Browsing Mathematics (Faculty of) by Subject "Symbolic Computation"
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Computational Approaches to Problems in Noncommutative Algebra  Theory, Applications and Implementations
(University of Waterloo, 20160928)Noncommutative rings appear in several areas of mathematics. Most prominently, they can be used to model operator equations, such as differential or difference equations. In the Ph.D. studies leading to this thesis, ... 
Computing Matrix Canonical Forms of Ore Polynomials
(University of Waterloo, 20170501)We present algorithms to compute canonical forms of matrices of Ore polynomials while controlling intermediate expression swell. Given a square nonsingular input matrix of Ore polynomials, we give an extension of the ... 
Hermite form computation of matrices of differential polynomials
(University of Waterloo, 20090827)Given a matrix A in F(t)[D;\delta]^{n\times n} over the ring of differential polynomials, we first prove the existence of the Hermite form H of A over this ring. Then we determine degree bounds on U and H such that UA=H. ... 
Hermite Forms of Polynomial Matrices
(University of Waterloo, 20110823)This thesis presents a new algorithm for computing the Hermite form of a polynomial matrix. Given a nonsingular n by n matrix A filled with degree d polynomials with coefficients from a field, the algorithm computes the ...