getWeights -- image of the flow on the vertices

Synopsis

Usage:

getWeights M

getWeights Q
Inputs:
- M, a matrix,
- Q, an instance of the type ToricQuiver,
Outputs:
- L, a list, of integers, corresponding to the image of the flow of the provided toric quiver under the $Inc$ map

Description

This method returns the weight of the quiver. This vector is the image of its flow under the $inc$ map, which is defined as $$ \text{inc}(\mathbf{w})(i) := \sum_{a\in Q_1 \atop a^{+} = i} \mathbf{w}(a) - \sum_{a\in Q_1 \atop a^{-} = i} \mathbf{w}(a) \quad \text{ for all } i \in Q_0. $$ where for any arrow $a\in Q_1$, we denote its head as $a^{+} \in Q_0$ and its tail as $a^{-} \in Q_0$.

i1 : Q = bipartiteQuiver(2, 3, Flow => "Random")

o1 = ToricQuiver{flow => {8, 1, 3, 7, 8, 3}                            }
                 IncidenceMatrix => | -1 -1 -1 0  0  0  |
                                    | 0  0  0  -1 -1 -1 |
                                    | 1  0  0  1  0  0  |
                                    | 0  1  0  0  1  0  |
                                    | 0  0  1  0  0  1  |
                 Q0 => {0, 1, 2, 3, 4}
                 Q1 => {{0, 2}, {0, 3}, {0, 4}, {1, 2}, {1, 3}, {1, 4}}
                 synonym => toric quiver
                 weights => {-12, -18, 15, 9, 6}

o1 : ToricQuiver

i2 : getWeights Q

o2 = {-12, -18, 15, 9, 6}

o2 : List

Ways to use getWeights :

getWeights(Matrix)
getWeights(ToricQuiver)

For the programmer

The object getWeights is a method function.

getWeights -- image of the flow on the vertices

Synopsis

Description

See also

Ways to use getWeights :

For the programmer