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- W2952502535 abstract "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 $${C_i(P):PinQ[x],i=0,ldots,°(P)}$$ defined by $$C_i(P)(x)= left{ begin{array}{cll}0 & mbox{ if } & x leq alpha P(x) & mbox{ if } & x geq alpha end{array} right.$$ where $alpha$ 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." @default.
- W2952502535 created "2019-06-27" @default.
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- W2952502535 date "2014-11-25" @default.
- W2952502535 modified "2023-10-18" @default.
- W2952502535 title "A canonical form for the continuous piecewise polynomial functions" @default.
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