polynomials to interpolate functions {#mainpage}

Feature	syntax
construction	`polynomial<> P( {t0,t1,t2,...,tp}, {y0,y1,y2,...,yp} )`
evaluation	`y = P( time )`
differentiation	`y = P.deriv( time, order )`
rootfinding	`t = P.findroot( rootfn, tlower, tupper )`
differentiation	`polynomial<> deriv = P[order]`
hermite interpolation	`polynomial<> P( {t0,t0,t0,t1}, {y0,dy0,ddy0,y1} )`
integration	`P.integrate( t0, t1 )`
addition/substraction	`polynomial<> sum = P1 + P2`
adding points*	`P.add_point( tnew, ynew )`

- limited support for adding derivatives ( that is tnew already exists in t_ )

plans

automatic sorting of input, so t_[0] <= t_[1] <= ... <= t_[p]
- in this case add_point will have to insert the new point at an appropriate spot
- this requires to store all finite differences
add spline class which stores all divided differences for dynamic order interpolation
set default the identical function for rootfn if state_type can be compared to 0. this way, a root of the polynomial is found