You can use (real!) real numbers (ok, computables only),
fixed point numbers with arbitrary precision,
power series, physical units, residue classes immediately with GHCi.
Just download the NumericPrelude package from

  http://hackage.haskell.org/cgi-bin/hackage-scripts/package/numeric-prelude

or get the cutting edge version (caution: frequent API changes!)

  wget -r --no-parent http://darcs.haskell.org/numericprelude/

or even better with 'darcs' (see http://darcs.net/) if available

  darcs get http://darcs.haskell.org/numericprelude/

then start GHCi as follows.


numericprelude$ make ghci
...
*Main> showReal (logBase 2 3 + pi + sqrt 2)
"6.14076871668404446871807105143701747152665568244453495460737698483964711254267460000070283458784688280
81425952192537Interrupted.

*Main> showFixedPoint (log 2 + sqrt 2 + pi)
"5.2489533965228335966815642289473775308423414091123091482723043397919425067180107530842856866661773283"
*Main> showFixedPoint (FixedPoint.lift0 (10^1000) Number.FixedPoint.piConst)
"3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201997"
*Main> showFixedPoint (sqrt $ log $ FixedPoint.fromIntegerBasis 10 1000 2)
"0.8325546111576977563531646448952010476305888522644407291668291172340794351973046371489980076416742886448482282410637851330108956418582929396049471528907228470171676350886723388423935936597108246765808570792700443622966196741818893190586581386252927024531072144299452636462660173046566333123423559517018232473131336553277397460554922101186525242623654599834751330464388563784517713133769314261857977824435543915784989600358362742619360874461618454558851154639567200399205141997756487547096515291667876389818410045279797332626020900120913715779072042123248766285273274106918375012034073383400019132961678929241754711455999383432933099386116049520197996591124299426029350053074823745166425774910775252128414873633138846561928632399126787643990250582692324765636262660441952182748966643014552842325814025874977948870859994990052332656663016056779182667586683292672622606377187398292031363768554806074838642380037406327808548247471555604075913559987467405262524094749104596792515303983594015683517043115422"

*Main> divMod (polynomial [1,3,3]) (polynomial [1,1::Rational])
(Polynomial.fromCoeffs [0 % 1,3 % 1],Polynomial.fromCoeffs [1 % 1])

*Main> 2*kilo*meter / mach :: SIDouble
6.024096385542169 s

*Main> sqrt (powerSeries [1,1::Double])
PowerSeries.fromCoeffs
[1.0,0.5,-0.125,6.25e-2,-3.90625e-2,2.734375e-2,-2.05078125e-2,1.611328125e-2,-1.3092041015625e-2,...

*Main> PowerSeries.sqrt (const 1) [1,1::Rational]
[1 % 1,1 % 2,-1 % 8,1 % 16,-5 % 128,7 % 256,-21 % 1024,33 % 2048,-429 % 32768,715 % 65536,-2431 % 262144,4199 % 524288,-29393 % 4194304,52003 % 8388608, ...

*Main> ResidueClass.concrete 7 (5*3/2) :: Integer
4


*Main> polynomial [1,5,6] % polynomial [1,4,4::Rational]
Polynomial.fromCoeffs [1 % 2,3 % 2] % Polynomial.fromCoeffs [1 % 2,1 % 1]

-- (1 + 2 * sqrt 2) * (3 + 4 * sqrt 2) == (19 + 10 * sqrt 2)
*Main> ResidueClass.concrete (polynomial [-2,0,1::Rational]) (polyResidueClass [1,2] * polyResidueClass[3,4])
Polynomial.fromCoeffs [19 % 1,10 % 1]



For given factorization of the denominator of a fraction,
you can compute the partial fraction decomposition and
you can do calculations in this representation.

*Main> let a = partialFraction [2,3,5] (1::Integer)
*Main> a
PartialFraction.fromFractionSum (-1) [(2,[1]),(3,[1]),(5,[1])]
*Main> a^2
PartialFraction.fromFractionSum (-1) [(2,[0,1]),(3,[0,1]),(5,[3,1])]
*Main> PartialFraction.toFraction (a^2) == 1/(2*3*5)^2
True

*Main> let x = polynomial [0,1::Rational]
*Main> partialFraction [x-4,x,x+4] ((x-2)*(x+2))
PartialFraction.fromFractionSum (Polynomial.fromCoeffs [0 % 1,0 % 1,0 % 1]) [(Polynomial.fromCoeffs [-4 %1,1 % 1],[Polynomial.fromCoeffs [3 % 8]]),(Polynomial.fromCoeffs [0 % 1,1 % 1],[Polynomial.fromCoeffs [1 % 4]]),(Polynomial.fromCoeffs [4 % 1,1 % 1],[Polynomial.fromCoeffs [3 % 8]])]