Linear Differential Operators for Polynomial Equations (2008)
Olivier Cormier, Michael F. Singer, Barry M. Trager, Barry M, Felix Ulmer, ...
Given a squarefree polynomial P k 0 [x, y], k 0 a number field, we construct a linear differential operator that allows one to calculate the genus of the complex curve defined by P = 0 (when P is...
Linear Dierential Operators for Polynomial Equations (2007)
Olivier Cormier, Felix Ulmer, Michael F. Singer, Barry M. Trager
Given a squarefree polynomial P 2 k 0 [x; y], k 0 a number eld, we construct a linear dierential operator that allows one to calculate the genus of the complex curve dened by P = 0 (when P is...
A Reduction for Regular Differential Systems (2003)
Manuel Bronstein, Inria Projet Café, Sophia Antipolis Cedex, Barry M. Trager
We propose a definition of regularity of a linear differential system with coefficients in a monomial extension of a differential field, as well as a global and truly rational (i.e....
Linear differential operators for polynomial equations (2002)
Olivier Cormier, Michael F. Singer, Barry M. Trager, Felix Ulmer
Given a squarefree polynomial P ∈ k0[x, y], k0 a number field, we construct a linear differential operator that allows one to calculate the genus of the complex curve defined by P = 0 (when P is...
Robert M. Corless, Patrizia M. Gianni, Barry M. Trager
polynomial systems with multiple roots
The singular value decomposition for polynomial systems (1995)
Robert M. Corless, Patrizia M. Gianni, Barry M. Trager, Stephen M. Watt
This paper introduces singular value decomposition (SVD) algorithms for some standard polynomial computations, in the case where the coeOEcients are inexact or imperfectly known. We rst give an...