I. Python Object Browser.
 II. Python to R Communicator.
 III. Manipulation of piecewise polynomial functions.
 1 History of changes (poly).
 2 Installation of the poly module.
 3 Introduction into the poly module.
 4 Calculus behind the poly module.
 IV. Building C++ projects.

## Introduction into the poly module. he poly module contains the public classes Poly, Piece, PiecewisePoly and the public functions Abs,Pow,Sqrt,T,S,Op,Convolution.

The class Poly is a representation of a polynomial. Piece is a representation of a left-closed, right-open interval. PiecewisePoly is a representation of a piecewise polynomial function with compact support.

The functions Abs and Sqrt take a PiecewisePoly object and return a callable object. Pow returns a PiecewisePoly object.

T is a transport operation. S is a scale operation. Op is a combined transport and scale. These take Piece,Poly or PiecewisePoly and act as described in the section ( Elementary definitions of wavelet analysis ).

The function Convolution performs the convolution of two piecewise polynomial functions.

The object PiecewisePoly is equipped with algebraic operations, taking an integral and restricting it to another interval.

The example code below assumes that the R Communicator of the section ( Python to R Communicator ) is installed and the pyServer is running in an R shell. The following function plots a graph of a function given by a poly.PiecewisePoly object.

import r_com

def plotPoly(func,N=10000) :

"Plot a PiecewisePoly-nomial via r_com"

spt=func.support()

a=numpy.floor(spt.a())

b=numpy.ceil(spt.b())

h=1.0*(b-a)/N

x=[a+h*i for i in range(0,N+1)]

y=[func(xx) for xx in x]

r_com.r.set('x',x)

r_com.r.set('y',y)

r_com.r.plot(r_com.r('x'),r_com.r('y'))

pp=plotPoly

Consider the following session.  The line  constructs a PiecewisePoly object. The argument of poly.Poly is a list of coefficients of the polynomial f(x)=1. The two arguments of poly.Piece are boundaries of the interval. The poly.PiecewisePoly accepts a list of tuples.

The example below constructs and plots a "centered hut" along the same guidelines.  Algebraic operations, integration and convolution are illustrated in the following session. 