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# sympy.combinatorics.permutations._af_commutes_with

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```Checks if the two permutations with array forms
given by ``a`` and ``b`` commute.

Examples
========

>>> from sympy.combinatorics.permutations import _af_commutes_with
>>> _af_commutes_with([1,2,0], [0,2,1])
False
(more...)
```

```        def _af_commutes_with(a, b):
"""
Checks if the two permutations with array forms
given by ``a`` and ``b`` commute.

Examples
========

>>> from sympy.combinatorics.permutations import _af_commutes_with
>>> _af_commutes_with([1,2,0], [0,2,1])
False

========

Permutation, commutes_with
"""
return not any(a[b[i]] != b[a[i]] for i in range(len(a) - 1))
```

```from sympy.core import Basic
from sympy.combinatorics import Permutation
from sympy.combinatorics.permutations import (_af_commutes_with, _af_invert,
_af_rmul, _af_rmuln, _af_pow, Cycle)
from sympy.combinatorics.util import (_check_cycles_alt_sym,
```
```                if y <= x:
continue
if not _af_commutes_with(x, y):
self._is_abelian = False
return False
```

```from sympy.core import Basic
from sympy.combinatorics import Permutation
from sympy.combinatorics.permutations import (_af_commutes_with, _af_invert,
_af_rmul, _af_rmuln, _af_pow, Cycle)
from sympy.combinatorics.util import (_check_cycles_alt_sym,
```
```                if y <= x:
continue
if not _af_commutes_with(x, y):
self._is_abelian = False
return False
```

```
"""
from sympy.combinatorics.permutations import _af_commutes_with
if hasattr(other, 'generators'):
elements = list(self.generate_dimino(af=True))
gens = [x._array_form for x in other.generators]
commutes_with_gens = lambda x: all(_af_commutes_with(x, gen) for gen in gens)
```

```