Lazy Power Series Rings
- Introduction
- Creation of Lazy Series Rings
- Functions on Lazy Series Rings
- Elements
- Creation of Finite Lazy Series
- Arithmetic with Lazy Series
- Finding Coefficients of Lazy Series
Coefficient(s, i): RngPowLazElt, RngIntElt → RngEltCoefficient(s, T): RngPowLazElt, SeqEnum → RngEltCoefficients(s, n): RngPowLazElt, RngIntElt → [RngElt]Coefficients(s, l, n): RngPowLazElt, RngIntElt, RngIntElt → [RngElt]Valuation(s): RngPowLazElt → AnyPrintToPrecision(s, n): RngPowLazElt, RngIntEltPrintTermsOfDegree(s, l, n): RngPowLazElt, RngIntElt, RngIntEltLeadingCoefficient(s): RngPowLazElt → RngEltLeadingTerm(s): RngPowLazElt → RngPowLazElt- Example: Coefficients by the Spiral Algorithm
CoefficientsNonSpiral(s, n): RngPowLazElt, [RngIntElt] → SeqEnumCoefficientsNonSpiral(s, n): RngPowLazElt, RngIntElt → SeqEnumIndex(s, i, n): RngPowLazElt, [RngIntElt], [RngIntElt] → RngIntElt- Example: Coefficients by the Non-Spiral Algorithm
- Predicates on Lazy Series
- Other Functions on Lazy Series
Derivative(s): RngPowLazElt → RngPowLazEltDerivative(s, v): RngPowLazElt, RngIntElt → RngPowLazEltDerivative(s, v, n): RngPowLazElt, RngIntElt, RngIntElt → RngPowLazEltIntegral(s): RngPowLazElt → RngPowLazEltIntegral(s, v): RngPowLazElt, RngIntElt → RngPowLazEltEvaluate(s, t): RngPowLazElt, RngPowLazElt → RngPowLazEltEvaluate(s, T): RngPowLazElt, [RngPowLazElt] → RngPowLazElt- Example: Evaluating a Lazy Series
SquareRoot(s): RngPowLazElt → RngPowLazEltSqrt(s): RngPowLazElt → RngPowLazEltIsSquare(s): RngPowLazElt → BoolElt, RngPowLazEltPolynomialCoefficient(s, i): RngPowLazElt, RngIntElt → RngPowLazEltPolynomialCoefficient(s, i): RngPowLazElt, [RngIntElt] → RngPowLazElt