2026-06-02T02:03:33Zhttps://riuma.uma.es/rest/oai/requestoai:riuma.uma.es:10630/404212026-02-03T11:16:43Zcom_10630_2254col_10630_37953
RIUMA. Repositorio Institucional de la Universidad de Málaga
author
Caravantes, Jorge
author
Gómez-Molleda, María de los Ángeles
author
González Vega, Laureano
2025-10-23T09:50:45Z
2025-10-23T09:50:45Z
2015-08-01
Journal of Computational and Applied Mathematics, 2015, 283(1), 17-27
https://hdl.handle.net/10630/40421
10.1016/j.cam.2014.11.033
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 in Q[x], i = 0, ..., deg(P)} defined by C_i(P)(x) = 0 if x is at most a and P(x) if x is at least a, where is the i-th real root of the polynomial P. These functions will allow us to represent and manipulate easily every continuous piecewise polynomial 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.
eng
Funciones (Matemáticas)
Álgebra abstracta
Algoritmos computacionales
A canonical form for the continuous piecewise polynomial functions.
journal article
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A+canonical+form+for+the+continuous+piecewise.pdf