George E. Collins

Publications

1996

[Collins]

Simple Truth Invariant CAD's and Solution Formula Construction

George E. Collins, Christopher W. Brown

Technical report no. 96-19 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. October 1996. [ps]

[bib]

@techreport{RISC1345,
author = {George E. Collins and Christopher W. Brown},
title = {{Simple Truth Invariant CAD's and Solution Formula Construction}},
number = {96-19},
year = {1996},
month = {October},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

1995

[Collins]

Application of Quantifier Elimination to Solotareff's Approximation Problem

George E. Collins

Technical report no. 95-31 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 1995. [ps]

[bib]

@techreport{RISC1324,
author = {George E. Collins},
title = {{Application of Quantifier Elimination to Solotareff's Approximation Problem}},
number = {95-31},
year = {1995},
sponsor = { Austrian Science Foundation, grant P8572-PHY.},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

[Collins]

Improved Techniques for Factoring Univariate Polynomials

George E. Collins, Mark J. Encarnacion

Technical report no. 95-19 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 1995.

[bib]

@techreport{RISC1579,
author = {George E. Collins and Mark J. Encarnacion},
title = {{Improved Techniques for Factoring Univariate Polynomials}},
number = {95-19},
year = {1995},
sponsor = { Austrian National Science Foundation (FWF), project no. P8572.},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

[Collins]

Adjacency Algorithms for Cylindrical Algebraic Decomposition of Three and Higher Dimensional Space I: Adjacencies Over a Non-nullifying $\{0, 1\}$ Adjacency

George E. Collins, Scott Mccallum

Technical report no. 95-32 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 1995.

[bib]

@techreport{RISC1583,
author = {George E. Collins and Scott Mccallum},
title = {{Adjacency Algorithms for Cylindrical Algebraic Decomposition of Three and Higher Dimensional Space I: Adjacencies Over a Non-nullifying $\{0,1\}$ Adjacency}},
number = {95-32},
year = {1995},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

1994

[Collins]

Efficient Rational Number Reconstruction

George E. Collins, Mark J. Encarnacion

Technical report no. 94-64 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 1994.

[bib]

@techreport{RISC1658,
author = {George E. Collins and Mark J. Encarnacion},
title = {{Efficient Rational Number Reconstruction}},
number = {94-64},
year = {1994},
sponsor = { Austrian Science Foundation (FWF) project no. P8572-PHY % and M022-PHY.},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

1993

[Collins]

SACLIB 1.1 User's Guide

Bruno Buchberger, George E. Collins, Mark J. Encarnacion, Hoon Hong, Jeremy R. Johnson, Werner Krandick, R\\

Technical report no. 93-19 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 1993.

[bib]

@techreport{RISC1682,
author = {Bruno Buchberger and George E. Collins and Mark J. Encarnacion and Hoon Hong and Jeremy R. Johnson and Werner Krandick and R\\},
title = {{SACLIB 1.1 User's Guide}},
language = {english},
number = {93-19},
year = {1993},
length = {0},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

[Collins]

An Efficient Algorithm for Infallible Polynomial Complex Root Isolation

George E. Collins, Werner Krandick

Technical report no. 93-73 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 1993. Published in Proceedings of the International Symposium on Symbolic and Algebraic Computation ISSAC'92, Paul S. Wang (ed.), ACM Order Department, P.O. box 64145, Baltimore, MD 21264, pp. 189-194..

[bib]

@techreport{RISC1729,
author = {George E. Collins and Werner Krandick},
title = {{An Efficient Algorithm for Infallible Polynomial Complex Root Isolation}},
number = {93-73},
year = {1993},
note = {Published in Proceedings of the International Symposium on Symbolic and Algebraic Computation ISSAC'92, Paul S. Wang (ed.), ACM Order Department, P.O. box 64145, Baltimore, MD 21264, pp. 189--194.},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

[Collins]

A Hybrid Method for High Precision Calculation of Polynomial Real Roots

George E. Collins, Werner Krandick

Technical report no. 93-75 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 1993. Published in Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC'93, M. Bronstein (ed.), Kiev, Ukraine, 1993, ACM Order Department, pp. 47-52..

[bib]

@techreport{RISC1731,
author = {George E. Collins and Werner Krandick},
title = {{A Hybrid Method for High Precision Calculation of Polynomial Real Roots}},
number = {93-75},
year = {1993},
note = {Published in Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC'93, M. Bronstein (ed.), Kiev, Ukraine, 1993, ACM Order Department, pp. 47--52.},
sponsor = { Austrian Science Foundation (FWF) projects no. P8572-PHY and M022-PHY.},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

[Collins]

A Tangent-Secant Method for Polynomial Complex Root Calculation

George E. Collins, Werner Krandick

Technical report no. 93-77 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 1993.

[bib]

@techreport{RISC1733,
author = {George E. Collins and Werner Krandick},
title = {{A Tangent-Secant Method for Polynomial Complex Root Calculation}},
number = {93-77},
year = {1993},
sponsor = { Austrian Science Foundation (FWF) projects no. P8572-PHY and M022-PHY.},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

1982

[Collins]

Arithmetic in Basic Algebraic Domains

G.E. Collins, M. Mignotte, F. Winkler

In: Computer Algebra - Symbolic and Algebraic Computation, B. Buchberger, G.E. Collins, R. Loos (ed.), pp. 189-220. 1982. Springer-Verlag, ISSN 0163-5824. [pdf]

[bib]

@incollection{RISC229,
author = {G.E. Collins and M. Mignotte and F. Winkler},
title = {{Arithmetic in Basic Algebraic Domains}},
booktitle = {{Computer Algebra - Symbolic and Algebraic Computation}},
language = {english},
pages = {189--220},
publisher = {Springer-Verlag},
isbn_issn = {ISSN 0163-5824},
year = {1982},
editor = {B. Buchberger and G.E. Collins and R. Loos},
refereed = {yes},
length = {32}
}