Data.Number.ER.Real.Approx.Sequence

Types and methods related to explicit convergent sequences of real number approximations.

Documentation

data ConvergRealSeq ra

A converging sequence of real number approximations.

• Every finite subsequence has a non-empty intersection.
• The limit should be a singleton.

Constructors

ConvergRealSeq (EffortIndex -> ra)

Instances

ERApprox ra => Eq (ConvergRealSeq ra)

ERApprox ra => Fractional (ConvergRealSeq ra)

ERApprox ra => Num (ConvergRealSeq ra)

ERApprox ra => Ord (ConvergRealSeq ra)

ERApprox ra => Show (ConvergRealSeq ra)

makeFastConvergRealSeq :: ERApprox ra => ConvergRealSeq ra -> ConvergRealSeq ra

Turn an arbitrary convergent sequence into one with a guaranteed convergence rate - the precision (as defined by RA.ERApprox.RA.getPrecision) of x_ix is at least ix.

convertFuncRA2Seq :: (EffortIndex -> ra -> ra) -> ConvergRealSeq ra -> ConvergRealSeq ra

Using this operator, a unary funtion working over approximations can be converted to one that works over exact numbers represented through a sequence of approximations.

convertBinFuncRA2Seq :: (EffortIndex -> ra -> ra -> ra) -> ConvergRealSeq ra -> ConvergRealSeq ra -> ConvergRealSeq ra

The same as above, where f is binary

convergRealSeqElem :: ConvergRealSeq ra -> EffortIndex -> ra

showConvergRealSeq :: ERApprox ra => Int -> Bool -> Bool -> Precision -> ConvergRealSeq ra -> String

Show function for ConvergRealSeq's with full arguments.

showConvergRealSeqAuto :: ERApprox ra => Int -> ConvergRealSeq ra -> String

Show function for ConvergRealSeq's with all parameters fixed except for number of digits