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A complete presentation of $(\mathbb{C}\mbox{[X]},\circ)$

Barbu Rudolf Berceanu

Abstract

We recall the fundamental theorem of J.F. Ritt, with a stress on the action of the affine group and canonical forms of complex polynomials. Then we give a complete presentation of the monoid $(\mathbb{C}\mbox{[X]},\circ)$. A list of decomposable polynomials is given in degrees $\leq 12$.

A complete presentation of $(\mathbb{C}\mbox{[X]},\circ)$

Abstract

We recall the fundamental theorem of J.F. Ritt, with a stress on the action of the affine group and canonical forms of complex polynomials. Then we give a complete presentation of the monoid . A list of decomposable polynomials is given in degrees .

Paper Structure

This paper contains 7 sections, 19 theorems, 71 equations.

Table of Contents

  1. Introduction and statement of results
  2. Canonical forms of polynomials
  3. Decomposition of polynomials
  4. Indecomposable polynomials
  5. Ritt presentation
  6. A complete presentation
  7. Appendix

Key Result

Theorem 1.3

A complete presentation of the monoid $(\mathbb{C}[X],\circ)$ is given by (the relations are up to a $G$-equivalence).

Theorems & Definitions (50)

  • Definition 1.1
  • Definition 1.2
  • Theorem 1.3
  • Definition 2.1
  • Example 2.2
  • Proposition 2.3
  • proof
  • Example 2.4
  • Remark 2.5
  • Example 2.6
  • ...and 40 more