úÎ)f%u=      !"#$%&'()*+,-./01234567 8 9 : ; < None  Step size\frac{\partial H}{\partial q}\frac{\partial H}{\partial p}Current (p, q) as a 2-dimensional vectorNew (p, q) as a 2-dimensional vector   None: ;Störmer-Verlet integration scheme for systems of the form !\mathbb{H}(p,q) = T(p,q) + V(p,q) .Störmer-Verlet integration scheme for system: !\ddot{\mathbf{q}} = f(\mathbf{q})  Step size\frac{\partial H}{\partial q}\frac{\partial H}{\partial p}Current (p, q) as a 2-dimensional vectorNew (p, q) as a 2-dimensional vector f Step sizeCurrent (p, q) as a 2-dimensional vectorNew (p, q) as a 2-dimensional vector   Safe type implicit solver     SafeInternal type that users bySafe=>?@ABCDEFGHIJ=>?@ABCDEFGHIJNone !"#$%&'()*+,-./0 !"#$%&'()*+,-./0 !"#$%&'()*+,-./0 !"#$%&'()*+,-./0Safe:Safe10Integrator function - Phi [h] |-> y_0 -> y_11Step Initial value Next value111None:2Implicit solver type3xFixed point method it iterates function f until it will break "" will be reached then it returns one but last iteration5Fsimple break rule that will break evaluatioin when value less then Eps6same as  breakNormR´ but assume that inner type is an instance of InnerField, so it's possible to use innerproduct to find norm N.B function uses $||v||^2 < eps$, so epsilon should be pre evaluated2implicit method breakRule initial value final value34function break rule initial valueresult56234562345623456 NoneK777K7 None:L888L8 None:9: Step sizeCurrent (p,q) as a 2-dimentional vectorNew (p, q) as a 2-dimetional vector9:9:9: None:;Integrator of form% \Phi[h] : y_{n+1} = y_n + h f (y_n) ;;;; None<ÖIntegrate ODE equation using fixed steps set by a vector, and returns a vector of solutions corrensdonded to times that was requested. It takes Vector of time points as a parameter and returns a vector of results<Internal integratorinitial valuevector of time pointsvector of solution<<<M !"#$%&'()*+,-./0123456789:;<=>?@ABCDE F G H I J KLMNOPQRSTUVWXY H HZ*numeric-ode-0.0.0.0-7uLap0gnPmNFz2CZlXlqSz!Math.Integrators.StormerVerletAltMath.Integrators.StormerVerletMath.Integrators.RK.TypesMath.Integrators.RK.InternalMath.Integrators.RK.ParserMath.Integrators.RK.TemplateMath.Integrators.InternalMath.Integrators.ImplicitMath.Integrators.ImplicitEuler%Math.Integrators.ImplicitMidpointRuleMath.Integrators.SympleticEulerMath.Integrators.ExplicitEulerMath.IntegratorsMath.Integrators.RK oneStepH98nablaQ'nablaP'eq10q20p10p20initsstormerVerlet2HstormerVerlet2ImplicitRkType FixedPointNewtonIterationMExp DelimeterRow isExplicit $fShowMExp$fEqMExpreadMatrixTableqrkjvjv'jldldplusvplusvmultmultld'plus'vplus'vmult'mult'vNfoldOp realToFracNzeroVNfthytpyrktestirk fpointRunfpoint IntegratorImplicitSolverfixedPointSolver fixedPoint breakNormR breakNormIR implicitEulerimrepssympleticEuler1 explicitEuler integrateVlexer whiteSpacelexemesymbolfloatparensnatural identifierreserved reservedOpexprfactortableerun