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This paper introduces singular value decomposition (SVD) algorithms for some standard polynomial computations, in the case where the coefficients are inexact or imperfectly known. We first give an… (More)

- Patrizia M. Gianni, Barry M. Trager, Gail Zacharias
- J. Symb. Comput.
- 1988

We present an algorithm to compute the primary decomposition of any ideal in a polynomial ring over a factorially closed algorithmic principal ideal domain R. This means that the ring R is a… (More)

- Erich Kaltofen, Barry M. Trager
- J. Symb. Comput.
- 1990

Algorithms are developed that adopt a ,ovel implicit representation ibr multivariate polynomials and rational functions with rational coefficients, that of black boxes for their evaluation. We show… (More)

- Barry M. Trager
- 1984

- Barry M. Trager
- SYMSACC
- 1976

This paper presents a new, simple, and efficient algorithm for factoring polynomials in several variables over an algebraic number field. The algorithm is then used iteratively, to construct the… (More)

- Robert M. Corless, Patrizia M. Gianni, Barry M. Trager
- ISSAC
- 1997

The technique of solving systems of multivariate polynomial equations via rigenproblems has become a topic of active research (with applications in computer-aided design and {untrul theory, for… (More)

- Patrizia M. Gianni, Victor Miller, Barry M. Trager
- ISSAC
- 1988

I. I n t r o d u c t i o n The well-known factoring algorithm of Berlekamp [Bet67, Ber70] can be understood by interpreting it in terms of idempotents in a commutative algebra [Zas69, Zas78, Mi173,… (More)

- Olivier Cormier, Michael F. Singer, Barry M. Trager, Felix Ulmer
- J. Symb. Comput.
- 2002

The results of this paper spring from the elementary fact that an algebraic function satisfies a linear differential equation. Let k0 be a number field and k0 be its algebraic closure. Let P ∈… (More)

- Patrizia M. Gianni, Barry M. Trager
- European Conference on Computer Algebra
- 1985

This paper shows how Grobner basis computations can be used to compute multivariate gcds, perform Hensel lifting, and reduce multivariate factorization to univariate. The essential idea is to produce… (More)

- Kartheek Chandu, Mikel Stanich, Chai Wah Wu, Barry M. Trager
- 19th IEEE International Conference on Image…
- 2012

Multi-bit screening is an extension of binary screening, in which every pixel in continuous-tone image can be rendered to one among multiple absorptance levels. Many multi-bit screen algorithms face… (More)