@article{DBLP:journals/corr/abs-2111-08160,
author = {Wenqiang Yang and
Wenyuan Wu and
Greg Reid},
journal = {CoRR},
title = {Implicit Method for Degenerated Differential-Algebraic Equations and
Applications},
url = {https://arxiv.org/abs/2111.08160},
volume = {abs/2111.08160},
year = {2021}
}
@article{DBLP:journals/mics/MohammadiRH21,
author = {Zahra Mohammadi and
Gregory J. Reid and
Tracy Shih{-}lung Huang},
doi = {10.1007/s11786-020-00483-z},
journal = {Math. Comput. Sci.},
pages = {293--316},
title = {Symmetry-Based Algorithms for Invertible Mappings of Polynomially
Nonlinear {PDE} to Linear {PDE}},
url = {https://doi.org/10.1007/s11786-020-00483-z},
volume = {15},
year = {2021}
}
@inproceedings{DBLP:conf/synasc/DengRJ21,
author = {Siyuan Deng and
Greg Reid and
D. J. Jeffrey},
booktitle = {23rd International Symposium on Symbolic and Numeric Algorithms for
Scientific Computing, {SYNASC} 2021, Timisoara, Romania, December
7-10, 2021},
doi = {10.1109/SYNASC54541.2021.00017},
editor = {Carsten Schneider and
Mircea Marin and
Viorel Negru and
Daniela Zaharie},
pages = {33--36},
publisher = {{IEEE}},
title = {Parametric Linear Algebra in Maple: Reduced Row Echelon Form},
url = {https://doi.org/10.1109/SYNASC54541.2021.00017},
year = {2021}
}
@inproceedings{DBLP:conf/issac/MohammadiRH19,
author = {Zahra Mohammadi and
Gregory J. Reid and
Tracy Shih{-}lung Huang},
booktitle = {Proceedings of the 2019 on International Symposium on Symbolic and
Algebraic Computation, {ISSAC} 2019, Beijing, China, July 15-18, 2019},
doi = {10.1145/3326229.3326259},
editor = {James H. Davenport and
Dongming Wang and
Manuel Kauers and
Russell J. Bradford},
pages = {331--338},
publisher = {{ACM}},
title = {Introduction of the MapDE Algorithm for Determination of Mappings
Relating Differential Equations},
url = {https://doi.org/10.1145/3326229.3326259},
year = {2019}
}
@inproceedings{DBLP:conf/mc2/MohammadiRH19,
author = {Zahra Mohammadi and
Gregory J. Reid and
Tracy Shih{-}lung Huang},
booktitle = {Maple in Mathematics Education and Research - Third Maple Conference,
{MC} 2019, Waterloo, Ontario, Canada, October 15-17, 2019, Proceedings},
doi = {10.1007/978-3-030-41258-6_27},
editor = {J{\"{u}}rgen Gerhard and
Ilias S. Kotsireas},
pages = {337--340},
publisher = {Springer},
title = {The Lie Algebra of Vector Fields Package with Applications to Mappings
of Differential Equations},
url = {https://doi.org/10.1007/978-3-030-41258-6_27},
volume = {1125},
year = {2019}
}
@article{DBLP:journals/cca/WangRW17,
author = {Fei Wang and
Greg Reid and
Henry Wolkowicz},
doi = {10.1145/3096730.3096740},
journal = {{ACM} Commun. Comput. Algebra},
pages = {35--37},
title = {Finding maximum rank moment matrices by facial reduction on primal
form and Douglas-Rachford iteration},
url = {https://doi.org/10.1145/3096730.3096740},
volume = {51},
year = {2017}
}
@article{DBLP:journals/tcs/WuRF17,
author = {Wenyuan Wu and
Greg Reid and
Yong Feng},
doi = {10.1016/j.tcs.2017.03.035},
journal = {Theor. Comput. Sci.},
pages = {217--231},
title = {Computing real witness points of positive dimensional polynomial systems},
url = {https://doi.org/10.1016/j.tcs.2017.03.035},
volume = {681},
year = {2017}
}
@incollection{MR3706577,
author = {Wu, Wenyuan and Chen, Changbo and Reid, Greg},
booktitle = {Computer algebra in scientific computing},
doi = {10.1007/978-3-319-66320-3},
pages = {377--391},
publisher = {Springer, Cham},
title = {Penalty function based critical point approach to compute real
witness solution points of polynomial systems},
url = {https://doi.org/10.1007/978-3-319-66320-3},
volume = {10490},
year = {2017}
}
@inproceedings{DBLP:conf/casc/WuCR17,
author = {Wenyuan Wu and
Changbo Chen and
Greg Reid},
booktitle = {Computer Algebra in Scientific Computing - 19th International Workshop,
{CASC} 2017, Beijing, China, September 18-22, 2017, Proceedings},
doi = {10.1007/978-3-319-66320-3_27},
editor = {Vladimir P. Gerdt and
Wolfram Koepf and
Werner M. Seiler and
Evgenii V. Vorozhtsov},
pages = {377--391},
publisher = {Springer},
title = {Penalty Function Based Critical Point Approach to Compute Real Witness
Solution Points of Polynomial Systems},
url = {https://doi.org/10.1007/978-3-319-66320-3_27},
volume = {10490},
year = {2017}
}
@inproceedings{DBLP:conf/synasc/WangRW17,
author = {Fei Wang and
Greg Reid and
Henry Wolkowicz},
booktitle = {19th International Symposium on Symbolic and Numeric Algorithms for
Scientific Computing, {SYNASC} 2017, Timisoara, Romania, September
21-24, 2017},
doi = {10.1109/SYNASC.2017.00025},
editor = {Tudor Jebelean and
Viorel Negru and
Dana Petcu and
Daniela Zaharie and
Tetsuo Ida and
Stephen M. Watt},
pages = {86--93},
publisher = {{IEEE} Computer Society},
title = {An SDP-based Method for the Real Radical Ideal Membership Test},
url = {https://doi.org/10.1109/SYNASC.2017.00025},
year = {2017}
}
@article{DBLP:journals/cca/KauersPR16,
author = {Manuel Kauers and
Peter Paule and
Greg Reid},
doi = {10.1145/2930964.2930968},
journal = {{ACM} Commun. Comput. Algebra},
pages = {27--34},
title = {Workshop on symbolic combinatorics and algorithmic differential algebra},
url = {https://doi.org/10.1145/2930964.2930968},
volume = {50},
year = {2016}
}
@article{DBLP:journals/corr/ReidWWW15,
author = {Greg Reid and
Fei Wang and
Henry Wolkowicz and
Wenyuan Wu},
journal = {CoRR},
title = {Facial Reduction and {SDP} Methods for Systems of Polynomial Equations},
url = {http://arxiv.org/abs/1504.00931},
volume = {abs/1504.00931},
year = {2015}
}
@article{DBLP:journals/corr/ReidWW14,
author = {Greg Reid and
Fei Wang and
Wenyuan Wu},
journal = {CoRR},
title = {Geometric involutive bases for positive dimensional polynomial ideals
and {SDP} methods},
url = {http://arxiv.org/abs/1405.7115},
volume = {abs/1405.7115},
year = {2014}
}
@inproceedings{DBLP:conf/snc/LisleHR14,
author = {Ian G. Lisle and
Tracy Shih{-}lung Huang and
Gregory J. Reid},
booktitle = {Symbolic-Numeric Computation 2014, {SNC} '14, Shanghai, China, July
28-31, 2014},
doi = {10.1145/2631948.2631962},
editor = {Lihong Zhi and
Stephen M. Watt},
pages = {61--69},
publisher = {{ACM}},
title = {Structure of symmetry of {PDE:} exploiting partially integrated systems},
url = {https://doi.org/10.1145/2631948.2631962},
year = {2014}
}
@inproceedings{DBLP:conf/snc/ReidWW14,
author = {Greg Reid and
Fei Wang and
Wenyuan Wu},
booktitle = {Symbolic-Numeric Computation 2014, {SNC} '14, Shanghai, China, July
28-31, 2014},
doi = {10.1145/2631948.2631958},
editor = {Lihong Zhi and
Stephen M. Watt},
pages = {41--42},
publisher = {{ACM}},
title = {A note on geometric involutive bases for positive dimensional polynomial
ideals and {SDP} methods},
url = {https://doi.org/10.1145/2631948.2631958},
year = {2014}
}
@inproceedings{DBLP:conf/snc/WuRF14,
author = {Wenyuan Wu and
Greg Reid and
Yong Feng},
booktitle = {Symbolic-Numeric Computation 2014, {SNC} '14, Shanghai, China, July
28-31, 2014},
doi = {10.1145/2631948.2631969},
editor = {Lihong Zhi and
Stephen M. Watt},
pages = {111--117},
publisher = {{ACM}},
title = {Numerical and geometric properties of a method for finding points
on real solution components},
url = {https://doi.org/10.1145/2631948.2631969},
year = {2014}
}
@inproceedings{MR3392712,
author = {Reid, Greg and Wang, Fei and Wu, Wenyuan},
booktitle = {S{NC} 2014---{P}roceedings of the 2014 {S}ymposium on
{S}ymbolic-{N}umeric {C}omputation},
pages = {41--42},
publisher = {ACM, New York},
title = {A note on geometric involutive bases for positive dimensional
polynomial ideals and {SDP} methods},
year = {2014}
}
@inproceedings{MR3392723,
author = {Wu, Wenyuan and Reid, Greg and Feng, Yong},
booktitle = {S{NC} 2014---{P}roceedings of the 2014 {S}ymposium on
{S}ymbolic-{N}umeric {C}omputation},
pages = {111--117},
publisher = {ACM, New York},
title = {Numerical and geometric properties of a method for finding
points on real solution components},
year = {2014}
}
@article{DBLP:journals/ijmssc/QinWFR13,
author = {Xiaolin Qin and
Wenyuan Wu and
Yong Feng and
Greg Reid},
doi = {10.1142/S1793962313420087},
journal = {Int. J. Model. Simul. Sci. Comput.},
pages = {1342008},
title = {Structural Analysis of High-Index {DAE} for Process simulation},
url = {https://doi.org/10.1142/S1793962313420087},
volume = {4},
year = {2013}
}
@inproceedings{DBLP:conf/issac/WuR13,
author = {Wenyuan Wu and
Greg Reid},
booktitle = {International Symposium on Symbolic and Algebraic Computation, ISSAC'13,
Boston, MA, USA, June 26-29, 2013},
doi = {10.1145/2465506.2465954},
editor = {Manuel Kauers},
pages = {339--346},
publisher = {{ACM}},
title = {Finding points on real solution components and applications to differential
polynomial systems},
url = {https://doi.org/10.1145/2465506.2465954},
year = {2013}
}
@article{DBLP:journals/jsc/ReidZ09,
author = {Greg Reid and
Lihong Zhi},
doi = {10.1016/j.jsc.2007.10.013},
journal = {J. Symb. Comput.},
pages = {280--291},
title = {Solving polynomial systems via symbolic-numeric reduction to geometric
involutive form},
url = {https://doi.org/10.1016/j.jsc.2007.10.013},
volume = {44},
year = {2009}
}
@article{DBLP:journals/jsc/WuRI09,
author = {Wenyuan Wu and
Greg Reid and
Silvana Ilie},
doi = {10.1016/j.jsc.2008.04.020},
journal = {J. Symb. Comput.},
pages = {923--941},
title = {Implicit Riquier Bases for {PDAE} and their semi-discretizations},
url = {https://doi.org/10.1016/j.jsc.2008.04.020},
volume = {44},
year = {2009}
}
@incollection{MR2641157,
author = {Wu, Wenyuan and Reid, Greg and Golubitsky, Oleg},
booktitle = {Approximate commutative algebra},
doi = {10.1007/978-3-211-99314-9_3},
pages = {79--97},
publisher = {SpringerWienNewYork, Vienna},
title = {Towards geometric completion of differential systems by
points},
url = {https://doi.org/10.1007/978-3-211-99314-9_3},
year = {2009}
}
@incollection{MR2641158,
author = {Scott, Robin and Reid, Greg and Wu, Wenyuan and Zhi, Lihong},
booktitle = {Approximate commutative algebra},
doi = {10.1007/978-3-211-99314-9_4},
pages = {99--124},
publisher = {SpringerWienNewYork, Vienna},
title = {Geometric involutive bases and applications to approximate
commutative algebra},
url = {https://doi.org/10.1007/978-3-211-99314-9_4},
year = {2009}
}
@article{DBLP:journals/jsc/MazaRSW07,
author = {Marc Moreno Maza and
Gregory J. Reid and
Robin Scott and
Wenyuan Wu},
doi = {10.1016/j.jsc.2006.12.004},
journal = {J. Symb. Comput.},
pages = {693--716},
title = {On approximate triangular decompositions in dimension zero},
url = {https://doi.org/10.1016/j.jsc.2006.12.004},
volume = {42},
year = {2007}
}
@incollection{MR2402285,
author = {Wu, Wenyuan and Reid, Greg},
booktitle = {I{SSAC} 2007},
doi = {10.1145/1277548.1277599},
pages = {377--385},
publisher = {ACM, New York},
title = {Symbolic-numeric computation of implicit {R}equier bases for
{PDE}},
url = {https://doi.org/10.1145/1277548.1277599},
year = {2007}
}
@incollection{MR2428453,
author = {Moreno Maza, Marc and Reid, Greg J. and Scott, Robin and Wu,
Wenyuan},
booktitle = {Symbolic-numeric computation},
doi = {10.1007/978-3-7643-7984-1_17},
pages = {279--298},
publisher = {Birkh\"{a}user, Basel},
title = {On approximate linearized triangular decompositions},
url = {https://doi.org/10.1007/978-3-7643-7984-1_17},
year = {2007}
}
@incollection{MR2428456,
author = {Zhou, Wenqin and Jeffrey, David J. and Reid, Greg J.},
booktitle = {Symbolic-numeric computation},
doi = {10.1007/978-3-7643-7984-1_20},
pages = {335--347},
publisher = {Birkh\"{a}user, Basel},
title = {Symbolic computation sequences and numerical analytic geometry
applied to multibody dynamical systems},
url = {https://doi.org/10.1007/978-3-7643-7984-1_20},
year = {2007}
}
@article{DBLP:journals/focm/LisleR06,
author = {Ian G. Lisle and
Gregory J. Reid},
doi = {10.1007/s10208-005-0186-x},
journal = {Found. Comput. Math.},
pages = {353--386},
title = {Symmetry Classification Using Noncommutative Invariant Differential
Operators},
url = {https://doi.org/10.1007/s10208-005-0186-x},
volume = {6},
year = {2006}
}
@article{DBLP:journals/na/IlieCR06,
author = {Silvana Ilie and
Robert M. Corless and
Greg Reid},
doi = {10.1007/s11075-005-9007-1},
journal = {Numer. Algorithms},
pages = {161--171},
title = {Numerical solutions of index-1 differential algebraic equations can
be computed in polynomial time},
url = {https://doi.org/10.1007/s11075-005-9007-1},
volume = {41},
year = {2006}
}
@incollection{MR2289141,
author = {Wu, Wenyuan and Reid, Greg},
booktitle = {I{SSAC} 2006},
doi = {10.1145/1145768.1145824},
pages = {345--352},
publisher = {ACM, New York},
title = {Application of numerical algebraic geometry and numerical
linear algebra to {PDE}},
url = {https://doi.org/10.1145/1145768.1145824},
year = {2006}
}
@inproceedings{DBLP:conf/iccS/ZhouJR05,
author = {Wenqin Zhou and
David J. Jeffrey and
Gregory J. Reid},
booktitle = {Computational Science - {ICCS} 2005, 5th International Conference,
Atlanta, GA, USA, May 22-25, 2005, Proceedings, Part {III}},
doi = {10.1007/11428862_80},
editor = {Vaidy S. Sunderam and
G. Dick van Albada and
Peter M. A. Sloot and
Jack J. Dongarra},
pages = {586--593},
publisher = {Springer},
title = {An Algebraic Method for Analyzing Open-Loop Dynamic Systems},
url = {https://doi.org/10.1007/11428862_80},
volume = {3516},
year = {2005}
}
@inproceedings{DBLP:conf/issac/ReidVWW05,
author = {Greg Reid and
Jan Verschelde and
Allan D. Wittkopf and
Wenyuan Wu},
booktitle = {Symbolic and Algebraic Computation, International Symposium {ISSAC}
2005, Beijing, China, July 24-27, 2005, Proceedings},
doi = {10.1145/1073884.1073922},
editor = {Manuel Kauers},
pages = {269--276},
publisher = {{ACM}},
title = {Symbolic-numeric completion of differential systems by homotopy continuation},
url = {https://doi.org/10.1145/1073884.1073922},
year = {2005}
}
@article{DBLP:journals/mcm/DoeschlDRR04,
author = {Andrea Doeschl and
Matt Davison and
Henning Rasmussen and
Greg Reid},
doi = {10.1016/j.mcm.2004.04.004},
journal = {Math. Comput. Model.},
pages = {977--994},
title = {Assessing cellular automata based models using partial differential
equations},
url = {https://doi.org/10.1016/j.mcm.2004.04.004},
volume = {40},
year = {2004}
}
@inproceedings{DBLP:conf/giae/ReidTYZ04,
author = {Gregory J. Reid and
Jianliang Tang and
Jianping Yu and
Lihong Zhi},
booktitle = {Computer Algebra and Geometric Algebra with Applications, 6th International
Workshop, {IWMM} 2004, Shanghai, China, May 19-21, 2004, and International
Workshop, {GIAE} 2004, Xian, China, May 24-28, 2004, Revised Selected
Papers},
doi = {10.1007/11499251_5},
editor = {Hongbo Li and
Peter J. Olver and
Gerald Sommer},
pages = {44--55},
publisher = {Springer},
title = {Hybrid Method for Solving New Pose Estimation Equation System},
url = {https://doi.org/10.1007/11499251_5},
volume = {3519},
year = {2004}
}
@inproceedings{DBLP:conf/giae/ZhouJRSM04,
author = {Wenqin Zhou and
David J. Jeffrey and
Gregory J. Reid and
Chad Schmitke and
John McPhee},
booktitle = {Computer Algebra and Geometric Algebra with Applications, 6th International
Workshop, {IWMM} 2004, Shanghai, China, May 19-21, 2004, and International
Workshop, {GIAE} 2004, Xian, China, May 24-28, 2004, Revised Selected
Papers},
doi = {10.1007/11499251_4},
editor = {Hongbo Li and
Peter J. Olver and
Gerald Sommer},
pages = {31--43},
publisher = {Springer},
title = {Implicit Reduced Involutive Forms and Their Application to Engineering
Multibody Systems},
url = {https://doi.org/10.1007/11499251_4},
volume = {3519},
year = {2004}
}
@inproceedings{DBLP:conf/issac/ReidTZ03,
author = {Gregory J. Reid and
Jianliang Tang and
Lihong Zhi},
booktitle = {Symbolic and Algebraic Computation, International Symposium {ISSAC}
2003, Drexel University, Philadelphia, Pennsylvania, USA, August 3-6,
2003, Proceedings},
doi = {10.1145/860854.860900},
editor = {J. Rafael Sendra},
pages = {215--223},
publisher = {{ACM}},
title = {A complete symbolic-numeric linear method for camera pose determination},
url = {https://doi.org/10.1145/860854.860900},
year = {2003}
}
@article{DBLP:journals/cca/ReidSV02,
author = {Greg Reid and
Chris Smith and
Jan Verschelde},
doi = {10.1145/581316.581317},
journal = {{SIGSAM} Bull.},
pages = {1--17},
title = {Geometric completion of differential systems using numeric-symbolic
continuation},
url = {https://doi.org/10.1145/581316.581317},
volume = {36},
year = {2002}
}
@inproceedings{DBLP:conf/issac/ReidW00,
author = {Gregory J. Reid and
Allan D. Wittkopf},
booktitle = {Proceedings of the 2000 International Symposium on Symbolic and Algebraic
Computation, {ISSAC} 2000, St. Andrews, United Kingdom, August 6-10,
2000},
doi = {10.1145/345542.345651},
editor = {Carlo Traverso},
pages = {272--280},
publisher = {{ACM}},
title = {Determination of maximal symmetry groups of classes of differential
equations},
url = {https://doi.org/10.1145/345542.345651},
year = {2000}
}
@inproceedings{DBLP:conf/issac/RustRW99,
author = {C. J. Rust and
Gregory J. Reid and
Allan D. Wittkopf},
booktitle = {Proceedings of the 1999 International Symposium on Symbolic and Algebraic
Computation, {ISSAC} '99, Vancouver, B.C., Canada, July 29-31, 1999},
doi = {10.1145/309831.309875},
editor = {Keith O. Geddes and
Bruno Salvy and
Samuel S. Dooley},
pages = {105--112},
publisher = {{ACM}},
title = {Existence and Uniqueness Theorems for Formal Power Series Solutions
of Analytic Differential Systems},
url = {https://doi.org/10.1145/309831.309875},
year = {1999}
}
@article{DBLP:journals/jsc/LisleR98,
author = {Ian G. Lisle and
Gregory J. Reid},
doi = {10.1006/jsco.1998.0218},
journal = {J. Symb. Comput.},
pages = {355--379},
title = {Geometry and Structure of Lie Pseudogroups from Infinitesimal Defining
Systems},
url = {https://doi.org/10.1006/jsco.1998.0218},
volume = {26},
year = {1998}
}
@inproceedings{DBLP:conf/eusipco/ReidM98,
author = {Greg Reid and
Evangelos E. Milios},
booktitle = {9th European Signal Processing Conference, {EUSIPCO} 1998, Island
of Rhodes, Greece, 8-11 September, 1998},
pages = {1--4},
publisher = {{IEEE}},
title = {Active binaural sound localization},
url = {https://ieeexplore.ieee.org/document/7089572/},
year = {1998}
}
@inproceedings{DBLP:conf/issac/RustR97,
author = {C. J. Rust and
Gregory J. Reid},
booktitle = {Proceedings of the 1997 International Symposium on Symbolic and Algebraic
Computation, {ISSAC} 1997, Maui, Hawaii, USA, July 21-23, 1997},
doi = {10.1145/258726.258737},
editor = {Bruce W. Char and
Paul S. Wang and
Wolfgang K{\"{u}}chlin},
pages = {9--16},
publisher = {{ACM}},
title = {Rankings of Partial Derivatives},
url = {https://doi.org/10.1145/258726.258737},
year = {1997}
}
@inproceedings{DBLP:conf/issac/LisleRB95,
author = {Ian G. Lisle and
Gregory J. Reid and
A. Boulton},
booktitle = {Proceedings of the 1995 International Symposium on Symbolic and Algebraic
Computation, {ISSAC} '95, Montreal, Canada, July 10-12, 1995},
doi = {10.1145/220346.220347},
editor = {A. H. M. Levelt},
pages = {1--6},
publisher = {{ACM}},
title = {Algorithmic Determination of Structure of Infinite Lie Pseudogroups
of Symmetries of PDEs},
url = {https://doi.org/10.1145/220346.220347},
year = {1995}
}
@inproceedings{DBLP:conf/issac/ReidLBW92,
author = {Gregory J. Reid and
Ian G. Lisle and
A. Boulton and
Allan D. Wittkopf},
booktitle = {Proceedings of the 1992 International Symposium on Symbolic and Algebraic
Computation, {ISSAC} '92, Berkeley, CA, USA, July 27-29, 1992},
doi = {10.1145/143242.143269},
editor = {Paul S. Wang},
pages = {63--68},
publisher = {{ACM}},
title = {Algorithmic Determination of Commutation Relations for Lie Symmetry
Algebras of PDEs},
url = {https://doi.org/10.1145/143242.143269},
year = {1992}
}
@inproceedings{DBLP:conf/issac/ReidB91,
author = {Gregory J. Reid and
A. Boulton},
booktitle = {Proceedings of the 1991 International Symposium on Symbolic and Algebraic
Computation, {ISSAC} '91, Bonn, Germany, July 15-17, 1991},
doi = {10.1145/120694.120741},
editor = {Stephen M. Watt},
pages = {308--312},
publisher = {{ACM}},
title = {Reduction of Systems of Differential Equations to Standard form and
Their Integration Using Directed Graphs},
url = {https://doi.org/10.1145/120694.120741},
year = {1991}
}