The maximal chains of P are totally orders subsets of P which are not properly contained in any other totally ordered subsets.
This method returns a list of all maximal chains. The maximal chains are themselves lists of elements in P ordered from smallest to largest.
The results of this method are cached.
i1 : S = QQ[a,b,c]; |
i2 : P = divisorPoset(a*b^2*c); |
i3 : C = maximalChains P
2 2 2
o3 = {{1, c, b*c, b c, a*b c}, {1, c, b*c, a*b*c, a*b c}, {1, c, a*c, a*b*c,
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2 2 2 2 2
a*b c}, {1, b, b*c, b c, a*b c}, {1, b, b*c, a*b*c, a*b c}, {1, b, b ,
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2 2 2 2 2 2
b c, a*b c}, {1, b, b , a*b , a*b c}, {1, b, a*b, a*b*c, a*b c}, {1, b,
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2 2 2 2
a*b, a*b , a*b c}, {1, a, a*c, a*b*c, a*b c}, {1, a, a*b, a*b*c, a*b c},
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2 2
{1, a, a*b, a*b , a*b c}}
o3 : List
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