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Structure Operations

Subsections

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

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Version: V2.19 of Wed Apr 24 15:09:57 EST 2013