# betti(BettiTally) -- view and set the weights of a betti display

## Synopsis

• Function: betti
• Usage:
betti(t, Weights => w)
• Inputs:
• t,
• Optional inputs:
• Weights => a list, default value null, a list of integers, w, with the same degree length as that of t
• Minimize => ..., default value false, minimal betti numbers of a non-minimal free resolution
• Outputs:
• , different from the input only in its degree weights. If w is non-null, then a new betti tally with new weight values is returned

## Description

 i1 : R = ZZ/101[a..d,Degrees=>{2:{1,0},2:{0,1}}]; i2 : I = ideal random(R^1, R^{2:{-2,-2},2:{-3,-3}}); o2 : Ideal of R i3 : t = betti res I 0 1 2 3 4 o3 = total: 1 4 13 14 4 0: 1 . . . . 1: . . . . . 2: . . . . . 3: . 2 . . . 4: . . . . . 5: . 2 . . . 6: . . 1 . . 7: . . 8 6 . 8: . . 4 8 4 o3 : BettiTally i4 : peek t o4 = BettiTally{(0, {0, 0}, 0) => 1 } (1, {2, 2}, 4) => 2 (1, {3, 3}, 6) => 2 (2, {3, 7}, 10) => 2 (2, {4, 4}, 8) => 1 (2, {4, 5}, 9) => 4 (2, {5, 4}, 9) => 4 (2, {7, 3}, 10) => 2 (3, {4, 7}, 11) => 4 (3, {5, 5}, 10) => 6 (3, {7, 4}, 11) => 4 (4, {5, 7}, 12) => 2 (4, {7, 5}, 12) => 2
The following three displays display the first degree, the second degree, and the total degree, respectively.
 i5 : betti(t,Weights=>{1,0}) 0 1 2 3 4 o5 = total: 1 4 13 14 4 0: 1 . . . . 1: . 2 2 4 2 2: . 2 5 6 . 3: . . 4 . 2 4: . . . 4 . 5: . . 2 . . o5 : BettiTally i6 : betti(t,Weights=>{0,1}) 0 1 2 3 4 o6 = total: 1 4 13 14 4 0: 1 . . . . 1: . 2 2 4 2 2: . 2 5 6 . 3: . . 4 . 2 4: . . . 4 . 5: . . 2 . . o6 : BettiTally i7 : t1 = betti(t,Weights=>{1,1}) 0 1 2 3 4 o7 = total: 1 4 13 14 4 0: 1 . . . . 1: . . . . . 2: . . . . . 3: . 2 . . . 4: . . . . . 5: . 2 . . . 6: . . 1 . . 7: . . 8 6 . 8: . . 4 8 4 o7 : BettiTally i8 : peek t1 o8 = BettiTally{(0, {0, 0}, 0) => 1 } (1, {2, 2}, 4) => 2 (1, {3, 3}, 6) => 2 (2, {3, 7}, 10) => 2 (2, {4, 4}, 8) => 1 (2, {4, 5}, 9) => 4 (2, {5, 4}, 9) => 4 (2, {7, 3}, 10) => 2 (3, {4, 7}, 11) => 4 (3, {5, 5}, 10) => 6 (3, {7, 4}, 11) => 4 (4, {5, 7}, 12) => 2 (4, {7, 5}, 12) => 2