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# all.SL2Z

All Samples(35)  |  Call(27)  |  Derive(0)  |  Import(8)

```        ArithmeticError: The generators [10] must be units modulo 14
"""
from all import Gamma0, Gamma1, SL2Z
if level == 1:
return SL2Z
```
```            ]
"""
from all import SL2Z
N = self.level()
return [SL2Z(lift_to_sl2z(0, d.lift(), N)) for d in _GammaH_coset_helper(N, self._list_of_elements_in_H())]
```
```            True
"""
from all import Gamma0, SL2Z
reps1 = Gamma0(self.level()).coset_reps()
for r in reps1:
```

```################################################################################

from all import SL2Z
from arithgroup_generic import ArithmeticSubgroup
from sage.rings.all import Zmod
```
```from sage.groups.perm_gps.permgroup_element import PermutationGroupElement

Idm = SL2Z([1,0,0,1])    # identity

Lm = SL2Z([1,1,0,1])     # parabolic that fixes infinity
Rm = SL2Z([1,0,1,1])     # parabolic that fixes 0
S2m = SL2Z([0,-1,1,0])   # elliptic of order 2 (fix i)
```

```        True
"""
from all import SL2Z
if N == 1: return SL2Z
try:
```
```            ]
"""
from all import SL2Z
N = self.level()
if N == 1: # P1List isn't very happy working modulo 1
yield SL2Z([1,0,0,1])
else:
for z in sage.modular.modsym.p1list.P1List(N):
yield SL2Z(lift_to_sl2z(z[0], z[1], N))
```

```        """
from sage.all import prod
from all import SL2Z
from arithgroup_perm import S2m,S3m,Lm

G = random_even_arithgroup(self.index)

m = {'l':Lm, 's':S2m}
tree,reps,wreps,gens = G._spanning_tree_verrill()
assert reps[0] == SL2Z([1,0,0,1])
```
```            assert prod(m[letter] for letter in wreps[i]) == reps[i]
tree,reps,wreps,gens = G._spanning_tree_verrill(on_right=False)
assert reps[0] == SL2Z([1,0,0,1])
assert wreps[0] == ''
for i in xrange(1,self.index):
assert prod(m[letter] for letter in wreps[i]) == reps[i]

m = {'s2':S2m, 's3':S3m}
tree,reps,wreps,gens = G._spanning_tree_kulkarni()
assert reps[0] == SL2Z([1,0,0,1])
```
```            assert prod(m[letter] for letter in wreps[i]) == reps[i]
tree,reps,wreps,gens = G._spanning_tree_kulkarni(on_right=False)
assert reps[0] == SL2Z([1,0,0,1])
assert wreps[0] == []
for i in xrange(1,self.index):
```