úÎÞ¹%      !"#$None  7<>LN 6Two common operations on types defined with intervals.IThe interval type (most of its operations are calls to the raw functions) Interval addition Interval substraction Interval multiplication Interval division  Converts an % value into an interval.Interval cosine Interval sineIntersection of two s.SUnion of two intersecting intervals (undefined behaviour if they do not intersect).iConverts an optimal IEEE-754 representation of a number into an optimal interval containing this number.#&'() *+,-./012  () *+,-.&/'012None34579<>LNHThe type for Bernstein polynomials with an arbitrary number of variables"=Computes the derivative of a univariate Bernstein polynomial.# Computes f(1-x)' (useful when used with Bezier curves).$ZComputes the intersection of a given Bezier hypersurface, given by its graph, with plane z=0.-3456789 !:"#;$<=>?@ABCDEFGHIJKLMNOP !"#$ !$"#3456789 !:"#;$<=>?@ABCDEFGHIJKLMNOPQ       !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTpolyn_3v9fRtCJw89G7XfBIBIvP6Algebra.Polynomials.NumericalAlgebra.Polynomials.Bernstein Intervalize intervalize intersectsIntervalilowiupfpredfsuccplusminustimesover fromIntegral#cos#sin#sqrt#acos#asin# intersectsdunioninterval Bernstein?constantscalepromoteelevateeval restriction BernsteinpboundscoefsderivatereorientsolvebaseGHC.RealIntegral V_Interval MV_Intervalc_fpredc_fsucc!#$fVectorVectorInterval$fMVectorMVectorInterval$fUnboxIntervalTFCo:R:VectorIntervalTFCo:R:MVectorsInterval$fFractionalInterval $fNumInterval$fFloatingIntervalBoxcutsize restriction# variablesInterParam binomials convexHull$fBox(,,,,,,,)(,,,)$fBox(,,,,,)(,,) $fBox(,,,)(,) $fBox(,)Int$fNumBernsteinp$fNumBernsteinp0$fNumBernsteinp1$fNumBernsteinp2$fBernstein(,,,)$fBernstein(,,)$fBernstein(,)$fBernsteinInt$fIntervalizeBernsteinpTFCo:R:Inter(,,,)aTFCo:R:Inter(,,)aTFCo:R:Inter(,)aTFCo:R:InterIntaTFCo:R:Param(,,,)aTFCo:R:Param(,,)aTFCo:R:Param(,)aTFCo:R:ParamInta