the K3 carpet of type b1,b2 is the correspondence scroll of type b1,b2 with respect to the ideal Delta^2, where Delta \subset P^1 x P^1 is the ideal of the diagonal.
i1 : betti res carpet{1,3}
0 1 2 3
o1 = total: 1 5 5 1
0: 1 . . .
1: . 3 2 .
2: . 2 3 .
3: . . . 1
o1 : BettiTally
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The object carpet is a method function with options.