# id

From permutations v1.0-5
by Robin K S Hankin

##### The identity permutation

The identity permutation leaves every element fixed

##### Usage

```
is.id(x)
is.id_single_cycle(x)
# S3 method for cycle
is.id(x)
# S3 method for list
is.id(x)
# S3 method for word
is.id(x)
```

##### Arguments

- x
Object to be tested

##### Details

The identity permutation is problematic because it potentially has zero size.

##### Value

The variable `id`

is a *cycle* as this is more convenient
than a zero-by-one matrix.

Function `is.id()`

returns a Boolean with `TRUE`

if the
corresponding element is the identity, and `FALSE`

otherwise. It
dispatches to either `is.id.cycle()`

or `is.id.word()`

as
appropriate.

Function `is.id.list()`

tests a cyclist for identityness.

##### Note

The identity permutations documented here are distinct from the null
permutations documented at `nullperm.Rd`

.

##### See Also

`is.derangement`

,`nullperm`

##### Examples

```
# NOT RUN {
is.id(id)
as.word(id) # weird
x <- rperm(10,4)
x[3] <- id
is.id(x*inverse(x))
# }
```

*Documentation reproduced from package permutations, version 1.0-5, License: GPL-2*

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