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Image: ubuntu2204
Kernel: SageMath 10.4

# Sage 10.4 on CoCalc

```version()
```
'SageMath version 10.4, Release Date: 2024-07-19'
```D12 = posets.DivisorLattice(12).hasse_diagram()
phi_VE = D12.incidence_matrix(vertices=True, edges=True)
phi_VE
```
Generic morphism: From: Free module generated by {(1, 2), (1, 3), (2, 4), (2, 6), (3, 6), (4, 12), (6, 12)} over Integer Ring To: Free module generated by {1, 2, 3, 4, 6, 12} over Integer Ring
```print(phi_VE._unicode_art_matrix())

```
(1, 2) (1, 3) (2, 4) (2, 6) (3, 6) (4, 12) (6, 12) 1⎛ -1 -1 0 0 0 0 0⎞ 2⎜ 1 0 -1 -1 0 0 0⎟ 3⎜ 0 1 0 0 -1 0 0⎟ 4⎜ 0 0 1 0 0 -1 0⎟ 6⎜ 0 0 0 1 1 0 -1⎟ 12⎝ 0 0 0 0 0 1 1⎠
```M = matroids.CompleteGraphic(7)
M.bases()
```
SetSystem of 16807 sets over 21 elements
```q = 5
A = GF(q)['T']
K.<T> = Frac(A)
M = DrinfeldModularForms(K, rank=3)
M
```
Ring of Drinfeld modular forms of rank 3 over Fraction Field of Univariate Polynomial Ring in T over Finite Field of size 5
```M.gens()
```
[g1, g2, g3]
```M.basis(20*(q - 1))
```
[g1^2*g2^3, g1^8*g2^2, g1^14*g2, g1^20]
```(1/T)*M.0 + 4*(M.2*M.1)/T
```
-1/T*g2*g3 + 1/T*g1
```
```