---
_id: '34846'
abstract:
- lang: eng
  text: Given a field extension K/k of degree n we are interested in finding the subfields
    of K containing k. There can be more than polynomially many subfields. We introduce
    the notion of generating subfields, a set of up to n subfields whose intersections
    give the rest. We provide an efficient algorithm which uses linear algebra in
    k or lattice reduction along with factorization in any extension of K. Implementations
    show that previously difficult cases can now be handled.
author:
- first_name: Mark
  full_name: van Hoeij, Mark
  last_name: van Hoeij
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Andrew
  full_name: Novocin, Andrew
  last_name: Novocin
citation:
  ama: van Hoeij M, Klüners J, Novocin A. Generating subfields. <i>Journal of Symbolic
    Computation</i>. 2011;52:17-34. doi:<a href="https://doi.org/10.1016/j.jsc.2012.05.010">10.1016/j.jsc.2012.05.010</a>
  apa: van Hoeij, M., Klüners, J., &#38; Novocin, A. (2011). Generating subfields.
    <i>Journal of Symbolic Computation</i>, <i>52</i>, 17–34. <a href="https://doi.org/10.1016/j.jsc.2012.05.010">https://doi.org/10.1016/j.jsc.2012.05.010</a>
  bibtex: '@article{van Hoeij_Klüners_Novocin_2011, title={Generating subfields},
    volume={52}, DOI={<a href="https://doi.org/10.1016/j.jsc.2012.05.010">10.1016/j.jsc.2012.05.010</a>},
    journal={Journal of Symbolic Computation}, publisher={Elsevier BV}, author={van
    Hoeij, Mark and Klüners, Jürgen and Novocin, Andrew}, year={2011}, pages={17–34}
    }'
  chicago: 'Hoeij, Mark van, Jürgen Klüners, and Andrew Novocin. “Generating Subfields.”
    <i>Journal of Symbolic Computation</i> 52 (2011): 17–34. <a href="https://doi.org/10.1016/j.jsc.2012.05.010">https://doi.org/10.1016/j.jsc.2012.05.010</a>.'
  ieee: 'M. van Hoeij, J. Klüners, and A. Novocin, “Generating subfields,” <i>Journal
    of Symbolic Computation</i>, vol. 52, pp. 17–34, 2011, doi: <a href="https://doi.org/10.1016/j.jsc.2012.05.010">10.1016/j.jsc.2012.05.010</a>.'
  mla: van Hoeij, Mark, et al. “Generating Subfields.” <i>Journal of Symbolic Computation</i>,
    vol. 52, Elsevier BV, 2011, pp. 17–34, doi:<a href="https://doi.org/10.1016/j.jsc.2012.05.010">10.1016/j.jsc.2012.05.010</a>.
  short: M. van Hoeij, J. Klüners, A. Novocin, Journal of Symbolic Computation 52
    (2011) 17–34.
date_created: 2022-12-22T10:54:15Z
date_updated: 2023-03-06T09:46:15Z
department:
- _id: '102'
doi: 10.1016/j.jsc.2012.05.010
intvolume: '        52'
keyword:
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 17-34
publication: Journal of Symbolic Computation
publication_identifier:
  issn:
  - 0747-7171
publication_status: published
publisher: Elsevier BV
status: public
title: Generating subfields
type: journal_article
user_id: '93826'
volume: 52
year: '2011'
...
---
_id: '34887'
abstract:
- lang: eng
  text: 'Let d be a nonsquare positive integer. We give the value of the natural probability
    that the narrow ideal class groups of the quadratic fields ℚ(√d) and ℚ(√−d) have
    the same 4-ranks. '
author:
- first_name: Étienne
  full_name: Fouvry, Étienne
  last_name: Fouvry
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Fouvry É, Klüners J. On the Spiegelungssatz for the 4-rank. <i>Algebra &#38;amp;
    Number Theory</i>. 2010;4(5):493-508. doi:<a href="https://doi.org/10.2140/ant.2010.4.493">10.2140/ant.2010.4.493</a>
  apa: Fouvry, É., &#38; Klüners, J. (2010). On the Spiegelungssatz for the 4-rank.
    <i>Algebra &#38;amp; Number Theory</i>, <i>4</i>(5), 493–508. <a href="https://doi.org/10.2140/ant.2010.4.493">https://doi.org/10.2140/ant.2010.4.493</a>
  bibtex: '@article{Fouvry_Klüners_2010, title={On the Spiegelungssatz for the 4-rank},
    volume={4}, DOI={<a href="https://doi.org/10.2140/ant.2010.4.493">10.2140/ant.2010.4.493</a>},
    number={5}, journal={Algebra &#38;amp; Number Theory}, publisher={Mathematical
    Sciences Publishers}, author={Fouvry, Étienne and Klüners, Jürgen}, year={2010},
    pages={493–508} }'
  chicago: 'Fouvry, Étienne, and Jürgen Klüners. “On the Spiegelungssatz for the 4-Rank.”
    <i>Algebra &#38;amp; Number Theory</i> 4, no. 5 (2010): 493–508. <a href="https://doi.org/10.2140/ant.2010.4.493">https://doi.org/10.2140/ant.2010.4.493</a>.'
  ieee: 'É. Fouvry and J. Klüners, “On the Spiegelungssatz for the 4-rank,” <i>Algebra
    &#38;amp; Number Theory</i>, vol. 4, no. 5, pp. 493–508, 2010, doi: <a href="https://doi.org/10.2140/ant.2010.4.493">10.2140/ant.2010.4.493</a>.'
  mla: Fouvry, Étienne, and Jürgen Klüners. “On the Spiegelungssatz for the 4-Rank.”
    <i>Algebra &#38;amp; Number Theory</i>, vol. 4, no. 5, Mathematical Sciences Publishers,
    2010, pp. 493–508, doi:<a href="https://doi.org/10.2140/ant.2010.4.493">10.2140/ant.2010.4.493</a>.
  short: É. Fouvry, J. Klüners, Algebra &#38;amp; Number Theory 4 (2010) 493–508.
date_created: 2022-12-23T09:10:12Z
date_updated: 2023-03-06T10:18:14Z
department:
- _id: '102'
doi: 10.2140/ant.2010.4.493
intvolume: '         4'
issue: '5'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 493-508
publication: Algebra &amp; Number Theory
publication_identifier:
  issn:
  - 1937-0652
publication_status: published
publisher: Mathematical Sciences Publishers
status: public
title: On the Spiegelungssatz for the 4-rank
type: journal_article
user_id: '93826'
volume: 4
year: '2010'
...
---
_id: '34889'
abstract:
- lang: eng
  text: We prove that van Hoeij’s original algorithm to factor univariate polynomials
    over the rationals runs in polynomial time, as well as natural variants. In particular,
    our approach also yields polynomial time complexity results for bivariate polynomials
    over a finite field.
author:
- first_name: Karim
  full_name: Belabas, Karim
  last_name: Belabas
- first_name: Mark
  full_name: van Hoeij, Mark
  last_name: van Hoeij
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Allan
  full_name: Steel, Allan
  last_name: Steel
citation:
  ama: Belabas K, van Hoeij M, Klüners J, Steel A. Factoring polynomials over global
    fields. <i>Journal de Théorie des Nombres de Bordeaux</i>. 2009;21(1):15-39. doi:<a
    href="https://doi.org/10.5802/jtnb.655">10.5802/jtnb.655</a>
  apa: Belabas, K., van Hoeij, M., Klüners, J., &#38; Steel, A. (2009). Factoring
    polynomials over global fields. <i>Journal de Théorie Des Nombres de Bordeaux</i>,
    <i>21</i>(1), 15–39. <a href="https://doi.org/10.5802/jtnb.655">https://doi.org/10.5802/jtnb.655</a>
  bibtex: '@article{Belabas_van Hoeij_Klüners_Steel_2009, title={Factoring polynomials
    over global fields}, volume={21}, DOI={<a href="https://doi.org/10.5802/jtnb.655">10.5802/jtnb.655</a>},
    number={1}, journal={Journal de Théorie des Nombres de Bordeaux}, publisher={Cellule
    MathDoc/CEDRAM}, author={Belabas, Karim and van Hoeij, Mark and Klüners, Jürgen
    and Steel, Allan}, year={2009}, pages={15–39} }'
  chicago: 'Belabas, Karim, Mark van Hoeij, Jürgen Klüners, and Allan Steel. “Factoring
    Polynomials over Global Fields.” <i>Journal de Théorie Des Nombres de Bordeaux</i>
    21, no. 1 (2009): 15–39. <a href="https://doi.org/10.5802/jtnb.655">https://doi.org/10.5802/jtnb.655</a>.'
  ieee: 'K. Belabas, M. van Hoeij, J. Klüners, and A. Steel, “Factoring polynomials
    over global fields,” <i>Journal de Théorie des Nombres de Bordeaux</i>, vol. 21,
    no. 1, pp. 15–39, 2009, doi: <a href="https://doi.org/10.5802/jtnb.655">10.5802/jtnb.655</a>.'
  mla: Belabas, Karim, et al. “Factoring Polynomials over Global Fields.” <i>Journal
    de Théorie Des Nombres de Bordeaux</i>, vol. 21, no. 1, Cellule MathDoc/CEDRAM,
    2009, pp. 15–39, doi:<a href="https://doi.org/10.5802/jtnb.655">10.5802/jtnb.655</a>.
  short: K. Belabas, M. van Hoeij, J. Klüners, A. Steel, Journal de Théorie Des Nombres
    de Bordeaux 21 (2009) 15–39.
date_created: 2022-12-23T09:33:37Z
date_updated: 2023-03-06T09:09:56Z
department:
- _id: '102'
doi: 10.5802/jtnb.655
external_id:
  arxiv:
  - 'math/0409510 '
intvolume: '        21'
issue: '1'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 15-39
publication: Journal de Théorie des Nombres de Bordeaux
publication_identifier:
  issn:
  - 1246-7405
publication_status: published
publisher: Cellule MathDoc/CEDRAM
status: public
title: Factoring polynomials over global fields
type: journal_article
user_id: '93826'
volume: 21
year: '2009'
...
---
_id: '11935'
abstract:
- lang: eng
  text: The generalized sidelobe canceller by Griffith and Jim is a robust beamforming
    method to enhance a desired (speech) signal in the presence of stationary noise.
    Its performance depends to a high degree on the construction of the blocking matrix
    which produces noise reference signals for the subsequent adaptive interference
    canceller. Especially in reverberated environments the beamformer may suffer from
    signal leakage and reduced noise suppression. In this paper a new blocking matrix
    is proposed. It is based on a generalized eigenvalue problem whose solution provides
    an indirect estimation of the transfer functions from the source to the sensors.
    The quality of the new generalized eigenvector blocking matrix is studied in simulated
    rooms with different reverberation times and is compared to alternatives proposed
    in the literature.
author:
- first_name: Ernst
  full_name: Warsitz, Ernst
  last_name: Warsitz
- first_name: Alexander
  full_name: Krueger, Alexander
  last_name: Krueger
- first_name: Reinhold
  full_name: Haeb-Umbach, Reinhold
  id: '242'
  last_name: Haeb-Umbach
citation:
  ama: 'Warsitz E, Krueger A, Haeb-Umbach R. Speech enhancement with a new generalized
    eigenvector blocking matrix for application in a generalized sidelobe canceller.
    In: <i>IEEE International Conference on Acoustics, Speech and Signal Processing
    (ICASSP 2008)</i>. ; 2008:73-76. doi:<a href="https://doi.org/10.1109/ICASSP.2008.4517549">10.1109/ICASSP.2008.4517549</a>'
  apa: Warsitz, E., Krueger, A., &#38; Haeb-Umbach, R. (2008). Speech enhancement
    with a new generalized eigenvector blocking matrix for application in a generalized
    sidelobe canceller. In <i>IEEE International Conference on Acoustics, Speech and
    Signal Processing (ICASSP 2008)</i> (pp. 73–76). <a href="https://doi.org/10.1109/ICASSP.2008.4517549">https://doi.org/10.1109/ICASSP.2008.4517549</a>
  bibtex: '@inproceedings{Warsitz_Krueger_Haeb-Umbach_2008, title={Speech enhancement
    with a new generalized eigenvector blocking matrix for application in a generalized
    sidelobe canceller}, DOI={<a href="https://doi.org/10.1109/ICASSP.2008.4517549">10.1109/ICASSP.2008.4517549</a>},
    booktitle={IEEE International Conference on Acoustics, Speech and Signal Processing
    (ICASSP 2008)}, author={Warsitz, Ernst and Krueger, Alexander and Haeb-Umbach,
    Reinhold}, year={2008}, pages={73–76} }'
  chicago: Warsitz, Ernst, Alexander Krueger, and Reinhold Haeb-Umbach. “Speech Enhancement
    with a New Generalized Eigenvector Blocking Matrix for Application in a Generalized
    Sidelobe Canceller.” In <i>IEEE International Conference on Acoustics, Speech
    and Signal Processing (ICASSP 2008)</i>, 73–76, 2008. <a href="https://doi.org/10.1109/ICASSP.2008.4517549">https://doi.org/10.1109/ICASSP.2008.4517549</a>.
  ieee: E. Warsitz, A. Krueger, and R. Haeb-Umbach, “Speech enhancement with a new
    generalized eigenvector blocking matrix for application in a generalized sidelobe
    canceller,” in <i>IEEE International Conference on Acoustics, Speech and Signal
    Processing (ICASSP 2008)</i>, 2008, pp. 73–76.
  mla: Warsitz, Ernst, et al. “Speech Enhancement with a New Generalized Eigenvector
    Blocking Matrix for Application in a Generalized Sidelobe Canceller.” <i>IEEE
    International Conference on Acoustics, Speech and Signal Processing (ICASSP 2008)</i>,
    2008, pp. 73–76, doi:<a href="https://doi.org/10.1109/ICASSP.2008.4517549">10.1109/ICASSP.2008.4517549</a>.
  short: 'E. Warsitz, A. Krueger, R. Haeb-Umbach, in: IEEE International Conference
    on Acoustics, Speech and Signal Processing (ICASSP 2008), 2008, pp. 73–76.'
date_created: 2019-07-12T05:31:06Z
date_updated: 2022-01-06T06:51:12Z
department:
- _id: '54'
doi: 10.1109/ICASSP.2008.4517549
keyword:
- adaptive interference canceller
- adaptive signal processing
- array signal processing
- beamforming method
- eigenvalues and eigenfunctions
- generalized eigenvector blocking matrix
- generalized sidelobe canceller
- interference suppression
- matrix algebra
- noise suppression
- speech enhancement
- transfer function estimation
- transfer functions
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://groups.uni-paderborn.de/nt/pubs/2008/WaKrHa08.pdf
oa: '1'
page: 73-76
publication: IEEE International Conference on Acoustics, Speech and Signal Processing
  (ICASSP 2008)
status: public
title: Speech enhancement with a new generalized eigenvector blocking matrix for application
  in a generalized sidelobe canceller
type: conference
user_id: '44006'
year: '2008'
...
---
_id: '39947'
author:
- first_name: Margit
  full_name: Rösler, Margit
  id: '37390'
  last_name: Rösler
citation:
  ama: Rösler M. Bessel convolutions on matrix cones. <i>Compositio Mathematica</i>.
    2007;143(03):749-779. doi:<a href="https://doi.org/10.1112/s0010437x06002594">10.1112/s0010437x06002594</a>
  apa: Rösler, M. (2007). Bessel convolutions on matrix cones. <i>Compositio Mathematica</i>,
    <i>143</i>(03), 749–779. <a href="https://doi.org/10.1112/s0010437x06002594">https://doi.org/10.1112/s0010437x06002594</a>
  bibtex: '@article{Rösler_2007, title={Bessel convolutions on matrix cones}, volume={143},
    DOI={<a href="https://doi.org/10.1112/s0010437x06002594">10.1112/s0010437x06002594</a>},
    number={03}, journal={Compositio Mathematica}, publisher={Wiley}, author={Rösler,
    Margit}, year={2007}, pages={749–779} }'
  chicago: 'Rösler, Margit. “Bessel Convolutions on Matrix Cones.” <i>Compositio Mathematica</i>
    143, no. 03 (2007): 749–79. <a href="https://doi.org/10.1112/s0010437x06002594">https://doi.org/10.1112/s0010437x06002594</a>.'
  ieee: 'M. Rösler, “Bessel convolutions on matrix cones,” <i>Compositio Mathematica</i>,
    vol. 143, no. 03, pp. 749–779, 2007, doi: <a href="https://doi.org/10.1112/s0010437x06002594">10.1112/s0010437x06002594</a>.'
  mla: Rösler, Margit. “Bessel Convolutions on Matrix Cones.” <i>Compositio Mathematica</i>,
    vol. 143, no. 03, Wiley, 2007, pp. 749–79, doi:<a href="https://doi.org/10.1112/s0010437x06002594">10.1112/s0010437x06002594</a>.
  short: M. Rösler, Compositio Mathematica 143 (2007) 749–779.
date_created: 2023-01-25T09:55:18Z
date_updated: 2023-01-26T17:47:42Z
department:
- _id: '555'
doi: 10.1112/s0010437x06002594
extern: '1'
intvolume: '       143'
issue: '03'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 749-779
publication: Compositio Mathematica
publication_identifier:
  issn:
  - 0010-437X
  - 1570-5846
publication_status: published
publisher: Wiley
status: public
title: Bessel convolutions on matrix cones
type: journal_article
user_id: '93826'
volume: 143
year: '2007'
...
---
_id: '34891'
abstract:
- lang: eng
  text: 'We study the asymptotics conjecture of Malle for dihedral groups Dℓ of order
    2ℓ, where ℓ is an odd prime. We prove the expected lower bound for those groups.
    For the upper bounds we show that there is a connection to class groups of quadratic
    number fields. The asymptotic behavior of those class groups is predicted by the
    Cohen--Lenstra heuristics. Under the assumption of this heuristic we are able
    to prove the expected upper bounds. '
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Klüners J. Asymptotics of number fields and the Cohen–Lenstra heuristics. <i>Journal
    de Théorie des Nombres de Bordeaux</i>. 2006;18(3):607-615. doi:<a href="https://doi.org/10.5802/jtnb.561">10.5802/jtnb.561</a>
  apa: Klüners, J. (2006). Asymptotics of number fields and the Cohen–Lenstra heuristics.
    <i>Journal de Théorie Des Nombres de Bordeaux</i>, <i>18</i>(3), 607–615. <a href="https://doi.org/10.5802/jtnb.561">https://doi.org/10.5802/jtnb.561</a>
  bibtex: '@article{Klüners_2006, title={Asymptotics of number fields and the Cohen–Lenstra
    heuristics}, volume={18}, DOI={<a href="https://doi.org/10.5802/jtnb.561">10.5802/jtnb.561</a>},
    number={3}, journal={Journal de Théorie des Nombres de Bordeaux}, publisher={Cellule
    MathDoc/CEDRAM}, author={Klüners, Jürgen}, year={2006}, pages={607–615} }'
  chicago: 'Klüners, Jürgen. “Asymptotics of Number Fields and the Cohen–Lenstra Heuristics.”
    <i>Journal de Théorie Des Nombres de Bordeaux</i> 18, no. 3 (2006): 607–15. <a
    href="https://doi.org/10.5802/jtnb.561">https://doi.org/10.5802/jtnb.561</a>.'
  ieee: 'J. Klüners, “Asymptotics of number fields and the Cohen–Lenstra heuristics,”
    <i>Journal de Théorie des Nombres de Bordeaux</i>, vol. 18, no. 3, pp. 607–615,
    2006, doi: <a href="https://doi.org/10.5802/jtnb.561">10.5802/jtnb.561</a>.'
  mla: Klüners, Jürgen. “Asymptotics of Number Fields and the Cohen–Lenstra Heuristics.”
    <i>Journal de Théorie Des Nombres de Bordeaux</i>, vol. 18, no. 3, Cellule MathDoc/CEDRAM,
    2006, pp. 607–15, doi:<a href="https://doi.org/10.5802/jtnb.561">10.5802/jtnb.561</a>.
  short: J. Klüners, Journal de Théorie Des Nombres de Bordeaux 18 (2006) 607–615.
date_created: 2022-12-23T09:37:01Z
date_updated: 2023-03-06T09:12:04Z
department:
- _id: '102'
doi: 10.5802/jtnb.561
external_id:
  arxiv:
  - 'math/0512260 '
intvolume: '        18'
issue: '3'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 607-615
publication: Journal de Théorie des Nombres de Bordeaux
publication_identifier:
  issn:
  - 1246-7405
publication_status: published
publisher: Cellule MathDoc/CEDRAM
status: public
title: Asymptotics of number fields and the Cohen–Lenstra heuristics
type: journal_article
user_id: '93826'
volume: 18
year: '2006'
...
---
_id: '34892'
abstract:
- lang: eng
  text: 'We prove that the number of quartic S4--extensions of the rationals of given
    discriminant d is $O_\eps(d^{1/2+\eps})$ for all $\eps>0$. For a prime number
    p we derive that the dimension of the space of octahedral modular forms of weight
    1 and conductor p or p² is bounded above by O(p¹/²log(p)²). '
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Klüners J. The number of S₄-fields with given discriminant. <i>Acta Arithmetica</i>.
    2006;122(2):185-194. doi:<a href="https://doi.org/10.4064/aa122-2-3">10.4064/aa122-2-3</a>
  apa: Klüners, J. (2006). The number of S₄-fields with given discriminant. <i>Acta
    Arithmetica</i>, <i>122</i>(2), 185–194. <a href="https://doi.org/10.4064/aa122-2-3">https://doi.org/10.4064/aa122-2-3</a>
  bibtex: '@article{Klüners_2006, title={The number of S₄-fields with given discriminant},
    volume={122}, DOI={<a href="https://doi.org/10.4064/aa122-2-3">10.4064/aa122-2-3</a>},
    number={2}, journal={Acta Arithmetica}, publisher={Institute of Mathematics, Polish
    Academy of Sciences}, author={Klüners, Jürgen}, year={2006}, pages={185–194} }'
  chicago: 'Klüners, Jürgen. “The Number of S₄-Fields with given Discriminant.” <i>Acta
    Arithmetica</i> 122, no. 2 (2006): 185–94. <a href="https://doi.org/10.4064/aa122-2-3">https://doi.org/10.4064/aa122-2-3</a>.'
  ieee: 'J. Klüners, “The number of S₄-fields with given discriminant,” <i>Acta Arithmetica</i>,
    vol. 122, no. 2, pp. 185–194, 2006, doi: <a href="https://doi.org/10.4064/aa122-2-3">10.4064/aa122-2-3</a>.'
  mla: Klüners, Jürgen. “The Number of S₄-Fields with given Discriminant.” <i>Acta
    Arithmetica</i>, vol. 122, no. 2, Institute of Mathematics, Polish Academy of
    Sciences, 2006, pp. 185–94, doi:<a href="https://doi.org/10.4064/aa122-2-3">10.4064/aa122-2-3</a>.
  short: J. Klüners, Acta Arithmetica 122 (2006) 185–194.
date_created: 2022-12-23T09:40:25Z
date_updated: 2023-03-06T09:52:41Z
department:
- _id: '102'
doi: 10.4064/aa122-2-3
external_id:
  arxiv:
  - math/0411484
intvolume: '       122'
issue: '2'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 185-194
publication: Acta Arithmetica
publication_identifier:
  issn:
  - 0065-1036
  - 1730-6264
publication_status: published
publisher: Institute of Mathematics, Polish Academy of Sciences
status: public
title: The number of S₄-fields with given discriminant
type: journal_article
user_id: '93826'
volume: 122
year: '2006'
...
---
_id: '34893'
abstract:
- lang: eng
  text: Let K be a global field and O be an order of K. We develop algorithms for
    the computation of the unit group of residue class rings for ideals O in . As
    an application we show how to compute the unit group and the Picard group of O
    provided that we are able to compute the unit group and class group of the maximal
    order O of K.
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Sebastian
  full_name: Pauli, Sebastian
  last_name: Pauli
citation:
  ama: Klüners J, Pauli S. Computing residue class rings and Picard groups of orders.
    <i>Journal of Algebra</i>. 2005;292(1):47-64. doi:<a href="https://doi.org/10.1016/j.jalgebra.2005.04.013">10.1016/j.jalgebra.2005.04.013</a>
  apa: Klüners, J., &#38; Pauli, S. (2005). Computing residue class rings and Picard
    groups of orders. <i>Journal of Algebra</i>, <i>292</i>(1), 47–64. <a href="https://doi.org/10.1016/j.jalgebra.2005.04.013">https://doi.org/10.1016/j.jalgebra.2005.04.013</a>
  bibtex: '@article{Klüners_Pauli_2005, title={Computing residue class rings and Picard
    groups of orders}, volume={292}, DOI={<a href="https://doi.org/10.1016/j.jalgebra.2005.04.013">10.1016/j.jalgebra.2005.04.013</a>},
    number={1}, journal={Journal of Algebra}, publisher={Elsevier BV}, author={Klüners,
    Jürgen and Pauli, Sebastian}, year={2005}, pages={47–64} }'
  chicago: 'Klüners, Jürgen, and Sebastian Pauli. “Computing Residue Class Rings and
    Picard Groups of Orders.” <i>Journal of Algebra</i> 292, no. 1 (2005): 47–64.
    <a href="https://doi.org/10.1016/j.jalgebra.2005.04.013">https://doi.org/10.1016/j.jalgebra.2005.04.013</a>.'
  ieee: 'J. Klüners and S. Pauli, “Computing residue class rings and Picard groups
    of orders,” <i>Journal of Algebra</i>, vol. 292, no. 1, pp. 47–64, 2005, doi:
    <a href="https://doi.org/10.1016/j.jalgebra.2005.04.013">10.1016/j.jalgebra.2005.04.013</a>.'
  mla: Klüners, Jürgen, and Sebastian Pauli. “Computing Residue Class Rings and Picard
    Groups of Orders.” <i>Journal of Algebra</i>, vol. 292, no. 1, Elsevier BV, 2005,
    pp. 47–64, doi:<a href="https://doi.org/10.1016/j.jalgebra.2005.04.013">10.1016/j.jalgebra.2005.04.013</a>.
  short: J. Klüners, S. Pauli, Journal of Algebra 292 (2005) 47–64.
date_created: 2022-12-23T09:41:06Z
date_updated: 2023-03-06T09:55:09Z
department:
- _id: '102'
doi: 10.1016/j.jalgebra.2005.04.013
intvolume: '       292'
issue: '1'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 47-64
publication: Journal of Algebra
publication_identifier:
  issn:
  - 0021-8693
publication_status: published
publisher: Elsevier BV
status: public
title: Computing residue class rings and Picard groups of orders
type: journal_article
user_id: '93826'
volume: 292
year: '2005'
...
---
_id: '34896'
abstract:
- lang: eng
  text: We apply class field theory to the computation of the minimal discriminants
    for certain solvable groups. In particular, we apply our techniques to small Frobenius
    groups and all imprimitive degree 8 groups such that the corresponding fields
    have only a degree 2 and no degree 4 subfield.
author:
- first_name: Claus
  full_name: Fieker, Claus
  last_name: Fieker
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Fieker C, Klüners J. Minimal discriminants for fields with small Frobenius
    groups as Galois groups. <i>Journal of Number Theory</i>. 2003;99(2):318-337.
    doi:<a href="https://doi.org/10.1016/s0022-314x(02)00071-9">10.1016/s0022-314x(02)00071-9</a>
  apa: Fieker, C., &#38; Klüners, J. (2003). Minimal discriminants for fields with
    small Frobenius groups as Galois groups. <i>Journal of Number Theory</i>, <i>99</i>(2),
    318–337. <a href="https://doi.org/10.1016/s0022-314x(02)00071-9">https://doi.org/10.1016/s0022-314x(02)00071-9</a>
  bibtex: '@article{Fieker_Klüners_2003, title={Minimal discriminants for fields with
    small Frobenius groups as Galois groups}, volume={99}, DOI={<a href="https://doi.org/10.1016/s0022-314x(02)00071-9">10.1016/s0022-314x(02)00071-9</a>},
    number={2}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Fieker,
    Claus and Klüners, Jürgen}, year={2003}, pages={318–337} }'
  chicago: 'Fieker, Claus, and Jürgen Klüners. “Minimal Discriminants for Fields with
    Small Frobenius Groups as Galois Groups.” <i>Journal of Number Theory</i> 99,
    no. 2 (2003): 318–37. <a href="https://doi.org/10.1016/s0022-314x(02)00071-9">https://doi.org/10.1016/s0022-314x(02)00071-9</a>.'
  ieee: 'C. Fieker and J. Klüners, “Minimal discriminants for fields with small Frobenius
    groups as Galois groups,” <i>Journal of Number Theory</i>, vol. 99, no. 2, pp.
    318–337, 2003, doi: <a href="https://doi.org/10.1016/s0022-314x(02)00071-9">10.1016/s0022-314x(02)00071-9</a>.'
  mla: Fieker, Claus, and Jürgen Klüners. “Minimal Discriminants for Fields with Small
    Frobenius Groups as Galois Groups.” <i>Journal of Number Theory</i>, vol. 99,
    no. 2, Elsevier BV, 2003, pp. 318–37, doi:<a href="https://doi.org/10.1016/s0022-314x(02)00071-9">10.1016/s0022-314x(02)00071-9</a>.
  short: C. Fieker, J. Klüners, Journal of Number Theory 99 (2003) 318–337.
date_created: 2022-12-23T09:53:23Z
date_updated: 2023-03-06T09:19:16Z
department:
- _id: '102'
doi: 10.1016/s0022-314x(02)00071-9
intvolume: '        99'
issue: '2'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 318-337
publication: Journal of Number Theory
publication_identifier:
  issn:
  - 0022-314X
publication_status: published
publisher: Elsevier BV
status: public
title: Minimal discriminants for fields with small Frobenius groups as Galois groups
type: journal_article
user_id: '93826'
volume: 99
year: '2003'
...
---
_id: '39421'
abstract:
- lang: eng
  text: We present a rigorous but transparent semantics definition of SystemC that
    covers method, thread, and clocked thread behavior as well as their interaction
    with the simulation kernel process. The semantics includes watching statements,
    signal assignment, and wait statements as they are introduced in SystemC V1.O.
    We present our definition in form of distributed Abstract State Machines (ASMs)
    rules reflecting the view given in the SystemC User's Manual and the reference
    implementation. We mainly see our formal semantics as a concise, unambiguous,
    high-level specification for SystemC-based implementations and for standardization.
    Additionally, it can be used as a sound basis to investigate SystemC interoperability
    with Verilog and VHDL.
author:
- first_name: Wolfgang
  full_name: Müller, Wolfgang
  id: '16243'
  last_name: Müller
- first_name: Jürgen
  full_name: Ruf, Jürgen
  last_name: Ruf
- first_name: D. W.
  full_name: Hoffmann, D. W.
  last_name: Hoffmann
- first_name: Joachim
  full_name: Gerlach, Joachim
  last_name: Gerlach
- first_name: Thomas
  full_name: Kropf, Thomas
  last_name: Kropf
- first_name: W.
  full_name: Rosenstiehl, W.
  last_name: Rosenstiehl
citation:
  ama: 'Müller W, Ruf J, Hoffmann DW, Gerlach J, Kropf T, Rosenstiehl W. The Simulation
    Semantics of SystemC. In: <i>Proceedings of the Design, Automation, and Test in
    Europe (DATE’01)</i>. IEEE; 2001. doi:<a href="https://doi.org/10.1109/DATE.2001.915002">10.1109/DATE.2001.915002</a>'
  apa: Müller, W., Ruf, J., Hoffmann, D. W., Gerlach, J., Kropf, T., &#38; Rosenstiehl,
    W. (2001). The Simulation Semantics of SystemC. <i>Proceedings of the Design,
    Automation, and Test in Europe (DATE’01)</i>.  Proceedings Design, Automation
    and Test in Europe. Conference and Exhibition 2001. <a href="https://doi.org/10.1109/DATE.2001.915002">https://doi.org/10.1109/DATE.2001.915002</a>
  bibtex: '@inproceedings{Müller_Ruf_Hoffmann_Gerlach_Kropf_Rosenstiehl_2001, place={Munich,
    Germany }, title={The Simulation Semantics of SystemC}, DOI={<a href="https://doi.org/10.1109/DATE.2001.915002">10.1109/DATE.2001.915002</a>},
    booktitle={Proceedings of the Design, Automation, and Test in Europe (DATE’01)},
    publisher={IEEE}, author={Müller, Wolfgang and Ruf, Jürgen and Hoffmann, D. W.
    and Gerlach, Joachim and Kropf, Thomas and Rosenstiehl, W.}, year={2001} }'
  chicago: 'Müller, Wolfgang, Jürgen Ruf, D. W. Hoffmann, Joachim Gerlach, Thomas
    Kropf, and W. Rosenstiehl. “The Simulation Semantics of SystemC.” In <i>Proceedings
    of the Design, Automation, and Test in Europe (DATE’01)</i>. Munich, Germany :
    IEEE, 2001. <a href="https://doi.org/10.1109/DATE.2001.915002">https://doi.org/10.1109/DATE.2001.915002</a>.'
  ieee: 'W. Müller, J. Ruf, D. W. Hoffmann, J. Gerlach, T. Kropf, and W. Rosenstiehl,
    “The Simulation Semantics of SystemC,” presented at the  Proceedings Design, Automation
    and Test in Europe. Conference and Exhibition 2001, 2001, doi: <a href="https://doi.org/10.1109/DATE.2001.915002">10.1109/DATE.2001.915002</a>.'
  mla: Müller, Wolfgang, et al. “The Simulation Semantics of SystemC.” <i>Proceedings
    of the Design, Automation, and Test in Europe (DATE’01)</i>, IEEE, 2001, doi:<a
    href="https://doi.org/10.1109/DATE.2001.915002">10.1109/DATE.2001.915002</a>.
  short: 'W. Müller, J. Ruf, D.W. Hoffmann, J. Gerlach, T. Kropf, W. Rosenstiehl,
    in: Proceedings of the Design, Automation, and Test in Europe (DATE’01), IEEE,
    Munich, Germany , 2001.'
conference:
  name: ' Proceedings Design, Automation and Test in Europe. Conference and Exhibition
    2001'
date_created: 2023-01-24T10:39:33Z
date_updated: 2023-01-24T10:39:38Z
department:
- _id: '672'
doi: 10.1109/DATE.2001.915002
keyword:
- Yarn
- Formal verification
- Kernel
- Hardware design languages
- Electronic design automation and methodology
- Algebra
- Computational modeling
- Logic functions
- Computer languages
- Clocks
language:
- iso: eng
place: 'Munich, Germany '
publication: Proceedings of the Design, Automation, and Test in Europe (DATE’01)
publication_identifier:
  isbn:
  - 0-7695-0993-2
publisher: IEEE
status: public
title: The Simulation Semantics of SystemC
type: conference
user_id: '5786'
year: '2001'
...
---
_id: '34900'
abstract:
- lang: eng
  text: We describe methods for the computation of Galois groups of univariate polynomials
    over the rationals which we have implemented up to degree 15. These methods are
    based on Stauduhar’s algorithm. All computations are done in unramified p -adic
    extensions. For imprimitive groups we give an improvement using subfields. In
    the primitive case we use known subgroups of the Galois group together with a
    combination of Stauduhar’s method and the absolute resolvent method.
author:
- first_name: Katharina
  full_name: Geissler, Katharina
  last_name: Geissler
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Geissler K, Klüners J. Galois Group Computation for Rational Polynomials. <i>Journal
    of Symbolic Computation</i>. 2000;30(6):653-674. doi:<a href="https://doi.org/10.1006/jsco.2000.0377">10.1006/jsco.2000.0377</a>
  apa: Geissler, K., &#38; Klüners, J. (2000). Galois Group Computation for Rational
    Polynomials. <i>Journal of Symbolic Computation</i>, <i>30</i>(6), 653–674. <a
    href="https://doi.org/10.1006/jsco.2000.0377">https://doi.org/10.1006/jsco.2000.0377</a>
  bibtex: '@article{Geissler_Klüners_2000, title={Galois Group Computation for Rational
    Polynomials}, volume={30}, DOI={<a href="https://doi.org/10.1006/jsco.2000.0377">10.1006/jsco.2000.0377</a>},
    number={6}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV},
    author={Geissler, Katharina and Klüners, Jürgen}, year={2000}, pages={653–674}
    }'
  chicago: 'Geissler, Katharina, and Jürgen Klüners. “Galois Group Computation for
    Rational Polynomials.” <i>Journal of Symbolic Computation</i> 30, no. 6 (2000):
    653–74. <a href="https://doi.org/10.1006/jsco.2000.0377">https://doi.org/10.1006/jsco.2000.0377</a>.'
  ieee: 'K. Geissler and J. Klüners, “Galois Group Computation for Rational Polynomials,”
    <i>Journal of Symbolic Computation</i>, vol. 30, no. 6, pp. 653–674, 2000, doi:
    <a href="https://doi.org/10.1006/jsco.2000.0377">10.1006/jsco.2000.0377</a>.'
  mla: Geissler, Katharina, and Jürgen Klüners. “Galois Group Computation for Rational
    Polynomials.” <i>Journal of Symbolic Computation</i>, vol. 30, no. 6, Elsevier
    BV, 2000, pp. 653–74, doi:<a href="https://doi.org/10.1006/jsco.2000.0377">10.1006/jsco.2000.0377</a>.
  short: K. Geissler, J. Klüners, Journal of Symbolic Computation 30 (2000) 653–674.
date_created: 2022-12-23T09:58:16Z
date_updated: 2023-03-06T09:58:06Z
department:
- _id: '102'
doi: 10.1006/jsco.2000.0377
intvolume: '        30'
issue: '6'
keyword:
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 653-674
publication: Journal of Symbolic Computation
publication_identifier:
  issn:
  - 0747-7171
publication_status: published
publisher: Elsevier BV
status: public
title: Galois Group Computation for Rational Polynomials
type: journal_article
user_id: '93826'
volume: 30
year: '2000'
...
---
_id: '34901'
abstract:
- lang: eng
  text: Let L = K(α) be an Abelian extension of degree n of a number field K, given
    by the minimal polynomial of α over K. We describe an algorithm for computing
    the local Artin map associated with the extension L / K at a finite or infinite
    prime v of K. We apply this algorithm to decide if a nonzero a ∈ K is a norm from
    L, assuming that L / K is cyclic.
author:
- first_name: Vincenzo
  full_name: Acciaro, Vincenzo
  last_name: Acciaro
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Acciaro V, Klüners J. Computing Local Artin Maps, and Solvability of Norm Equations.
    <i>Journal of Symbolic Computation</i>. 2000;30(3):239-252. doi:<a href="https://doi.org/10.1006/jsco.2000.0361">10.1006/jsco.2000.0361</a>
  apa: Acciaro, V., &#38; Klüners, J. (2000). Computing Local Artin Maps, and Solvability
    of Norm Equations. <i>Journal of Symbolic Computation</i>, <i>30</i>(3), 239–252.
    <a href="https://doi.org/10.1006/jsco.2000.0361">https://doi.org/10.1006/jsco.2000.0361</a>
  bibtex: '@article{Acciaro_Klüners_2000, title={Computing Local Artin Maps, and Solvability
    of Norm Equations}, volume={30}, DOI={<a href="https://doi.org/10.1006/jsco.2000.0361">10.1006/jsco.2000.0361</a>},
    number={3}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV},
    author={Acciaro, Vincenzo and Klüners, Jürgen}, year={2000}, pages={239–252} }'
  chicago: 'Acciaro, Vincenzo, and Jürgen Klüners. “Computing Local Artin Maps, and
    Solvability of Norm Equations.” <i>Journal of Symbolic Computation</i> 30, no.
    3 (2000): 239–52. <a href="https://doi.org/10.1006/jsco.2000.0361">https://doi.org/10.1006/jsco.2000.0361</a>.'
  ieee: 'V. Acciaro and J. Klüners, “Computing Local Artin Maps, and Solvability of
    Norm Equations,” <i>Journal of Symbolic Computation</i>, vol. 30, no. 3, pp. 239–252,
    2000, doi: <a href="https://doi.org/10.1006/jsco.2000.0361">10.1006/jsco.2000.0361</a>.'
  mla: Acciaro, Vincenzo, and Jürgen Klüners. “Computing Local Artin Maps, and Solvability
    of Norm Equations.” <i>Journal of Symbolic Computation</i>, vol. 30, no. 3, Elsevier
    BV, 2000, pp. 239–52, doi:<a href="https://doi.org/10.1006/jsco.2000.0361">10.1006/jsco.2000.0361</a>.
  short: V. Acciaro, J. Klüners, Journal of Symbolic Computation 30 (2000) 239–252.
date_created: 2022-12-23T09:58:48Z
date_updated: 2023-03-06T09:57:34Z
department:
- _id: '102'
doi: 10.1006/jsco.2000.0361
intvolume: '        30'
issue: '3'
keyword:
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 239-252
publication: Journal of Symbolic Computation
publication_identifier:
  issn:
  - 0747-7171
publication_status: published
publisher: Elsevier BV
status: public
title: Computing Local Artin Maps, and Solvability of Norm Equations
type: journal_article
user_id: '93826'
volume: 30
year: '2000'
...
---
_id: '34899'
abstract:
- lang: eng
  text: We describe methods for the construction of polynomials with certain types
    of Galois groups. As an application we deduce that all transitive groups G up
    to degree 15 occur as Galois groups of regular extensions of ℚ (t), and in each
    case compute a polynomial f ∈ ℚ [ x ] with Gal(f)  = G.
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Gunter
  full_name: Malle, Gunter
  last_name: Malle
citation:
  ama: Klüners J, Malle G. Explicit Galois Realization of Transitive Groups of Degree
    up to 15. <i>Journal of Symbolic Computation</i>. 2000;30(6):675-716. doi:<a href="https://doi.org/10.1006/jsco.2000.0378">10.1006/jsco.2000.0378</a>
  apa: Klüners, J., &#38; Malle, G. (2000). Explicit Galois Realization of Transitive
    Groups of Degree up to 15. <i>Journal of Symbolic Computation</i>, <i>30</i>(6),
    675–716. <a href="https://doi.org/10.1006/jsco.2000.0378">https://doi.org/10.1006/jsco.2000.0378</a>
  bibtex: '@article{Klüners_Malle_2000, title={Explicit Galois Realization of Transitive
    Groups of Degree up to 15}, volume={30}, DOI={<a href="https://doi.org/10.1006/jsco.2000.0378">10.1006/jsco.2000.0378</a>},
    number={6}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV},
    author={Klüners, Jürgen and Malle, Gunter}, year={2000}, pages={675–716} }'
  chicago: 'Klüners, Jürgen, and Gunter Malle. “Explicit Galois Realization of Transitive
    Groups of Degree up to 15.” <i>Journal of Symbolic Computation</i> 30, no. 6 (2000):
    675–716. <a href="https://doi.org/10.1006/jsco.2000.0378">https://doi.org/10.1006/jsco.2000.0378</a>.'
  ieee: 'J. Klüners and G. Malle, “Explicit Galois Realization of Transitive Groups
    of Degree up to 15,” <i>Journal of Symbolic Computation</i>, vol. 30, no. 6, pp.
    675–716, 2000, doi: <a href="https://doi.org/10.1006/jsco.2000.0378">10.1006/jsco.2000.0378</a>.'
  mla: Klüners, Jürgen, and Gunter Malle. “Explicit Galois Realization of Transitive
    Groups of Degree up to 15.” <i>Journal of Symbolic Computation</i>, vol. 30, no.
    6, Elsevier BV, 2000, pp. 675–716, doi:<a href="https://doi.org/10.1006/jsco.2000.0378">10.1006/jsco.2000.0378</a>.
  short: J. Klüners, G. Malle, Journal of Symbolic Computation 30 (2000) 675–716.
date_created: 2022-12-23T09:57:28Z
date_updated: 2023-03-06T10:48:05Z
department:
- _id: '102'
doi: 10.1006/jsco.2000.0378
intvolume: '        30'
issue: '6'
keyword:
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 675-716
publication: Journal of Symbolic Computation
publication_identifier:
  issn:
  - 0747-7171
publication_status: published
publisher: Elsevier BV
status: public
title: Explicit Galois Realization of Transitive Groups of Degree up to 15
type: journal_article
user_id: '93826'
volume: 30
year: '2000'
...
---
_id: '34898'
abstract:
- lang: eng
  text: We compute a polynomial with Galois group SL₂(11) over ℚ. Furthermore we prove
    that SL₂(11) is the Galois group of a regular extension of ℚ (t).
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Klüners J. A Polynomial with Galois GroupSL2(11). <i>Journal of Symbolic Computation</i>.
    2000;30(6):733-737. doi:<a href="https://doi.org/10.1006/jsco.2000.0380">10.1006/jsco.2000.0380</a>
  apa: Klüners, J. (2000). A Polynomial with Galois GroupSL2(11). <i>Journal of Symbolic
    Computation</i>, <i>30</i>(6), 733–737. <a href="https://doi.org/10.1006/jsco.2000.0380">https://doi.org/10.1006/jsco.2000.0380</a>
  bibtex: '@article{Klüners_2000, title={A Polynomial with Galois GroupSL2(11)}, volume={30},
    DOI={<a href="https://doi.org/10.1006/jsco.2000.0380">10.1006/jsco.2000.0380</a>},
    number={6}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV},
    author={Klüners, Jürgen}, year={2000}, pages={733–737} }'
  chicago: 'Klüners, Jürgen. “A Polynomial with Galois GroupSL2(11).” <i>Journal of
    Symbolic Computation</i> 30, no. 6 (2000): 733–37. <a href="https://doi.org/10.1006/jsco.2000.0380">https://doi.org/10.1006/jsco.2000.0380</a>.'
  ieee: 'J. Klüners, “A Polynomial with Galois GroupSL2(11),” <i>Journal of Symbolic
    Computation</i>, vol. 30, no. 6, pp. 733–737, 2000, doi: <a href="https://doi.org/10.1006/jsco.2000.0380">10.1006/jsco.2000.0380</a>.'
  mla: Klüners, Jürgen. “A Polynomial with Galois GroupSL2(11).” <i>Journal of Symbolic
    Computation</i>, vol. 30, no. 6, Elsevier BV, 2000, pp. 733–37, doi:<a href="https://doi.org/10.1006/jsco.2000.0380">10.1006/jsco.2000.0380</a>.
  short: J. Klüners, Journal of Symbolic Computation 30 (2000) 733–737.
date_created: 2022-12-23T09:56:52Z
date_updated: 2023-03-06T10:48:40Z
department:
- _id: '102'
doi: 10.1006/jsco.2000.0380
intvolume: '        30'
issue: '6'
keyword:
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 733-737
publication: Journal of Symbolic Computation
publication_identifier:
  issn:
  - 0747-7171
publication_status: published
publisher: Elsevier BV
status: public
title: A Polynomial with Galois GroupSL2(11)
type: journal_article
user_id: '93826'
volume: 30
year: '2000'
...
---
_id: '34902'
abstract:
- lang: eng
  text: We present a new polynomial decomposition which generalizes the functional
    and homogeneous bivariate decomposition of irreducible monic polynomials in one
    variable over the rationals. With these decompositions it is possible to calculate
    the roots of an imprimitive polynomial by solving polynomial equations of lower
    degree.
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Klüners J. On Polynomial Decompositions. <i>Journal of Symbolic Computation</i>.
    1999;27(3):261-269. doi:<a href="https://doi.org/10.1006/jsco.1998.0252">10.1006/jsco.1998.0252</a>
  apa: Klüners, J. (1999). On Polynomial Decompositions. <i>Journal of Symbolic Computation</i>,
    <i>27</i>(3), 261–269. <a href="https://doi.org/10.1006/jsco.1998.0252">https://doi.org/10.1006/jsco.1998.0252</a>
  bibtex: '@article{Klüners_1999, title={On Polynomial Decompositions}, volume={27},
    DOI={<a href="https://doi.org/10.1006/jsco.1998.0252">10.1006/jsco.1998.0252</a>},
    number={3}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV},
    author={Klüners, Jürgen}, year={1999}, pages={261–269} }'
  chicago: 'Klüners, Jürgen. “On Polynomial Decompositions.” <i>Journal of Symbolic
    Computation</i> 27, no. 3 (1999): 261–69. <a href="https://doi.org/10.1006/jsco.1998.0252">https://doi.org/10.1006/jsco.1998.0252</a>.'
  ieee: 'J. Klüners, “On Polynomial Decompositions,” <i>Journal of Symbolic Computation</i>,
    vol. 27, no. 3, pp. 261–269, 1999, doi: <a href="https://doi.org/10.1006/jsco.1998.0252">10.1006/jsco.1998.0252</a>.'
  mla: Klüners, Jürgen. “On Polynomial Decompositions.” <i>Journal of Symbolic Computation</i>,
    vol. 27, no. 3, Elsevier BV, 1999, pp. 261–69, doi:<a href="https://doi.org/10.1006/jsco.1998.0252">10.1006/jsco.1998.0252</a>.
  short: J. Klüners, Journal of Symbolic Computation 27 (1999) 261–269.
date_created: 2022-12-23T10:01:15Z
date_updated: 2023-03-06T09:21:29Z
department:
- _id: '102'
doi: 10.1006/jsco.1998.0252
intvolume: '        27'
issue: '3'
keyword:
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 261-269
publication: Journal of Symbolic Computation
publication_identifier:
  issn:
  - 0747-7171
publication_status: published
publisher: Elsevier BV
status: public
title: On Polynomial Decompositions
type: journal_article
user_id: '93826'
volume: 27
year: '1999'
...
---
_id: '34903'
abstract:
- lang: eng
  text: The software packageKANT V4for computations in algebraic number fields is
    now available in version 4. In addition a new user interface has been released.
    We will outline the features of this new software package.
author:
- first_name: M.
  full_name: DABERKOW, M.
  last_name: DABERKOW
- first_name: C.
  full_name: FIEKER, C.
  last_name: FIEKER
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: M.
  full_name: POHST, M.
  last_name: POHST
- first_name: K.
  full_name: ROEGNER, K.
  last_name: ROEGNER
- first_name: M.
  full_name: SCHÖRNIG, M.
  last_name: SCHÖRNIG
- first_name: K.
  full_name: WILDANGER, K.
  last_name: WILDANGER
citation:
  ama: DABERKOW M, FIEKER C, Klüners J, et al. KANT V4. <i>Journal of Symbolic Computation</i>.
    1997;24(3-4):267-283. doi:<a href="https://doi.org/10.1006/jsco.1996.0126">10.1006/jsco.1996.0126</a>
  apa: DABERKOW, M., FIEKER, C., Klüners, J., POHST, M., ROEGNER, K., SCHÖRNIG, M.,
    &#38; WILDANGER, K. (1997). KANT V4. <i>Journal of Symbolic Computation</i>, <i>24</i>(3–4),
    267–283. <a href="https://doi.org/10.1006/jsco.1996.0126">https://doi.org/10.1006/jsco.1996.0126</a>
  bibtex: '@article{DABERKOW_FIEKER_Klüners_POHST_ROEGNER_SCHÖRNIG_WILDANGER_1997,
    title={KANT V4}, volume={24}, DOI={<a href="https://doi.org/10.1006/jsco.1996.0126">10.1006/jsco.1996.0126</a>},
    number={3–4}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV},
    author={DABERKOW, M. and FIEKER, C. and Klüners, Jürgen and POHST, M. and ROEGNER,
    K. and SCHÖRNIG, M. and WILDANGER, K.}, year={1997}, pages={267–283} }'
  chicago: 'DABERKOW, M., C. FIEKER, Jürgen Klüners, M. POHST, K. ROEGNER, M. SCHÖRNIG,
    and K. WILDANGER. “KANT V4.” <i>Journal of Symbolic Computation</i> 24, no. 3–4
    (1997): 267–83. <a href="https://doi.org/10.1006/jsco.1996.0126">https://doi.org/10.1006/jsco.1996.0126</a>.'
  ieee: 'M. DABERKOW <i>et al.</i>, “KANT V4,” <i>Journal of Symbolic Computation</i>,
    vol. 24, no. 3–4, pp. 267–283, 1997, doi: <a href="https://doi.org/10.1006/jsco.1996.0126">10.1006/jsco.1996.0126</a>.'
  mla: DABERKOW, M., et al. “KANT V4.” <i>Journal of Symbolic Computation</i>, vol.
    24, no. 3–4, Elsevier BV, 1997, pp. 267–83, doi:<a href="https://doi.org/10.1006/jsco.1996.0126">10.1006/jsco.1996.0126</a>.
  short: M. DABERKOW, C. FIEKER, J. Klüners, M. POHST, K. ROEGNER, M. SCHÖRNIG, K.
    WILDANGER, Journal of Symbolic Computation 24 (1997) 267–283.
date_created: 2022-12-23T10:02:24Z
date_updated: 2023-03-06T09:23:30Z
ddc:
- '000'
department:
- _id: '102'
doi: 10.1006/jsco.1996.0126
has_accepted_license: '1'
intvolume: '        24'
issue: 3-4
keyword:
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 267-283
publication: Journal of Symbolic Computation
publication_identifier:
  issn:
  - 0747-7171
publication_status: published
publisher: Elsevier BV
status: public
title: KANT V4
type: journal_article
user_id: '93826'
volume: 24
year: '1997'
...
---
_id: '34904'
abstract:
- lang: eng
  text: The purpose of this article is to determine all subfields ℚ(β) of fixed degree
    of a given algebraic number field ℚ(α). It is convenient to describe each subfield
    by a pair (h,g) of polynomials in ℚ[t] resp. Z[t] such thatgis the minimal polynomial
    of β = h(α). The computations are done in unramifiedp-adic extensions and use
    information concerning subgroups of the Galois group of the normal closure of
    ℚ(α) obtained from the van der Waerden criterion.
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Michael
  full_name: Pohst, Michael
  last_name: Pohst
citation:
  ama: Klüners J, Pohst M. On Computing Subfields. <i>Journal of Symbolic Computation</i>.
    1997;24(3-4):385-397. doi:<a href="https://doi.org/10.1006/jsco.1996.0140">10.1006/jsco.1996.0140</a>
  apa: Klüners, J., &#38; Pohst, M. (1997). On Computing Subfields. <i>Journal of
    Symbolic Computation</i>, <i>24</i>(3–4), 385–397. <a href="https://doi.org/10.1006/jsco.1996.0140">https://doi.org/10.1006/jsco.1996.0140</a>
  bibtex: '@article{Klüners_Pohst_1997, title={On Computing Subfields}, volume={24},
    DOI={<a href="https://doi.org/10.1006/jsco.1996.0140">10.1006/jsco.1996.0140</a>},
    number={3–4}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV},
    author={Klüners, Jürgen and Pohst, Michael}, year={1997}, pages={385–397} }'
  chicago: 'Klüners, Jürgen, and Michael Pohst. “On Computing Subfields.” <i>Journal
    of Symbolic Computation</i> 24, no. 3–4 (1997): 385–97. <a href="https://doi.org/10.1006/jsco.1996.0140">https://doi.org/10.1006/jsco.1996.0140</a>.'
  ieee: 'J. Klüners and M. Pohst, “On Computing Subfields,” <i>Journal of Symbolic
    Computation</i>, vol. 24, no. 3–4, pp. 385–397, 1997, doi: <a href="https://doi.org/10.1006/jsco.1996.0140">10.1006/jsco.1996.0140</a>.'
  mla: Klüners, Jürgen, and Michael Pohst. “On Computing Subfields.” <i>Journal of
    Symbolic Computation</i>, vol. 24, no. 3–4, Elsevier BV, 1997, pp. 385–97, doi:<a
    href="https://doi.org/10.1006/jsco.1996.0140">10.1006/jsco.1996.0140</a>.
  short: J. Klüners, M. Pohst, Journal of Symbolic Computation 24 (1997) 385–397.
date_created: 2022-12-23T10:03:02Z
date_updated: 2023-03-06T10:36:21Z
ddc:
- '000'
department:
- _id: '102'
doi: 10.1006/jsco.1996.0140
has_accepted_license: '1'
intvolume: '        24'
issue: 3-4
keyword:
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 385-397
publication: Journal of Symbolic Computation
publication_identifier:
  issn:
  - 0747-7171
publication_status: published
publisher: Elsevier BV
status: public
title: On Computing Subfields
type: journal_article
user_id: '93826'
volume: 24
year: '1997'
...