{
  "id": "2310.12812",
  "version": "v1",
  "published": "2023-10-19T15:09:42.000Z",
  "updated": "2023-10-19T15:09:42.000Z",
  "title": "Systems of Discrete Differential Equations, Constructive Algebraicity of the Solutions",
  "authors": [
    "Hadrien Notarantonio",
    "Sergey Yurkevich"
  ],
  "categories": [
    "math.CO",
    "cs.CC"
  ],
  "abstract": "In this article, we study systems of $n \\geq 1$, not necessarily linear, discrete differential equations (DDEs) of order $k \\geq 1$ with one catalytic variable. We provide a constructive and elementary proof of algebraicity of the solutions of such equations. This part of the present article can be seen as a generalization of the pioneering work by Bousquet-M\\'elou and Jehanne~(2006) who settled down the case $n=1$. Moreover, we obtain effective bounds for the algebraicity degrees of the solutions and provide an algorithm for computing annihilating polynomials of the algebraic series. Finally, we carry out a first analysis in the direction of effectivity for solving systems of DDEs in view of practical applications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-19T15:09:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete differential equations",
      "constructive algebraicity",
      "study systems",
      "elementary proof",
      "algebraicity degrees"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}