Elementary Invariants

These functions return some simple information which can partially define a p-adic ring or field.

Prime(P) : FldLoc -> RngIntElt

Prime(P) : RngLoc -> RngIntElt

UniformizingElement(P) : RngLoc -> RngLocElt

P . 1 : RngLoc -> RngLocElt

UniformizingElement(P) : FldLoc -> FldLocElt

P . 1 : FldLoc -> FldLocElt

Returns the prime p defining the p-adic ring or field P. This is also the characteristic of the residue class field of the ring P or the ring of integers of the field P.

ResidueClassField(P) : RngLoc -> FldFin, Map

Return the finite field isomorphic to the quotient of the p-adic ring P by its maximal ideal p P (generated by the prime).

Precision(P) : RngLoc -> RngIntElt

Precision(P) : FldLoc -> RngIntElt

The precision with which P has been created. If P is a p-adic ring this is the maximum absolute precision its elements can be created with. If L is a p-adic field this is the maximum relative precision its elements can be created with.

Example RngPad_elinvar (H42E2)

> Zp<p> := pAdicRing(5, 20);
> ResidueClassField(Zp);
Finite field of size 5
Mapping from: RngLoc: Zp to GF(5)
> UniformizingElement(Zp);
5
> Precision(Zp);
20
> Zp<p> := pAdicRing(5);
> Precision(Zp);
Infinity