4 papers
math.AG2025
Separated Variables on Plane Algebraic Curves
Manfred Buchacher
We investigate the problem of deciding whether the restriction of a rational function to the curve associated with an irreducible polynomial $p\in\mathbb{K}[x…
math.CO2025
The Newton-Puiseux algorithm and effective algebraic series
Manfred Buchacher
We explain how to encode an algebraic series by finite data and how to do effective arithmetic on the level of these encodings. The reasoning is based on the Newton-Puiseux algorit…
math.CO2025
The Orbit-Sum Method for Higher Order Equations
Manfred Buchacher, Manuel Kauers
The orbit-sum method is an algebraic version of the reflection-principle that was introduced by Bousquet-Mélou and Mishna to solve functional equations that arise in the enumerati…
math.AC2025
Separating Variables in Bivariate Polynomial Ideals: the Local Case
Manfred Buchacher
We present a semi-algorithm which for any irreducible finds all elements of that are of the form for some $q\in\mathbb{K}…