# Structure Operations

## Related Structures

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

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

### `Parent(R): FldRe -> PowerStructure`

### `Parent(R): FldCom -> PowerStructure`

### `PrimeField(R): FldRe -> FldRat`

### `PrimeField(R): FldCom -> FldRat`

## Numerical Invariants

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

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

## Ring Predicates and Booleans

### `IsCommutative(R): FldRe -> BoolElt`

### `IsCommutative(R): FldCom -> BoolElt`

### `IsUnitary(R): FldRe -> BoolElt`

### `IsUnitary(R): FldCom -> BoolElt`

### `IsFinite(R): FldRe -> BoolElt`

### `IsFinite(R): FldCom -> BoolElt`

### `IsOrdered(R): FldRe -> BoolElt`

### `IsOrdered(R): FldCom -> BoolElt`

### `IsField(R): FldRe -> BoolElt`

### `IsField(R): FldCom -> BoolElt`

### `IsEuclideanDomain(R): FldRe -> BoolElt`

### `IsEuclideanDomain(R): FldCom -> BoolElt`

### `IsPID(R): FldRe -> BoolElt`

### `IsPID(R): FldCom -> BoolElt`

### `IsUFD(R): FldRe -> BoolElt`

### `IsUFD(R): FldCom -> BoolElt`

### `IsDivisionRing(R): FldRe -> BoolElt`

### `IsDivisionRing(R): FldCom -> BoolElt`

### `IsEuclideanRing(R): FldRe -> BoolElt`

### `IsEuclideanRing(R): FldCom -> BoolElt`

### `IsPrincipalIdealRing(R): FldRe -> BoolElt`

### `IsPrincipalIdealRing(R): FldCom -> BoolElt`

### `IsDomain(R): FldRe -> BoolElt`

### `IsDomain(R): FldCom -> BoolElt`

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

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

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

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

## Other Structure Functions

### `Precision(R): FldCom -> RngIntElt`

### `Precision(R): FldRe -> RngIntElt`

Return the decimal precision $p$ to which calculations are performed in the real or complex field $R$.

### `BitPrecision(R): FldCom -> RngIntElt`

### `BitPrecision(R): FldRe -> RngIntElt`

Return the (internally used) bit precision $p$ to which calculations are performed in the real or complex field $R$.