Creation of Lazy Series Rings#
Both univariate and multivariate lazy series rings can be created.
- LazyPowerSeriesRing(C, n): Rng, RngIntElt -> RngPowLaz#
The lazy power series ring with coefficient ring \(C\) and \(n\) variables. Any ring is valid input for \(C\) and \(n\) can be any positive integer.
- ChangeRing(L, C): RngPowLaz, Rng -> RngPowLaz, Map#
Given a lazy series ring \(L\) defined over a ring \(R\) and some ring \(C\), return the lazy series ring with coefficient ring \(C\) but the same number of variables as \(L\). A map from \(L\) to the new lazy series ring is also returned which takes a series \(s\) in \(L\) to a series whose coefficients are those of \(s\) coerced into \(C\).
- Example: Ring Create (ex-085add)#
Here we illustrate the creation and printing of lazy power series rings.
> L := LazyPowerSeriesRing(Rationals(), 5); > L; Lazy power series ring in 5 variables over Rational Field > ChangeRing(L, MaximalOrder(CyclotomicField(7))); Lazy power series ring in 5 variables over Maximal Equation Order with defining polynomial x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 over Z