=3:没有条目[1,0,0,1],因为x^3+1分解,以及x^3-1分解。
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高度n=4,度k=2,带符号多项式:
[2,0,1]表示2*x^2+1,2*x^2-1,[1,0,2]表示x^2+2,x^2-2,以及[1,1,1]表示x^2+x+1,x^2+x-1,x^2-x+1,x^2-x-1。相应的实代数数只有2*x^2-1、x^2-2、x^2+x-1和x^2-x-1的有符号对,即-sqrt(1/2)、+sqrt(1/2)、-sqrt-A001622号,φ-1,和-(φ-1),φ。所以康托的φ(我们的φ)是φ(4,2)=8。将[3,1]和[1,3]的有符号多项式的四个实k=1根加在一起,得出Phi(4)=12。请参见A362364飞机.
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