# Structure Operations

## Related Structures

### `Parent(R): RngSer -> Pow`

### `Category(R): RngSer -> Cat`

### `BaseRing(R): RngSer -> Rng`

### `CoefficientRing(R): RngSer -> Rng`

Return the coefficient ring of the series ring $R$.

### `IntegerRing(R): RngSer -> RngSerPow`

### `Integers(R): RngSer -> RngSerPow`

### `RingOfIntegers(R): RngSer -> RngSerPow`

Return the power series ring which is the integer ring of the laurent series ring $R$.

### `FieldOfFractions(R): RngSer -> RngSerLaur`

Return the laurent series ring which is the field of fractions of the series ring $R$.

### `ChangePrecision(R, r): RngSer, Any -> RngSer`

### `ChangePrecision(~R, r): RngSer, Any -> RngSer`

Return a series ring identical to the series ring $R$ but having precision $r$.

### `ChangeRing(R, C): RngSer, Rng -> RngSer, Map`

Return the series ring identical to the series ring $R$ but having coefficient ring $C$.

### `ResidueClassField(R): RngSer -> Rng, Map`

Return the residue class field of the series ring $R$ (which will be the same as the coefficient ring of $R$) and the map from $R$ into the residue class field.

## Invariants

### `Characteristic(R): RngSer -> RngIntElt`

### `Precision(R): RngSer -> ExtReElt`

### `GetPrecision(R): RngSer -> ExtReElt`

Return the precision of the fixed precision series ring $R$. If $R$ is a fixed precision power series ring, then this is the fixed absolute precision for all elements of the ring. If $R$ is a fixed precision Laurent series ring, then this is the maximum relative precision for all elements of the ring.

## Ring Predicates and Booleans

### `IsCommutative(Q): RngSer -> BoolElt`

### `IsUnitary(Q): RngSer -> BoolElt`

### `IsFinite(Q): RngSer -> BoolElt`

### `IsOrdered(Q): RngSer -> BoolElt`

### `IsField(Q): RngSer -> BoolElt`

### `IsEuclideanDomain(Q): RngSer -> BoolElt`

### `IsPID(Q): RngSer -> BoolElt`

### `IsUFD(Q): RngSer -> BoolElt`

### `IsDivisionRing(Q): RngSer -> BoolElt`

### `IsEuclideanRing(Q): RngSer -> BoolElt`

### `IsPrincipalIdealRing(Q): RngSer -> BoolElt`

### `IsDomain(Q): RngSer -> BoolElt`

### `R eq S: RngSer, RngSer -> BoolElt`

### `R ne S: RngSer, RngSer -> BoolElt`