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- research-articleJuly 2024
Solving Third Order Linear Difference Equations in Terms of Second Order Equations
ISSAC '24: Proceedings of the 2024 International Symposium on Symbolic and Algebraic ComputationPages 457–463https://doi.org/10.1145/3666000.3669719We present two algorithms for computing what we call the absolute factorization of a difference operator. We also give an algorithm for solving third order difference equations in terms of second order equations, together with applications to OEIS ...
- research-articleAugust 2009
Continuations and monodromy on random riemann surfaces
SNC '09: Proceedings of the 2009 conference on Symbolic numeric computationPages 115–124https://doi.org/10.1145/1577190.1577210Our main motivation is to analyze and improve factorization algorithms for bivariate polynomials in C[x,y], which proceed by continuation methods.
We consider a Riemann surface X defined by a polynomial f(x,y) of degree d, whose coefficients are choosen ...
- ArticleJuly 2004
Absolute polynomial factorization in two variables and the knapsack problem
ISSAC '04: Proceedings of the 2004 international symposium on Symbolic and algebraic computationPages 87–94https://doi.org/10.1145/1005285.1005300A recent algorithmic procedure for computing the absolute factorization of a polynomial P(X,Y), after a linear change of coordinates, is via a factorization modulo X3. This was proposed by A. Galligo and D. Rupprecht in [7],[16]. Then absolute ...
