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, ------------------------------------------------------------------------ 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 , ------------------------------------------------------------------------ 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, ------------------------------------------------------------------------ 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}, ------------------------------------------------------------------------ 2 2 {1, a, a*b, a*b , a*b c}} o3 : List |