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