betti(BettiTally) -- view and set the weight vector of a Betti diagram

Function: betti
Usage:

betti(t, Weights => w)
Inputs:
- t, a Betti tally,
Optional inputs:
- Weights => a list, default value null, with the same length as the multidegrees in t, used as the weight vector w
- Minimize => ..., default value false,
Outputs:
- a Betti tally, with the same homological degrees, multidegrees, and ranks. If a weight vector w is provided, the total degree weights in the resulting Betti tally will be recomputed by taking the dot products of w with the multidegrees in the tally.

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 show 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 : 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 oo

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

Ways to use this method:

betti(BettiTally) -- view and set the weight vector of a Betti diagram

The source of this document is in Macaulay2Doc/functions/betti-doc.m2:249:0.

betti(BettiTally) -- view and set the weight vector of a Betti diagram

Description

See also

Ways to use this method: