{"paper":{"title":"A canonical form for the continuous piecewise polynomial functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Jorge Caravantes, Laureano Gonzalez-Vega, M. Angeles Gomez-Molleda","submitted_at":"2014-11-25T16:57:51Z","abstract_excerpt":"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 $$\\{C_i(P):P\\in\\Q[x],i=0,\\ldots,\\deg(P)\\}$$ 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 canonic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6919","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}