• {0, 1,..., m − 1} (nonnegative representation); (2009)
These notes record seven lectures given in the computer algebra course in the fall of 2004. The theory of subresultants is not required for the final exam due to its complicated constructions. 1...
Testing Linear Dependence of Hyperexponential Elements ∗ (2008)
Ziming Li, Min Wu, Dabin Zheng
A Wronskian (resp. Casoratian) criterion is useful to test linear dependence of elements in a differential (resp. difference) field over constants. We generalize this criterion for invertible...
Abstract Finding Roots of Unity among Quotients of the Roots of an Integral Polynomial (2008)
We present an efficient algorithm for testing whether a given integral polynomial has two distinct roots a, B such that fflp is a root of unity. The test is based on results obtained by investigation...
On Solutions of Linear Functional Systems and Factorization of Laurent-Ore Modules (2008)
Abstract. We summarize some recent results on partial linear functional systems. By associating a finite-dimensional linear functional system to a Laurent-Ore module, Picard-Vessiot extensions are...
A Recursive Method for Determining the One-Dimensional Submodules of Laurent-Ore Modules (2006)
Li, Ziming, Singer, Michael F., Wu, Min, Zheng, Dabin
We present a method for determining the one-dimensional submodules of a Laurent-Ore module. The method is based on a correspondence between hyperexponential solutions of associated systems and...
Determining whether a multivariate hyperexponential function is algebraic (2006)
Abstract. Let F = C(x1,..., xℓ, xℓ+1,..., xm), where x1,..., xℓ are continuous variables, and xℓ+1,..., xm are discrete variables. We show that a hyperexponential function, which is algebraic...
A Recursive Method for Determining the One-Dimensional Submodules of Laurent-Ore Modules (2006)
We present a method for determining the one-dimensional submodules of a Laurent-Ore module. The method is based on a correspondence between hyperexponential solutions of associated systems and...
A Recursive Method for Determining the One-Dimensional Submodules of Laurent-Ore Modules (2006)
We present a method for determining the one-dimensional submodules of a Laurent-Ore module. The method is based on a correspondence between hyperexponential solutions of associated systems and...
Hyperexponential solutions of finite-rank ideals in orthogonal ore rings (2004)
Abstract. An orthogonal Ore algebra is an abstraction of common properties of linear partial differential, shift and q-shift operators. Using orthogonal Ore algebras, we present an algorithm for...
Factoring zero-dimensional ideals of linear partial differential operators (2002)
We present an algorithm for factoring a zero-dimensional left ideal in the ring ¯ Q(x, y)[∂x, ∂y], i.e. factoring a linear homogeneous partial differential system whose coefficients belong to ¯...
Rational solutions of Riccati-like partial differential equations (2001)
Abstract. When factoring linear partial differential systems with a finite-dimensional solution space or analyzing symmetries of nonlinear ode’s, we need to look for rational solutions of certain...
Rational solutions of Riccati-like partial differential equations (2001)
When factoring linear partial differential systems with a finite-dimensional solution space or analysing symmetries of nonlinear ODEs, we need to look for rational solutions of certain nonlinear...
A subresultant theory for Ore polynomials with applications (1998)
Abstract. The subresultant theory for univariate commutative polynomials is generalized to Ore polynomials. The generalization includes: the subresultant theorem, gap structure, and subresultant...
A modular algorithm for computing greatest common right divisors of ore polynomials (1997)
Abstract. This paper presents a modular algorithm for computing the greatest common right divisor (gcrd) of two univariate Ore polynomials over Z[t]. The subresultants of Ore polynomials are used to...
A Modular Algorithm for Computing Greatest Common Right Divisors of Ore Polynomials (1997)
This paper presents a modular algorithm for computing the greatest common right divisor (gcrd) of two univariate Ore polynomials over Z[t]. The subresultants of Ore polynomials are used to compute...