Technical Reports of research area 'Computer Algebra'
2020
S.Dewar, G. Grasegger, J. Legerský.Flexible placements of graphs with rotational symmetry. arXiv. Technical report, 2020.[url][bib]
M. Gallet, G. Grasegger, J. Legerský, J. Schicho.Combinatorics of Bricard’s octahedra. arXiv. Technical report, 2020.[url][bib]
G. Grasegger, J. Legerský.Bracing frameworks consisting of parallelograms. arXiv. Technical report, 2020.[url][bib]
M. Gallet, G. Grasegger, J. Legerský, J. Schicho.Zero-sum cycles in flexible polyhedra. arXiv. Technical report, 2020.[url][bib]
2018
S. McCallum, F. Winkler.Resultants: Algebraic and Differential. Technical report no. 18-08 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).August2018.[pdf][bib]
2017
Jose Capco, Georg Grasegger, Matteo Gallet, Christoph Koutschan, Niels Lubbes, Josef Schicho.The number of realizations of a Laman graph. Research Institute for Symbolic Computation (RISC/JKU). Technical report, 2017.[url][pdf][bib]
2016
G. Grasegger, N.T. Vo, F. Winkler.Computation of All Rational Solutions of First-Order Algebraic ODEs. Technical report no. 16-01 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).2016.[pdf][bib]
G. Grasegger, N.T. Vo.An Algebraic-Geometric Method for Computing Zolotarev Polynomials. Technical report no. 16-02 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).2016.[pdf][bib]
G. Grasegger.An Algebraic-Geometric Method for Computing Zolotarev Polynomials — Additional Information. Technical report no. 16-07 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).2016.[pdf][bib]
N. Thieu Vo.Rational and Algebraic Solutions of First-Order Algebraic ODEs. Technical report no. 16-11 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).122016.Thesis Dissertation.[pdf][bib]
2015
Christoph Fuerst, Guenter Landsmann.Three Examples of Gröbner Reduction over Noncommutative Rings. Technical report no. 15-16 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).October2015.[pdf][bib]
G. Grasegger, A. Lastra, J.R. Sendra, F. Winkler.A solution method for autonomous first-order algebraic partial differential equations in several variables. Technical report no. 15-01 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).2015.[pdf][bib]
Georg Grasegger.Symbolic Solutions of First-Order Algebraic Differential Equations. Technical report no. 15-07 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).2015.PhD Thesis.[bib]
N.T. Vo, G. Grasegger, F. Winkler.Rational General Solutions of First-Order Algebraic ODEs. Technical report no. 15-18 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).2015.[bib]
G. Grasegger, N.T. Vo, F. Winkler.Statistical Investigation of First-Order Algebraic ODEs and their Rational General Solutions. Technical report no. 15-19 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).2015.[pdf][bib]
2014
Christoph Fuerst, Guenter Landsmann.The Concept of Gröbner Reduction for Dimension in filtered free modules. Technical report no. 14-12 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).October2014.[pdf][bib]
G. Grasegger, A. Lastra, J.R. Sendra, F. Winkler.A solution method for autonomous first-order algebraic partial differential equations. Technical report no. 14-03 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).2014.[pdf][bib]
2013
Georg Grasegger.A procedure for solving autonomous AODEs. Technical report no. 13-03 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).2013.[pdf][bib]
Muhammad Taimoor Khan.Translation of MiniMaple to Why3ML. Technical report no. 13-01 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).February2013.[pdf][bib]
A. Lastra, J. R. Sendra, L. X. C. Ngo, F. Winkler.Rational General Solution of 1-Dimensional Systems of Autonomous Ordinary Differential Equations. Technical report no. 13-09 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).December2013.[pdf][pdf][bib]
2012
C. Doench, J. Middeke, F. Winkler.DEAM 2 Proceedings. Technical report no. 00-00 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).2012.[pdf][bib]
C. Dönch.Standard Bases in Finitely Generated Difference-Skew-Differential Modules and Their Application to Dimension Polynomials. Technical report no. 12-09 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).2012.[pdf][bib]
Muhammad Taimoor Khan.Formal Semantics of MiniMaple. Technical report no. 12-04 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).January2012.[pdf][bib]
Muhammad Taimoor Khan.Formal Semantics of a Specification Language for MiniMaple. Technical report no. 12-05 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).April2012.[pdf][bib]
L. X. C. Ngo, J. R. Sendra, F. Winkler.Birational Transformations on Algebraic Ordinary Differential Equations. Technical report no. 12-18 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).December2012.[pdf][bib]
2011
Muhammad Taimoor Khan.A Type Checker for MiniMaple. Technical report no. 11-05 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).April2011.[pdf][bib]
Muhammad Taimoor Khan.Towards a Behavioral Analysis of Computer Algebra Programs. Technical report no. 11-13 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).November2011.[pdf][bib]
2010
Christian Aistleitner.Differential aspects of differential characteristic set computations. Technical report no. 10-12 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).June2010.[pdf][bib]
Christian Aistleitner.Relations between Groebner bases, differential Groebner bases, and differential characteristic sets. Technical report no. 11-02 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).December2010.[pdf][bib]
E.Kartashova, V. Lvov, S. Nazarenko, I. Procaccia.Towards a Theory of Discrete and Mesoscopic Wave Turbulence. Submitted to the RISC Report Series. Technical report no. 10-04 in RISC Report Series,February2010.[pdf][bib]
Johannes Middeke. Converting between the Popov and the Hermite form of matrices of differential operators using an FGLM-like algorithm. Technical report no. 10-16 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).2010.[pdf][bib]
L.X.Chau Ngo.Finding rational solutions of rational systems of autonomous ODEs. Technical report no. 10-02 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).February2010.[pdf][bib]
Y. Huang, L. X. Chau Ngo.Rational General Solutions of High Order Non-autonomous ODEs. Technical report no. 10-13 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).June2010.[pdf][bib]
Y. Huang, L. X. Chau Ngo.Rational Solutions of a Rational System of Autonomous ODEs: Generalization to Trivariate Case and Problems. Technical report no. 10-20 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).November2010.[pdf][bib]
2009
Christian Doench.Bivariate difference-differential dimension polynomials and their computation in Maple. Technical report no. 09-19 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).2009.[pdf][bib]
Johannes Middeke, Ekaterina Shemyakova, Franz Winkler.Proceedings of DEAM (Workshop for Differential Equations by Algebraic Methods). Technical report no. 09-08 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).2009.Proceedings.[pdf][bib]
L.X. Chau Ngo.A criterion for existence of rational general solutions of planar systems of ODEs. Technical report no. 09-13 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).July2009.[pdf][bib]
L.X.Chau Ngo.Rational general solutions of first order non-autonomous parametric ODEs. Technical report no. 09-02 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).January2009.[pdf][bib]
2008
Johannes Middeke.A polynomial-time algorithm for the Jacobson form for matrices of differential operators . Submitted to the RISC Report Series. Technical report no. 08-13 in RISC Report Series,July2008.[pdf][bib]
2007
Katsusuke Nabeshima.Comprehensive {G}roebner {B}ases in Various Domains. Technical report no. 07-15 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).April2007.PhD thesis.PhD thesis.[pdf][bib]
E. Shemyakova.Symbolic-Algebraic Methods for Linear Partial Differential Operators. Technical report no. 07-03 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).July2007.PhD thesis.[pdf][bib]
Meng Zhou, Franz Winkler.Computing difference-differential Groebner Bases and difference-differential dimension polynomials. Technical report no. 07-01 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).January2007.[pdf][pdf][bib]
2006
Glauco Alfredo Lopez Diaz.Symbolic Methods for Factoring Linear Differential Operators. RISC. Technical report no. 06-02, February2006.[pdf][ps][bib]
N. Tongsiri.Constructive Solid Geometry with Projection: An Approach to Piano Movers' Problem. RISC. Technical report, September2006.[pdf][bib]
2005
Christian Aistleitner.A generic implementation of differential characteristic set algorithms in Aldor. Technical report no. 05-15 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).December2005.[pdf][bib]
MARTIN BURGER, HONG GU.Numerical-Symbolic methods for parameter-dependent geometric differential equations. J. Kepler University, SFB project. Technical report no. 1, 2005.[bib]
Hong Gu, Martin Burger.Preprocessing for Finite Element Discretizations of Geometric Problems. Technical report no. 05-02 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).May2005.accepted to be published in proceeding of SNC'05.[ps][bib]
E. Kartashova.Diophantine equations of nonlinear physics. Part 1. Technical report no. 05-11 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).042005.[pdf][bib]
E. Kartashova, A. Shabat.Computable Integrability. Chapter 1: General notions and ideas. Technical report no. 05-07 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).042005.[pdf][bib]
E. Kartashova, A. Shabat.Computable Integrability. Chapter 2: Riccati equation. Technical report no. 05-08 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).82005.[pdf][bib]
E. Kartashova, A. Shabat.Computable Integrability. Chapter 3: Integrability of linear PDEs. Technical report no. 05-09 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).92005.[pdf][bib]
F.Winkler and M.Zhou.On computing Groebner bases in rings of differential operators with coefficients in a ring. Technical report no. 05-04 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).2005.[pdf][bib]
M. Borges-Quintana, M. A. Borges-Trenard, E. Martinez-Moro, F. Winkler.Using Groebner bases for determining the equivalence of linear codes and solving the decoding problem. Technical report no. 05-12 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).2005.[ps][bib]
Meng Zhou and Franz Winkler.Grobner bases in difference-differential modules and their applications. Technical report no. 05-14 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).October2005.[ps][pdf][bib]
2004
Rahul Athale.Symbolic computation in number theory. Technical report no. 04-20 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).2004.[pdf][bib]
2003
HONG GU, STEFAN KINDERMANN.Solution analysis of PDEs related to the Mumford-Shah functional with symbolic computation. J. Kepler University, SFB project. Technical report no. 17, 2003.[bib]
Ralf Hemmecke.Involutive Bases for Polynomial Ideals. Technical report no. 03-02 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).May2003.PhD Thesis.[ps][bib]
Erik Hillgarter, Ralf Hemmecke, Günter Landsmann, Franz Winkler.Symbolic Differential Elimination Theory for Symmetry Analysis. Technical report no. 03-12 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).October2003.[ps][bib]
2002
Joachim Apel, Ralf Hemmecke.Detecting Unnecessary Reductions in an Involutive Basis Computation. Technical report no. 02-22 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).October2002.[ps][bib]
G.Landsmann.Implicitization of Algebraic Varieties. RISC-Linz. Technical report no. 02-18, 2002.[bib]
2001
Ralf Hemmecke.Dynamical Aspects of Involutive Bases Computations. Technical report no. 01-28 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).December2001.presented at ACA'2001, Albuquerque, New Mexico, June, 2001.[ps][bib]
2000
Ralf Hemmecke, Franz Winkler.CASA User Manual (Version CASA 2.5). Technical report no. 00-30 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).December2000.RISC Report.[ps][bib]
1999
W.Herfort, G.Landsmann.Simultaneous Existence of Right Inverses for 1-ab and 1-ba.. RISC Linz. Technical report no. 99-26, 1999.[bib]
1998
Ralf Hemmecke, Erik Hillgarter, Wolfgang Schreiner, Franz Winkler.An Evaluation of the State of the CASA System. Technical report no. 98-16 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).October1998.[ps][bib]
1995
Elena Kartashova.Applicability of Weakly Nonlinear Theory for Planetary-Scale Flows. KNMI (Koninklijk Nederlands Meteorologisch Instituut). Technical report no. WR 95-03, KNMI, DeBilt, The Netherlands, Scientific Report, 1995.[url][bib]
1979
B. Buchberger, F. Winkler.Miscellaneous Results on the Construction of Groebner-Bases for Polynomial Ideals. Johannes Kepler University, Technisch-Naturwissenschaftliche Fakultaet, Insitut fuer Mathematik. Technical report no. 137, June1979.[bib]