9y1      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~ Safe The - type implements (constructive) real numbers.'Note that the comparison operations on k may diverge since it is (by necessity) impossible to implementent them correctly and always terminating.9This implementation is really David Lester's ERA package.The  function connverts a  to a .The number of decimalsThe real numberThe resulting stringSafe  The   type is the type of differentiable numbers. It's an instance of all the usual numeric classes. The computed derivative of a function is is correct except where the function is discontinuous, at these points the derivative should be a Dirac pulse, but it isn't.The  [ numbers are printed with a trailing ~~ to indicate that there is a "tail" of derivatives.The ' function turns a normal number into a   number with the same value. Not that numeric literals do not need an explicit conversion due to the normal Haskell overloading of literals.The ~ function turns a number into a variable number. This is the number with with respect to which the derivaticve is computed.The  takes a  f number and returns its first derivative. The function can be iterated to to get higher derivaties.The  function takes a  L number back to a normal number, thus forgetting about all the derivatives.The  takes a value and   value and makes a  ? number that has the given value as its normal value, and the   number as its derivatives.The o function is a simple utility to take the derivative of a (single argument) function. It is simply defined as  deriv f = val . df . f . dVar Convert a  " function to an ordinary function.   Safe!e !"#$%&'()*+,-./0123456 !"#$%&'()*+,-./0123456NoneEKQV(9 500 decimals.: 50 decimals.; Ten decimals.<@A type construct that gives one more decimals than the argument.=#An epsilon of 1, i.e., no decimals.>The >L class contains the types that can be used to determine the precision of a 7 number.@4Convert between two arbitrary fixed precision types.B The call with_added_precision r f v evaluates f v2, while temporarily multiplying the precision of v by r. 789:;<=>?@AB 7>=<;:89@A?B7>None*TDFloating point number where the precision is determined by the type e.8:;<=>TT>=<;:8TSafe+9^_`^_`^Safe, gThe infinite natural number.fgfgfSafe0o6Symbolic numbers over some base type for the literals.pCreate a variable.q4Create a constant (useful when it is not a literal).rThe expression  subst x v e substitutes the expression v% for each occurence of the variable x in e.opqrsopqrso Safe>?A1NClass of vector spaces v with scalar s.     !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  )numbers-3000.2.0.2-D87q23acK4LG7MabMFXIqIData.Number.CRealData.Number.DifData.Number.FixedFunctionsData.Number.FixedData.Number.BigFloatData.Number.IntervalData.Number.NaturalData.Number.SymbolicData.Number.VectorspaceCReal showCReal $fShowCReal $fReadCReal$fRealFloatCReal$fRealFracCReal $fRealCReal $fEnumCReal$fFloatingCReal$fFractionalCReal $fNumCReal $fOrdCReal $fEqCRealDifdCondVardfvalmkDifderivunDif$fRealFloatDif $fRealFracDif $fRealDif $fFloatingDif$fFractionalDif$fNumDif$fOrdDif$fEqDif $fReadDif $fShowDifCFapproxfromCFtoCFapproxCFfromTaylorToCFfac integerRoot2pitansincosatanasinacossqrtexpcoshsinhtanhatanhasinhacoshlogFixed PrecPlus20Prec500Prec50Prec10EpsDiv10Eps1Epsilon precision convertFixed dynamicEpswith_added_precision $fEpsilonEps1$fEpsilonEpsDiv10$fEpsilonPrec10$fEpsilonPrec50$fEpsilonPrec500$fEpsilonPrecPlus20$fRealFloatFixed$fFloatingFixed $fReadFixed $fShowFixed$fFractionalFixed $fNumFixed $fEqFixed $fOrdFixed $fEnumFixed $fRealFixed$fRealFracFixedBigFloat$fRealFloatBigFloat$fFloatingBigFloat$fRealFracBigFloat$fFractionalBigFloat $fOrdBigFloat$fRealBigFloat $fNumBigFloat$fShowBigFloat $fEqBigFloatIntervalivalgetIval$fFractionalInterval $fNumInterval$fShowInterval $fOrdInterval $fEqIntervalNaturalinfinity $fEnumNatural $fRealNatural$fIntegralNatural $fNumNatural $fOrdNatural $fEqNatural $fShowNaturalSymvarconsubstunSym$fRealFloatSym $fFloatingSym $fRealFracSym $fRealSym $fEnumSym $fIntegralSym$fFractionalSym$fNumSym $fShowSym$fOrdSym$fEqSym Vectorspace*><+>vnegatevzerobaseGHC.BaseStringCRDCFepsBFIZSConApp