QuillenSuslin

QuillenSuslin is a Maple implementation of a constructive version of the Quillen-Suslin Theorem. It provides an algorithm which computes a basis of a free module over a polynomial ring. In terms of matrices, this algorithm completes a unimodular rectangular matrix (e.g. a unimodular row) to an invertible matrix over the given polynomial ring with rational or integer coefficients. The package was also extended with Park’s Algorithm to deal with unimodular rows over Laurent polynomial rings and with heuristic methods for localizations of polynomial rings.


References in zbMATH (referenced in 13 articles )

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  1. Lu, Dong; Wang, Dingkang; Xiao, Fanghui: Factorizations for a class of multivariate polynomial matrices (2020)
  2. Barthel, Tobias (ed.); Krause, Henning (ed.); Stojanoska, Vesna (ed.): Mini-workshop: Chromatic phenomena and duality in homotopy theory and representation theory. Abstracts from the mini-workshop held March 4--10, 2018 (2018)
  3. Feragen, Aasa (ed.); Hotz, Thomas (ed.); Huckemann, Stephan (ed.); Miller, Ezra (ed.): Statistics for data with geometric structure. Abstracts from the workshop held January 21--27, 2018 (2018)
  4. Grip, N.; Pfander, G. E.: Efficient analysis of OFDM channels (2017)
  5. Lu, Dong; Ma, Xiaodong; Wang, Dingkang: A new algorithm for general factorizations of multivariate polynomial matrices (2017)
  6. Monceur, Samiha; Yengui, Ihsen: Suslin’s lemma for rings containing an infinite field (2017)
  7. Jambor, Sebastian: An (L_2)-quotient algorithm for finitely presented groups on arbitrarily many generators. (2015)
  8. Robertz, Daniel: Recent progress in an algebraic analysis approach to linear systems (2015)
  9. Barwick, Brett; Stone, Branden: Computing free bases for projective modules (2013)
  10. Brett Barwick, Branden Stone: The QuillenSuslin Package for Macaulay2 (2011) arXiv
  11. Jambor, Sebastian: Computing minimal associated primes in polynomial rings over the integers (2011)
  12. Barakat, Mohamed; Robertz, Daniel: \texttthomalg: a meta-package for homological algebra (2008)
  13. Fabiańska, Anna; Quadrat, Alban: Applications of the Quillen-Suslin theorem to multidimensional systems theory (2007)