Gfrktyl

Consider lists of vectors of elements like

list[1]={{a1,b1,c11},{a2,b2,c12},{a3,b3,c13},{a4,b4,c14},{a5,b5,c15}};

list[2]={{a1,b1,c21}            ,{a3,b3,c23},{a4,b4,c24},{a5,b5,c25}};

list[3]={{a1,b1,c31},{a2,b2,c32},{a3,b3,c33}            ,{a5,b5,c35}};

where the length 3 of vectors in lists is just an example and could be longer, and there may be more than 3 such lists.

I would like to have a function truncate[listoflists_] that takes all these lists and truncates them to only have the vectors containing ai,bi entries that are present in all of them:

{list[1],list[2],list[3]}=truncate[{list[1],list[2],list[3]}];

list[1]

list[2]

list[3]

{{a1,b1,c11},{a3,b3,c13},{a5,b5,c15}}

{{a1,b1,c21},{a3,b3,c23},{a5,b5,c25}}

{{a1,b1,c31},{a3,b3,c33},{a5,b5,c35}}

Is there a quick way to do this in Mathematica? Thanks for any suggestion.

It is short (does not mean quick) to get it via associations:

truncate = Values @ KeyIntersection @ Map[#[[;; 2]] -> # &, #, {2}] &

We convert {a1,b1,c11} to {a1,b1}->{a1,b1,c11} and everything else is straightforward.

Also

tF = Module[{i = Intersection@@#[[;;, ;;, #2]], k = #2}, Select[MemberQ[i, #[[k]]]&]/@ #]&



lists = list /@ {1, 2, 3};

tF[lists, {1, 2}]

{{{a1, b1, c11}, {a3, b3, c13}, {a5, b5, c15}},

{{a1, b1, c21}, {a3, b3, c23}, {a5, b5, c25}},

{{a1, b1, c31}, {a3, b3, c33}, {a5, b5, c35}}}