Schw"achen: konstante Funktionen werden nicht erkannt.
---------------------------------------------------------------------- > module Integrate ( integrate > ) > where ----------------------------------------------------------------------
---------------------------------------------------------------------- > import CPS renaming (zero to dontknow) > import Sort ( mergeSort ) > renaming (mergeSort to sort) > > import Function ( Function(..), Prim(..), constant, > factors, prod, > (+++), (***), half, one, mone, two ) > import Derive ( derive ) > import Simplify hiding (prod) > import Table ( Table(..), retrieve ) ----------------------------------------------------------------------
---------------------------------------------------------------------- > integrate :: Table -> Function -> Maybe Function > integrate t f = firstSolution (integr 25 t f) () ----------------------------------------------------------------------
---------------------------------------------------------------------- > integr 0 _ _ = dontknow > integr d t f = retrieve t f ? int f > where > int (Const c) = unit (Const c *** Id) > int (Ratio n) = unit (Ratio n *** Id) > int Id = unit (half *** Id :^: two) > int (Prim Abs) = dontknow > int (Prim f) = unit (case f of > Sin -> mone *** Prim Cos > Cos -> Prim Sin > Tan -> mone *** (Prim Ln :.: Prim Abs :.: Prim Cos) > Cot -> Prim Ln :.: Prim Abs :.: Prim Sin > Exp -> Prim Exp > Ln -> Id *** Prim Ln +++ mone *** Id > Arcsin -> Id *** Prim Arcsin +++ h1 > Arccos -> Id *** Prim Arccos +++ mone *** h1 > Arctan -> Id *** Prim Arctan +++ mone *** h2 > Arccot -> Id *** Prim Arccot +++ h2 > Sinh -> Prim Cosh > Cosh -> Prim Sinh > Tanh -> Prim Ln :.: Prim Abs :.: Prim Cosh > Coth -> Prim Ln :.: Prim Abs :.: Prim Sinh) > where > h1 = (one +++ mone *** Id :^: two) :^: half > h2 = half *** (Prim Ln :.: Id :^: two +++ one) > int (Fun f) = dontknow > int (Derive 1 f) = unit f > int (Derive (n + 1) f) = unit (Derive n f) > int (Summ fs) = accumulat [ integr d t f| f<-fs ] &= \ffs -> > unit (Summ ffs) > int (Id :^: n) > | n == mone = unit (Prim Ln :.: Prim Abs) > int (Id :^: n) > | constant n = unit ((n +++ one) :^: mone *** Id :^: (n +++ one)) > int h = (substIntegr d t hs > ?? partIntegr d t hs) &= \hh -> > unit (prod ns *** hh) > where > (ns, hs) = partition constant (factors h) ----------------------------------------------------------------------
Realisiert die Regel @int (f @circ g)@cdot g' = F @circ g.
---------------------------------------------------------------------- > substIntegr d t hs = select hs &= \(f, g, gs)-> > let g' = standard1 (derive g) in > match gs (factors g') &= \n -> > integr (d - 1) t f &= \ff -> > unit (n *** ff :.: g) ----------------------------------------------------------------------
---------------------------------------------------------------------- > select hs = (pick1 hs &= \(h, gs) -> > case h of > f :.: g -> unit (f, g, gs) > g :^: n | constant n -> unit (Id :^: n, g, gs) > _ -> dontknow) > ?? (split hs &= \(fs, gs) -> > unit (Id, prod fs, gs)) ----------------------------------------------------------------------
---------------------------------------------------------------------- > match fs gs > | sort fs' == sort gs' = unit (prod m *** prod n :^: mone) > | otherwise = dontknow > where (m, fs') = partition constant fs > (n, gs') = partition constant gs ----------------------------------------------------------------------
Realisiert die Regel @[ @int f @cdot g = f @cdot G - @int f' @cdot G . @]
---------------------------------------------------------------------- > partIntegr d t hs = let hs' = sort hs in > (pickn 1 hs' > ?? pickn 2 hs' > ?? pickn 3 hs') &= \(gs, fs) -> > let g = prod gs in > let f = prod fs in > integr (d - 1) t g &= \gg -> > let h = standard1 (derive f *** gg) in > integr (d - 1) t h &= \hh -> > unit (f *** gg +++ mone *** hh) ----------------------------------------------------------------------
---------------------------------------------------------------------- > pick1 [] = dontknow > pick1 (a:x) = unit (a, x) > ?? pick1 x &= \(b, y) -> unit (b, a:y) ----------------------------------------------------------------------
---------------------------------------------------------------------- > pickn 0 x = unit ([], x) > pickn (n + 1) x = pick1 x &= \(a, x') -> pickn n x' &= \(as, y) -> > unit (a:as, y) ----------------------------------------------------------------------
---------------------------------------------------------------------- > split x = alternate [ pickn i x | i<-[1..length x-1] ] ----------------------------------------------------------------------
Go to the first, previous, next, last section, table of contents.