2019
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Brakhage, K H; Niemeyer, A C; Plesken, W; Robertz, D; Strzelczyk, A The icosahedra of edge length 1 Journal Article Journal of Algebra, 545 , pp. 4–26, 2019. Abstract | Links | BibTeX @article{BrakhageNiemeyerPleskenRobertzStrzelczyk,
title = {The icosahedra of edge length 1},
author = {Brakhage, K. H. and Niemeyer, A. C. and Plesken, W. and Robertz, D. and Strzelczyk, A.},
doi = {doi:10.1016/j.jalgebra.2019.04.028},
year = {2019},
date = {2019-05-14},
journal = {Journal of Algebra},
volume = {545},
pages = {4--26},
abstract = {Retaining the combinatorial Euclidean structure of a regular icosahedron, namely the 20 equiangular (planar) triangles, the 30 edges of length 1, and the 12 different vertices together with the incidence structure, we investigate variations of the regular icosahedron admitting self-intersections of faces. We determine all rigid equivalence classes of these icosahedra with non-trivial automorphism group and find one curve of flexible icosahedra. Visualisations and explicit data for this paper are available under http://algebra.data.rwth-aachen. de/Icosahedra/visualplusdata.html.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Retaining the combinatorial Euclidean structure of a regular icosahedron, namely the 20 equiangular (planar) triangles, the 30 edges of length 1, and the 12 different vertices together with the incidence structure, we investigate variations of the regular icosahedron admitting self-intersections of faces. We determine all rigid equivalence classes of these icosahedra with non-trivial automorphism group and find one curve of flexible icosahedra. Visualisations and explicit data for this paper are available under http://algebra.data.rwth-aachen. de/Icosahedra/visualplusdata.html. |
Gerdt, V P; Robertz, D Algorithmic Approach to Strong Consistency Analysis of Finite Difference Approximations to PDE Systems Inproceedings Proceedings of the 2019 International Symposium on Symbolic and Algebraic Computation, 15-18 July 2019, Beihang University, Beijing, China, pp. 163–170, 2019. Abstract | BibTeX @inproceedings{GerdtRobertz6,
title = {Algorithmic Approach to Strong Consistency Analysis of Finite Difference Approximations to PDE Systems},
author = {Gerdt, V. P. and Robertz, D.},
year = {2019},
date = {2019-01-01},
booktitle = {Proceedings of the 2019 International Symposium on Symbolic and Algebraic Computation, 15-18 July 2019, Beihang University, Beijing, China},
pages = {163--170},
abstract = {For a wide class of polynomially nonlinear systems of partial differential equations we suggest an algorithmic approach to the s(trong)-consistency analysis of their finite difference approximations on Cartesian grids. First we apply the differential Thomas decomposition to the input system, resulting in a partition of the solution set. We consider the output simple subsystem that contains a solution of interest. Then, for this subsystem, we suggest an algorithm for verification of s-consistency for its finite difference approximation. For this purpose we develop a difference analogue of the differential Thomas decomposition, both of which jointly allow to verify the s-consistency of the approximation. As an application of our approach, we show how to produce s-consistent difference approximations to the incompressible Navier-Stokes equations including the pressure Poisson equation.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
For a wide class of polynomially nonlinear systems of partial differential equations we suggest an algorithmic approach to the s(trong)-consistency analysis of their finite difference approximations on Cartesian grids. First we apply the differential Thomas decomposition to the input system, resulting in a partition of the solution set. We consider the output simple subsystem that contains a solution of interest. Then, for this subsystem, we suggest an algorithm for verification of s-consistency for its finite difference approximation. For this purpose we develop a difference analogue of the differential Thomas decomposition, both of which jointly allow to verify the s-consistency of the approximation. As an application of our approach, we show how to produce s-consistent difference approximations to the incompressible Navier-Stokes equations including the pressure Poisson equation. |
2018
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Gerdt, V P; Lange-Hegermann, M; Robertz, D The MAPLE package TDDS for computing Thomas decompositions of systems of nonlinear PDEs Journal Article Computer Physics Communications, 234 , pp. 202–215, 2018. Abstract | BibTeX @article{GerdtLangeHegermannRobertzc,
title = {The MAPLE package TDDS for computing Thomas decompositions of systems of nonlinear PDEs},
author = {Gerdt, V. P. and Lange-Hegermann, M. and Robertz, D.},
year = {2018},
date = {2018-08-10},
journal = {Computer Physics Communications},
volume = {234},
pages = {202--215},
abstract = {We present the Maple package TDDS (Thomas Decomposition of Differential Systems). Given a polynomially nonlinear differential system, which in addition to equations may contain inequations, this package computes a decomposition of it into a finite set of differentially triangular and algebraically simple subsystems whose subsets of equations are involutive. Usually the decomposed system is substantially easier to investigate and solve both analytically and numerically. The distinctive property of a Thomas decomposition is disjointness of the solution sets of the output subsystems. Thereby, a solution of a well-posed initial problem belongs to one and only one output subsystem. The Thomas decomposition is fully algorithmic. It allows to perform important elements of algebraic analysis of an input differential system such as: verifying consistency, i.e., the existence of solutions; detecting the arbitrariness in the general analytic solution; given an additional equation, checking whether this equation is satisfied by all common solutions of the input system; eliminating a part of dependent variables from the system if such elimination is possible; revealing hidden constraints on dependent variables, etc. Examples illustrating the use of the package are given.
},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We present the Maple package TDDS (Thomas Decomposition of Differential Systems). Given a polynomially nonlinear differential system, which in addition to equations may contain inequations, this package computes a decomposition of it into a finite set of differentially triangular and algebraically simple subsystems whose subsets of equations are involutive. Usually the decomposed system is substantially easier to investigate and solve both analytically and numerically. The distinctive property of a Thomas decomposition is disjointness of the solution sets of the output subsystems. Thereby, a solution of a well-posed initial problem belongs to one and only one output subsystem. The Thomas decomposition is fully algorithmic. It allows to perform important elements of algebraic analysis of an input differential system such as: verifying consistency, i.e., the existence of solutions; detecting the arbitrariness in the general analytic solution; given an additional equation, checking whether this equation is satisfied by all common solutions of the input system; eliminating a part of dependent variables from the system if such elimination is possible; revealing hidden constraints on dependent variables, etc. Examples illustrating the use of the package are given.
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2016
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Craven, Matthew J; Robertz, Daniel A parallel evolutionary approach to solving systems of equations in polycyclic groups Journal Article Groups Complexity Cryptology, 8 (2), pp. 109–125, 2016. Abstract | Links | BibTeX @article{craven2016parallel,
title = {A parallel evolutionary approach to solving systems of equations in polycyclic groups},
author = {Matthew J Craven and Daniel Robertz},
doi = {10.1515/gcc-2016-0012},
year = {2016},
date = {2016-11-01},
journal = {Groups Complexity Cryptology},
volume = {8},
number = {2},
pages = {109--125},
publisher = {De Gruyter},
abstract = {The Anshel–Anshel–Goldfeld (AAG) key exchange protocol is based upon the multiple conjugacy problem for a finitely-presented group. The hardness in breaking this protocol relies on the supposed difficulty in solving the corresponding equations for the conjugating element in the group. Two such protocols based on polycyclic groups as a platform were recently proposed and were shown to be resistant to length-based attack. In this article we propose a parallel evolutionary approach which runs on multicore high-performance architectures. The approach is shown to be more efficient than previous attempts to break these protocols, and also more successful. Comprehensive data of experiments run with a GAP implementation are provided and compared to the results of earlier length-based attacks. These demonstrate that the proposed platform is not as secure as first thought and also show that existing measures of cryptographic complexity are not optimal. A more accurate alternative measure is suggested. Finally, a linear algebra attack for one of the protocols is introduced.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The Anshel–Anshel–Goldfeld (AAG) key exchange protocol is based upon the multiple conjugacy problem for a finitely-presented group. The hardness in breaking this protocol relies on the supposed difficulty in solving the corresponding equations for the conjugating element in the group. Two such protocols based on polycyclic groups as a platform were recently proposed and were shown to be resistant to length-based attack. In this article we propose a parallel evolutionary approach which runs on multicore high-performance architectures. The approach is shown to be more efficient than previous attempts to break these protocols, and also more successful. Comprehensive data of experiments run with a GAP implementation are provided and compared to the results of earlier length-based attacks. These demonstrate that the proposed platform is not as secure as first thought and also show that existing measures of cryptographic complexity are not optimal. A more accurate alternative measure is suggested. Finally, a linear algebra attack for one of the protocols is introduced. |
Gerdt, V P; Robertz, D Lagrangian Constraints and Differential Thomas Decomposition Journal Article Advances in Applied Mathematics, 72 , pp. 113–138, 2016. Abstract | BibTeX @article{GerdtRobertz5,
title = {Lagrangian Constraints and Differential Thomas Decomposition},
author = {Gerdt, V. P. and Robertz, D.},
year = {2016},
date = {2016-01-01},
journal = {Advances in Applied Mathematics},
volume = {72},
pages = {113--138},
abstract = {In this paper we show how to compute algorithmically the full set of algebraically independent constraints for singular mechanical and field-theoretical models with polynomial Lagrangians. If a model under consideration is not singular as a whole but has domains of dynamical (field) variables where its Lagrangian becomes singular, then our approach allows to detect such domains and compute the relevant constraints. In doing so, we assume that the Lagrangian of a model is a differential polynomial and apply the differential Thomas decomposition algorithm to the Euler-Lagrange equations.
},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In this paper we show how to compute algorithmically the full set of algebraically independent constraints for singular mechanical and field-theoretical models with polynomial Lagrangians. If a model under consideration is not singular as a whole but has domains of dynamical (field) variables where its Lagrangian becomes singular, then our approach allows to detect such domains and compute the relevant constraints. In doing so, we assume that the Lagrangian of a model is a differential polynomial and apply the differential Thomas decomposition algorithm to the Euler-Lagrange equations.
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2015
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Robertz, D Recent Progress in an Algebraic Analysis Approach to Linear Systems Journal Article Multidimensional Systems and Signal Processing, 26 (2), pp. 349–388, 2015. BibTeX @article{Robertz7,
title = {Recent Progress in an Algebraic Analysis Approach to Linear Systems},
author = {Robertz, D.},
year = {2015},
date = {2015-04-01},
journal = {Multidimensional Systems and Signal Processing},
volume = {26},
number = {2},
pages = {349--388},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
2014
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Quadrat, A; Robertz, D A constructive study of the module structure of rings of partial differential operators Journal Article Acta Applicandae Mathematicae, 133 (1), pp. 187–234, 2014. Abstract | BibTeX @article{QuadratRobertz9,
title = {A constructive study of the module structure of rings of partial differential operators},
author = {Quadrat, A. and Robertz, D.},
year = {2014},
date = {2014-01-01},
journal = {Acta Applicandae Mathematicae},
volume = {133},
number = {1},
pages = {187--234},
abstract = {The purpose of this paper is to develop constructive versions of Stafford's theorems on the module structure of Weyl algebras $A_n(k)$ (i.e., the rings of partial differential operators with polynomial coefficients) over a base field $k$ of characteristic zero. Using the very
simplicity of the ring $A_n(k)$, we show how to explicitly compute a unimodular element of a finitely generated left $A_n(k)$-module of rank at least two. This result is used to constructively decompose any finitely generated left $A_n(k)$-module into a direct sum of a free left $A_n(k)$-module and a left $A_n(k)$-module of rank at most one. If the latter is torsion-free, then we explicitly show that it is isomorphic to a left ideal of $A_n(k)$ which can be generated by two elements. Then, we give an algorithm which reduces the number of generators of a finitely presented left $A_n(k)$-module with module of relations of rank at least two to two. In particular, any finitely generated torsion left $A_n(k)$-module can be generated by two elements and is the image of a projective ideal whose construction is explicitly given. Moreover, a non-torsion but non-free left $A_n(k)$-module of rank $r$ can be generated by $r+1$ elements but no fewer. These results are implemented in the Stafford package and their system-theoretical interpretations are given within a $D$-module approach. Finally, we prove that the above results also hold for the ring of ordinary differential operators with either formal power series or locally convergent power series coefficients and, using a result due to Caro and Levcovitz, also for the ring of partial differential operators with coefficients in the field of fractions of the ring of formal power series or of the ring of locally convergent power series.
},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The purpose of this paper is to develop constructive versions of Stafford's theorems on the module structure of Weyl algebras $A_n(k)$ (i.e., the rings of partial differential operators with polynomial coefficients) over a base field $k$ of characteristic zero. Using the very
simplicity of the ring $A_n(k)$, we show how to explicitly compute a unimodular element of a finitely generated left $A_n(k)$-module of rank at least two. This result is used to constructively decompose any finitely generated left $A_n(k)$-module into a direct sum of a free left $A_n(k)$-module and a left $A_n(k)$-module of rank at most one. If the latter is torsion-free, then we explicitly show that it is isomorphic to a left ideal of $A_n(k)$ which can be generated by two elements. Then, we give an algorithm which reduces the number of generators of a finitely presented left $A_n(k)$-module with module of relations of rank at least two to two. In particular, any finitely generated torsion left $A_n(k)$-module can be generated by two elements and is the image of a projective ideal whose construction is explicitly given. Moreover, a non-torsion but non-free left $A_n(k)$-module of rank $r$ can be generated by $r+1$ elements but no fewer. These results are implemented in the Stafford package and their system-theoretical interpretations are given within a $D$-module approach. Finally, we prove that the above results also hold for the ring of ordinary differential operators with either formal power series or locally convergent power series coefficients and, using a result due to Caro and Levcovitz, also for the ring of partial differential operators with coefficients in the field of fractions of the ring of formal power series or of the ring of locally convergent power series.
|
Robertz, D Formal Algorithmic Elimination for PDEs Book Springer, Cham, 2014. BibTeX @book{Robertz6,
title = {Formal Algorithmic Elimination for PDEs},
author = {Robertz, D.},
year = {2014},
date = {2014-01-01},
volume = {2121},
publisher = {Springer},
address = {Cham},
series = {Lecture Notes in Mathematics},
keywords = {},
pubstate = {published},
tppubtype = {book}
}
|
2013
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Lange-Hegermann, M; Robertz, D Thomas decompositions of parametric nonlinear control systems Inproceedings Proceedings of the 5th Symposium on System Structure and Control, Grenoble (France), pp. 291–296, 2013. BibTeX @inproceedings{LangeHegermannRobertz1,
title = {Thomas decompositions of parametric nonlinear control systems},
author = {Lange-Hegermann, M. and Robertz, D.},
year = {2013},
date = {2013-01-01},
booktitle = {Proceedings of the 5th Symposium on System Structure and Control, Grenoble (France)},
pages = {291--296},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
Quadrat, A; Robertz, D Stafford's reduction of linear partial differential systems Inproceedings Proceedings of the 5th Symposium on System Structure and Control, Grenoble (France), pp. 309–314, 2013. BibTeX @inproceedings{QuadratRobertz8,
title = {Stafford's reduction of linear partial differential systems},
author = {Quadrat, A. and Robertz, D.},
year = {2013},
date = {2013-01-01},
booktitle = {Proceedings of the 5th Symposium on System Structure and Control, Grenoble (France)},
pages = {309--314},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
Robertz, D Applying Thomas decomposition and algebraic analysis to certain nonlinear PDE systems Inproceedings Mathematisches Forschungsinstitut Oberwolfach Report No. ??/2013, pp. ???, 2013. BibTeX @inproceedings{Robertz8,
title = {Applying Thomas decomposition and algebraic analysis to certain nonlinear PDE systems},
author = {Robertz, D.},
year = {2013},
date = {2013-01-01},
booktitle = {Mathematisches Forschungsinstitut Oberwolfach Report No. ??/2013},
pages = {???},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
2012
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Bächler, T; Gerdt, V P; Lange-Hegermann, M; Robertz, D Algorithmic Thomas Decomposition of Algebraic and Differential Systems Journal Article Journal of Symbolic Computation, 47 (10), pp. 1233–1266, 2012. Abstract | BibTeX @article{BaechlerGerdtLangeHegermannRobertz2,
title = {Algorithmic Thomas Decomposition of Algebraic and Differential Systems},
author = {Bächler, T. and Gerdt, V. P. and Lange-Hegermann, M. and Robertz, D.},
year = {2012},
date = {2012-01-01},
journal = {Journal of Symbolic Computation},
volume = {47},
number = {10},
pages = {1233--1266},
abstract = {In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these system into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems, simplicity means triangularity, square-freeness and non-vanishing initials. Differential simplicity extends algebraic simplicity with involutivity. We build upon the constructive ideas of J. M. Thomas and develop them into a new algorithm for disjoint decomposition. The given paper is a revised version of Bächler et al. (2010) and includes the proofs of correctness and termination of our decomposition algorithm. In addition, we illustrate the algorithm with further instructive examples and describe its Maple implementation together with an experimental comparison to some other triangular decomposition algorithms.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these system into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems, simplicity means triangularity, square-freeness and non-vanishing initials. Differential simplicity extends algebraic simplicity with involutivity. We build upon the constructive ideas of J. M. Thomas and develop them into a new algorithm for disjoint decomposition. The given paper is a revised version of Bächler et al. (2010) and includes the proofs of correctness and termination of our decomposition algorithm. In addition, we illustrate the algorithm with further instructive examples and describe its Maple implementation together with an experimental comparison to some other triangular decomposition algorithms. |
Gerdt, V P; Robertz, D Computation of Difference Gröbner Bases Journal Article Computer Science Journal of Moldova, 20 (2 (59)), pp. 203–226, 2012. BibTeX @article{GerdtRobertz4,
title = {Computation of Difference Gröbner Bases},
author = {Gerdt, V. P. and Robertz, D.},
year = {2012},
date = {2012-01-01},
journal = {Computer Science Journal of Moldova},
volume = {20},
number = {2 (59)},
pages = {203--226},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
2010
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Plesken, W; Robertz, D Linear differential elimination for analytic functions Journal Article Mathematics in Computer Science, 4 (2--3), pp. 231–242, 2010. BibTeX @article{PleskenRobertz7,
title = {Linear differential elimination for analytic functions},
author = {Plesken, W. and Robertz, D.},
year = {2010},
date = {2010-01-01},
journal = {Mathematics in Computer Science},
volume = {4},
number = {2--3},
pages = {231--242},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Quadrat, A; Robertz, D Controllability and differential flatness of linear analytic ordinary differential systems Inproceedings Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010), Budapest, Hungary, 2010. BibTeX @inproceedings{QuadratRobertz7,
title = {Controllability and differential flatness of linear analytic ordinary differential systems},
author = {Quadrat, A. and Robertz, D.},
year = {2010},
date = {2010-01-01},
booktitle = {Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010), Budapest, Hungary},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
Gerdt, V ~P; Robertz, D Consistency of Finite Difference Approximations for Linear PDE Systems and its Algorithmic Verification Inproceedings Watt, S ~M (Ed.): Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, 25-28 July 2010, TU M"unchen, Germany, pp. 53–59, 2010. BibTeX @inproceedings{GerdtRobertz3,
title = {Consistency of Finite Difference Approximations for Linear PDE Systems and its Algorithmic Verification},
author = {Gerdt, V.~P. and Robertz, D.},
editor = {S.~M. Watt},
year = {2010},
date = {2010-01-01},
booktitle = {Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, 25-28 July 2010, TU M"unchen, Germany},
pages = {53--59},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
B"achler, T; Gerdt, V ~P; Lange-Hegermann, M; Robertz, D Thomas Decomposition of Algebraic and Differential Systems Inproceedings Gerdt, V P; Koepf, W; Mayr, E W; Vorozhtsov, E H (Ed.): Computer Algebra in Scientific Computing, 12th International Workshop, CASC 2010, Tsakhkadzor, Armenia, pp. 31–54, Springer, 2010. BibTeX @inproceedings{BaechlerGerdtLangeHegermannRobertz1,
title = {Thomas Decomposition of Algebraic and Differential Systems},
author = {B"achler, T. and Gerdt, V.~P. and Lange-Hegermann, M. and Robertz, D.},
editor = {Gerdt, V. P. and Koepf, W. and Mayr, E. W. and Vorozhtsov, E. H.},
year = {2010},
date = {2010-01-01},
booktitle = {Computer Algebra in Scientific Computing, 12th International Workshop, CASC 2010, Tsakhkadzor, Armenia},
pages = {31--54},
publisher = {Springer},
series = {Lecture Notes in Computer Science, Vol. 6244},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
2009
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Plesken, W; Robertz, D The average number of cycles Journal Article Archiv der Mathematik, 93 (5), pp. 445–449, 2009. BibTeX @article{PleskenRobertz6,
title = {The average number of cycles},
author = {Plesken, W. and Robertz, D.},
year = {2009},
date = {2009-11-01},
journal = {Archiv der Mathematik},
volume = {93},
number = {5},
pages = {445--449},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Barakat, M; Robertz, D conley: Computing connection matrices in Maple Journal Article Journal of Symbolic Computation, 44 (5), pp. 540–557, 2009. BibTeX @article{BarakatRobertz4,
title = {conley: Computing connection matrices in Maple},
author = {Barakat, M. and Robertz, D.},
year = {2009},
date = {2009-01-01},
journal = {Journal of Symbolic Computation},
volume = {44},
number = {5},
pages = {540--557},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Robertz, D Noether normalization guided by monomial cone decompositions Journal Article Journal of Symbolic Computation, 44 (10), pp. 1359–1373, 2009. BibTeX @article{Robertz3,
title = {Noether normalization guided by monomial cone decompositions},
author = {Robertz, D.},
year = {2009},
date = {2009-01-01},
journal = {Journal of Symbolic Computation},
volume = {44},
number = {10},
pages = {1359--1373},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Robertz, D The Auslander-Buchsbaum-Serre theorem Inproceedings Mathematisches Forschungsinstitut Oberwolfach Report No. 50/2009, pp. 2750–2751, 2009. BibTeX @inproceedings{Robertz4,
title = {The Auslander-Buchsbaum-Serre theorem},
author = {Robertz, D.},
year = {2009},
date = {2009-01-01},
booktitle = {Mathematisches Forschungsinstitut Oberwolfach Report No. 50/2009},
pages = {2750--2751},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
Robertz, D Parametrizing linear systems Inproceedings Mathematisches Forschungsinstitut Oberwolfach Report No. 50/2009, pp. 2755–2758, 2009. BibTeX @inproceedings{Robertz5,
title = {Parametrizing linear systems},
author = {Robertz, D.},
year = {2009},
date = {2009-01-01},
booktitle = {Mathematisches Forschungsinstitut Oberwolfach Report No. 50/2009},
pages = {2755--2758},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
2008
|
Barakat, M; Robertz, D homalg: A meta-package for homological algebra Journal Article Journal of Algebra and Its Applications, 7 (3), pp. 299–317, 2008. BibTeX @article{BarakatRobertz1,
title = {homalg: A meta-package for homological algebra},
author = {Barakat, M. and Robertz, D.},
year = {2008},
date = {2008-01-01},
journal = {Journal of Algebra and Its Applications},
volume = {7},
number = {3},
pages = {299--317},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Plesken, W; Robertz, D Elimination for coefficients of special characteristic polynomials Journal Article Experimental Mathematics, 17 (4), pp. 499–510, 2008. BibTeX @article{PleskenRobertz5,
title = {Elimination for coefficients of special characteristic polynomials},
author = {Plesken, W. and Robertz, D.},
year = {2008},
date = {2008-01-01},
journal = {Experimental Mathematics},
volume = {17},
number = {4},
pages = {499--510},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Quadrat, A; Robertz, D Baer's extension problem for multidimensional linear systems Inproceedings Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2008), Virginia Tech, Blacksburg, Virginia (USA), 2008. BibTeX @inproceedings{QuadratRobertz6,
title = {Baer's extension problem for multidimensional linear systems},
author = {Quadrat, A. and Robertz, D.},
year = {2008},
date = {2008-01-01},
booktitle = {Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2008), Virginia Tech, Blacksburg, Virginia (USA)},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
2007
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Chyzak, F; Quadrat, A; Robertz, D OreModules: A Symbolic Package for the Study of Multidimensional Linear Systems Inproceedings Chiasson, J; Loiseau, J -J (Ed.): Applications of Time-Delay Systems, pp. 233–264, Springer, 2007. BibTeX @inproceedings{ChyzakQuadratRobertz4,
title = {OreModules: A Symbolic Package for the Study of Multidimensional Linear Systems},
author = {Chyzak, F. and Quadrat, A. and Robertz, D.},
editor = {Chiasson, J. and Loiseau, J.-J.},
year = {2007},
date = {2007-01-01},
booktitle = {Applications of Time-Delay Systems},
pages = {233--264},
publisher = {Springer},
series = {LNCIS 352},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
Robertz, D Janet Bases and Applications Inproceedings Rosenkranz, M; Wang, D (Ed.): Groebner Bases in Symbolic Analysis, pp. 139–168, de Gruyter, 2007. BibTeX @inproceedings{Robertz2,
title = {Janet Bases and Applications},
author = {Robertz, D.},
editor = {Rosenkranz, M. and Wang, D.},
year = {2007},
date = {2007-01-01},
booktitle = {Groebner Bases in Symbolic Analysis},
pages = {139--168},
publisher = {de Gruyter},
series = {Radon Series on Computational and Applied Mathematics 2},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
Quadrat, A; Robertz, D Computation of bases of free modules over the Weyl algebras Journal Article Journal of Symbolic Computation, 42 (11--12), pp. 1113–1141, 2007. BibTeX @article{QuadratRobertz5,
title = {Computation of bases of free modules over the Weyl algebras},
author = {Quadrat, A. and Robertz, D.},
year = {2007},
date = {2007-01-01},
journal = {Journal of Symbolic Computation},
volume = {42},
number = {11--12},
pages = {1113--1141},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Plesken, W; Robertz, D Some Elimination Problems for Matrices Inproceedings Ganzha, V G; Mayr, E W; Vorozhtsov, E V (Ed.): Computer Algebra in Scientific Computing, 10th International Workshop, CASC 2007, Bonn, Germany, pp. 350–359, Springer, 2007. BibTeX @inproceedings{PleskenRobertz4,
title = {Some Elimination Problems for Matrices},
author = {Plesken, W. and Robertz, D.},
editor = {Ganzha, V. G. and Mayr, E. W. and Vorozhtsov, E. V.},
year = {2007},
date = {2007-01-01},
booktitle = {Computer Algebra in Scientific Computing, 10th International Workshop, CASC 2007, Bonn, Germany},
pages = {350--359},
publisher = {Springer},
series = {Lecture Notes in Computer Science, Vol. 4770},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
2006
|
Gerdt, V P; Robertz, D A Maple Package for Computing Gröbner Bases for Linear Recurrence Relations Journal Article Nuclear Instruments and Methods in Physics Research, A: Accelerators, Spectrometers, Detectors and Associated Equipment, 559 (1), pp. 215–219, 2006. BibTeX @article{GerdtRobertz1,
title = {A Maple Package for Computing Gröbner Bases for Linear Recurrence Relations},
author = {Gerdt, V. P. and Robertz, D.},
year = {2006},
date = {2006-01-01},
journal = {Nuclear Instruments and Methods in Physics Research, A: Accelerators, Spectrometers, Detectors and Associated Equipment},
volume = {559},
number = {1},
pages = {215--219},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Plesken, W; Robertz, D Representations, commutative algebra, and Hurwitz groups Journal Article Journal of Algebra, 300 (1), pp. 223–247, 2006. BibTeX @article{PleskenRobertz3,
title = {Representations, commutative algebra, and Hurwitz groups},
author = {Plesken, W. and Robertz, D.},
year = {2006},
date = {2006-01-01},
journal = {Journal of Algebra},
volume = {300},
number = {1},
pages = {223--247},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Barakat, M; Robertz, D homalg: First steps to an abstract package for homological algebra Inproceedings Proceedings of the X meeting on computational algebra and its applications (EACA 2006), Seville (Spain), pp. 29–32, 2006. BibTeX @inproceedings{BarakatRobertz2,
title = {homalg: First steps to an abstract package for homological algebra},
author = {Barakat, M. and Robertz, D.},
year = {2006},
date = {2006-01-01},
booktitle = {Proceedings of the X meeting on computational algebra and its applications (EACA 2006), Seville (Spain)},
pages = {29--32},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
Quadrat, A; Robertz, D Constructive computation of flat outputs of a class of multidimensional linear systems with variable coefficients Inproceedings Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006), Kyoto (Japan), pp. 583–595, 2006. BibTeX @inproceedings{QuadratRobertz3,
title = {Constructive computation of flat outputs of a class of multidimensional linear systems with variable coefficients},
author = {Quadrat, A. and Robertz, D.},
year = {2006},
date = {2006-01-01},
booktitle = {Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006), Kyoto (Japan)},
pages = {583--595},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
Barakat, M; Robertz, D Computing invariants of multidimensional linear systems on an abstract homological level Inproceedings Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006), Kyoto (Japan), pp. 542–559, 2006. BibTeX @inproceedings{BarakatRobertz3,
title = {Computing invariants of multidimensional linear systems on an abstract homological level},
author = {Barakat, M. and Robertz, D.},
year = {2006},
date = {2006-01-01},
booktitle = {Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006), Kyoto (Japan)},
pages = {542--559},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
Quadrat, A; Robertz, D On the Monge problem and multidimensional optimal control Inproceedings Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006), Kyoto (Japan), pp. 596–605, 2006. BibTeX @inproceedings{QuadratRobertz4,
title = {On the Monge problem and multidimensional optimal control},
author = {Quadrat, A. and Robertz, D.},
year = {2006},
date = {2006-01-01},
booktitle = {Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006), Kyoto (Japan)},
pages = {596--605},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
Robertz, D Representations, commutative algebra, and Hurwitz groups (joint work with Wilhelm Plesken) Inproceedings Mathematisches Forschungsinstitut Oberwolfach Report No. 30/2006, pp. 1842–1843, 2006. BibTeX @inproceedings{Robertz0,
title = {Representations, commutative algebra, and Hurwitz groups (joint work with Wilhelm Plesken)},
author = {Robertz, D.},
year = {2006},
date = {2006-01-01},
booktitle = {Mathematisches Forschungsinstitut Oberwolfach Report No. 30/2006},
pages = {1842--1843},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
Robertz, D Formal Computational Methods for Control Theory PhD Thesis RWTH Aachen, Germany, 2006, (This thesis is available at tt http://darwin.bth.rwth-aachen.de/opus/volltexte/ 2006/1586). BibTeX @phdthesis{Robertz1,
title = {Formal Computational Methods for Control Theory},
author = {Robertz, D.},
year = {2006},
date = {2006-01-01},
school = {RWTH Aachen, Germany},
note = {This thesis is available at tt http://darwin.bth.rwth-aachen.de/opus/volltexte/ 2006/1586},
keywords = {},
pubstate = {published},
tppubtype = {phdthesis}
}
|
Corves, B; Abel, D; Plesken, W; Harmeling, F; Robertz, D; Maschuw, J Methoden und Werkzeuge zum Entwurf mechatronischer Bewegungssysteme mit ungleichmäßig übersetzenden Getrieben Inproceedings VDI Berichte 1963, pp. 557–573, VDI-Verlag, 2006. BibTeX @inproceedings{CorvesAbelPleskenHarmelingRobertzMaschuw,
title = {Methoden und Werkzeuge zum Entwurf mechatronischer Bewegungssysteme mit ungleichmäßig übersetzenden Getrieben},
author = {Corves, B. and Abel, D. and Plesken, W. and Harmeling, F. and Robertz, D. and Maschuw, J.},
year = {2006},
date = {2006-01-01},
booktitle = {VDI Berichte 1963},
pages = {557--573},
publisher = {VDI-Verlag},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
2005
|
Chyzak, F; Quadrat, A; Robertz, D Effective algorithms for parametrizing linear control systems over Ore algebras Journal Article Applicable Algebra in Engineering, Communication and Computing, 16 (5), pp. 319–376, 2005. BibTeX @article{ChyzakQuadratRobertz2,
title = {Effective algorithms for parametrizing linear control systems over Ore algebras},
author = {Chyzak, F. and Quadrat, A. and Robertz, D.},
year = {2005},
date = {2005-01-01},
journal = {Applicable Algebra in Engineering, Communication and Computing},
volume = {16},
number = {5},
pages = {319--376},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Plesken, W; Robertz, D Constructing Invariants for Finite Groups Journal Article Experimental Mathematics, 14 (2), pp. 175–188, 2005. BibTeX @article{PleskenRobertz1,
title = {Constructing Invariants for Finite Groups},
author = {Plesken, W. and Robertz, D.},
year = {2005},
date = {2005-01-01},
journal = {Experimental Mathematics},
volume = {14},
number = {2},
pages = {175--188},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Plesken, W; Robertz, D Janet's approach to presentations and resolutions for polynomials and linear pdes Journal Article Archiv der Mathematik, 84 (1), pp. 22–37, 2005. BibTeX @article{PleskenRobertz2,
title = {Janet's approach to presentations and resolutions for polynomials and linear pdes},
author = {Plesken, W. and Robertz, D.},
year = {2005},
date = {2005-01-01},
journal = {Archiv der Mathematik},
volume = {84},
number = {1},
pages = {22--37},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Quadrat, A; Robertz, D Parametrizing all solutions of uncontrollable multidimensional linear systems Inproceedings Proceedings of the 16th IFAC World Congress, Prague (Czech Republic), July 4-8, 2005, 2005. BibTeX @inproceedings{QuadratRobertz1,
title = {Parametrizing all solutions of uncontrollable multidimensional linear systems},
author = {Quadrat, A. and Robertz, D.},
year = {2005},
date = {2005-01-01},
booktitle = {Proceedings of the 16th IFAC World Congress, Prague (Czech Republic), July 4-8, 2005},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
Quadrat, A; Robertz, D On the blowing-up of stably free behaviours Inproceedings Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005, Seville (Spain), December 12-15, 2005, pp. 1541–1546, 2005. BibTeX @inproceedings{QuadratRobertz2,
title = {On the blowing-up of stably free behaviours},
author = {Quadrat, A. and Robertz, D.},
year = {2005},
date = {2005-01-01},
booktitle = {Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005, Seville (Spain), December 12-15, 2005},
pages = {1541--1546},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
Gerdt, V ~P; Robertz, D Computation of Gr"obner Bases for Systems of Linear Difference Equations Journal Article Computeralgebra-Rundbrief, 37 , pp. 8–16, 2005. BibTeX @article{GerdtRobertz2,
title = {Computation of Gr"obner Bases for Systems of Linear Difference Equations},
author = {Gerdt, V.~P. and Robertz, D.},
year = {2005},
date = {2005-01-01},
journal = {Computeralgebra-Rundbrief},
volume = {37},
pages = {8--16},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
2004
|
Chyzak, F; Quadrat, A; Robertz, D OreModules: A symbolic package for the study of multidimensional linear systems Inproceedings Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2004), Katholieke Universiteit Leuven (Belgium), 2004. BibTeX @inproceedings{ChyzakQuadratRobertz3,
title = {OreModules: A symbolic package for the study of multidimensional linear systems},
author = {Chyzak, F. and Quadrat, A. and Robertz, D.},
year = {2004},
date = {2004-01-01},
booktitle = {Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2004), Katholieke Universiteit Leuven (Belgium)},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
2003
|
Chyzak, F; Quadrat, A; Robertz, D Linear Control Systems over Ore Algebras: Effective Algorithms for the Computation of Parametrizations Inproceedings IFAC Workshop on Time-Delay Systems, Sep. 8-10, 2003, INRIA, Rocquencourt (France), 2003. BibTeX @inproceedings{ChyzakQuadratRobertz1,
title = {Linear Control Systems over Ore Algebras: Effective Algorithms for the Computation of Parametrizations},
author = {Chyzak, F. and Quadrat, A. and Robertz, D.},
year = {2003},
date = {2003-01-01},
booktitle = {IFAC Workshop on Time-Delay Systems, Sep. 8-10, 2003, INRIA, Rocquencourt (France)},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
Blinkov, Y ~A; Cid, C ~F; Gerdt, V ~P; Plesken, W; Robertz, D The MAPLE Package ``Janet'': I. Polynomial Systems Inproceedings Ganzha, V ~G; Mayr, E ~W; Vorozhtsov, E ~V (Ed.): Proceedings of the 6th International Workshop on Computer Algebra in Scientific Computing, Sep. 20-26, 2003, Passau (Germany), pp. 31–40, 2003. BibTeX @inproceedings{BlinkovCidetal1,
title = {The MAPLE Package ``Janet'': I. Polynomial Systems},
author = {Blinkov, Y.~A. and Cid, C.~F. and Gerdt, V.~P. and Plesken, W. and Robertz, D.},
editor = {Ganzha, V.~G. and Mayr, E.~W. and Vorozhtsov, E.~V.},
year = {2003},
date = {2003-01-01},
booktitle = {Proceedings of the 6th International Workshop on Computer Algebra in Scientific Computing, Sep. 20-26, 2003, Passau (Germany)},
pages = {31--40},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|
Blinkov, Y ~A; Cid, C ~F; Gerdt, V ~P; Plesken, W; Robertz, D The MAPLE Package ``Janet'': II. Linear Partial Differential Equations Inproceedings Ganzha, V ~G; Mayr, E ~W; Vorozhtsov, E ~V (Ed.): Proceedings of the 6th International Workshop on Computer Algebra in Scientific Computing, Sep. 20-26, 2003, Passau (Germany), pp. 41–54, 2003. BibTeX @inproceedings{BlinkovCidetal2,
title = {The MAPLE Package ``Janet'': II. Linear Partial Differential Equations},
author = {Blinkov, Y.~A. and Cid, C.~F. and Gerdt, V.~P. and Plesken, W. and Robertz, D.},
editor = {Ganzha, V.~G. and Mayr, E.~W. and Vorozhtsov, E.~V.},
year = {2003},
date = {2003-01-01},
booktitle = {Proceedings of the 6th International Workshop on Computer Algebra in Scientific Computing, Sep. 20-26, 2003, Passau (Germany)},
pages = {41--54},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
|