# Decomposing and Composing Units¶

## Reducing a Unit to Its Irreducible Parts¶

A unit or quantity can be decomposed into its irreducible parts using
the `Unit.decompose()`

or
`Quantity.decompose()`

methods.

### Examples¶

To decompose a unit with `decompose()`

:

```
>>> from astropy import units as u
>>> u.Ry
Unit("Ry")
>>> u.Ry.decompose()
Unit("2.17987e-18 m2 kg / s2")
```

To get the list of units in the decomposition, the
`bases`

and `powers`

properties can be used:

```
>>> Ry = u.Ry.decompose()
>>> [unit**power for unit, power in zip(Ry.bases, Ry.powers)]
[Unit("m2"), Unit("kg"), Unit("1 / s2")]
```

You can limit the selection of units that you want to decompose by
using the `bases`

keyword argument:

```
>>> u.Ry.decompose(bases=[u.m, u.N])
Unit("2.17987e-18 N m")
```

This is also useful to decompose to a particular system. For example, to decompose the Rydberg unit of energy in terms of CGS units:

```
>>> u.Ry.decompose(bases=u.cgs.bases)
Unit("2.17987e-11 cm2 g / s2")
```

Finally, if you want to know how a unit was defined:

```
>>> u.Ry.represents
Unit("13.6057 eV")
```

## Automatically Composing a Unit into More Complex Units¶

Conversely, a unit may be recomposed back into more complex units
using the `compose()`

method. Since there
may be multiple equally good results, a list is always returned.

### Examples¶

To recompose a unit with `compose()`

:

```
>>> x = u.Ry.decompose()
>>> x.compose()
[Unit("Ry"),
Unit("2.17987e-18 J"),
Unit("2.17987e-11 erg"),
Unit("13.6057 eV")]
```

Some other interesting examples:

```
>>> (u.s ** -1).compose()
[Unit("Bq"), Unit("Hz"), Unit("2.7027e-11 Ci")]
```

Composition can be combined with Equivalencies:

```
>>> (u.s ** -1).compose(equivalencies=u.spectral())
[Unit("m"),
Unit("Hz"),
Unit("J"),
Unit("Bq"),
Unit("3.24078e-17 pc"),
Unit("1.057e-16 lyr"),
Unit("6.68459e-12 AU"),
Unit("1.4378e-09 solRad"),
Unit("0.01 k"),
Unit("100 cm"),
Unit("1e+06 micron"),
Unit("1e+07 erg"),
Unit("1e+10 Angstrom"),
Unit("3.7e+10 Ci"),
Unit("4.58743e+17 Ry"),
Unit("6.24151e+18 eV")]
```

A name does not exist for every arbitrary derived unit imaginable. In that case, the system will do its best to reduce the unit to the fewest possible symbols:

```
>>> (u.cd * u.sr * u.V * u.s).compose()
[Unit("Wb lm"), Unit("1e+08 Mx lm")]
```

## Converting Between Systems¶

Built on top of this functionality is a convenience method to convert between unit systems.

### Examples¶

To convert between unit systems:

```
>>> u.Pa.to_system(u.cgs)
[Unit("10 P / s"), Unit("10 Ba")]
```

There is also a shorthand for this which only returns the first of many possible matches:

```
>>> u.Pa.cgs
Unit("10 P / s")
```

This is equivalent to decomposing into the new system and then
composing into the most complex units possible, though
`to_system()`

adds some extra logic to
return the results sorted in the most useful order:

```
>>> u.Pa.decompose(bases=u.cgs.bases)
Unit("10 g / (cm s2)")
>>> _.compose(units=u.cgs)
[Unit("10 Ba"), Unit("10 P / s")]
```