We present in this paper a canonical form for the elements in the ring of continuous piecewise polynomial functions. This new representation is based on the use of a particular class of functions {C-i(P) : P is an ele...
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We present in this paper a canonical form for the elements in the ring of continuous piecewise polynomial functions. This new representation is based on the use of a particular class of functions {C-i(P) : P is an element of Q[x], i = 0,..., deg(P)} defined by C-i(P)(x) ={(0)(p(x)) (if x >=alpha) (if x <=alpha) where a is the ith real root of the polynomial P. These functions will allow us to represent and manipulate easily every continuouspiecewisepolynomial function through the use of the corresponding canonical form. It will be also shown how to produce a "rational" representation of each function C-i(P) allowing its evaluation by performing only operations in Q and avoiding the use of any real algebraic number. (C) 2014 Elsevier B.V. All rights reserved.
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