Functions on Lazy Series Rings

Lazy series rings have variables, names for their variables, and a coefficient ring.

R . i: RngPowLaz, RngIntElt -> RngPowLazElt

The \(i\)th variable of the lazy power series ring \(R\), where \(i\) is between \(1\) and the rank of \(R\).

AssignNames(~R, S): RngPowLaz, [MonStgElt]

Given a lazy series ring \(R\) with \(n\) indeterminates and a sequence \(S\) of \(n\) strings, assign the elements of \(S\) to the names of the variables of \(R\).

BaseRing(R): RngPowLaz -> Rng

CoefficientRing(R): RngPowLaz -> Rng

The coefficient ring of the lazy power series ring \(R\). The coefficients of all the series in \(R\) will lie in this ring.

Rank(R): RngPowLaz -> RngIntElt

The number of variables associated with the lazy power series ring \(R\).

R1 eq R2: RngPowLaz, RngPowLaz -> BoolElt

Return true if the lazy series rings \(R1\) and \(R2\) are the same ring, that is, they have the same coefficient ring and rank.

Example: Names and Properties of a Lazy Series Ring (ex-aee740)

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The functions on lazy power series rings are illustrated here.

> L := LazyPowerSeriesRing(FiniteField(73), 7);
> L.4;
Lazy power series
> AssignNames(~L, ["a", "b", "c", "d", "fifth", "sixth", "seventh"]);
> L.4;
Lazy power series

The names for the variables of \(L\) are not used in default series printing. However they are used when printing an element to a given precision using PrintToPrecision.

> CoefficientRing(L);
Finite field of size 73
> Rank(L);
7
> L eq LazyPowerSeriesRing(CoefficientRing(L), Rank(L));
true

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