<bibliography>
 <citation type="book" key="adams">
  <author>William W. <surname>Adams</surname></author>
  <author>Philippe <surname>Loustaunau</surname></author>
  <year>1994</year>
  <title>An Introduction to Gr&#246;bner Bases</title>
  <volume>3</volume>
  <publisher>American Mathematical Society</publisher>
  <doi>10.1090/gsm/003</doi>
 </citation>
 <citation type="article" key="APEL20051131">
  <author>Joachim <surname>Apel</surname></author>
  <author>Ralf <surname>Hemmecke</surname></author>
  <year>2005</year>
  <title>Detecting unnecessary reductions in an involutive basis computation</title>
  <journal>Journal of Symbolic Computation</journal>
  <volume>40</volume>
  <number>4</number>
  <pages>1131 &#8211; 1149</pages>
  <doi>10.1016/j.jsc.2004.04.004</doi>
  <note>Applications of Computer Algebra (ACA) 2001 and 2002</note>
 </citation>
 <citation type="book" key="becker1993grobner">
  <author>T. <surname>Becker</surname></author>
  <author>V. <surname>Weispfenning</surname></author>
  <author>H. <surname>Kredel</surname></author>
  <year>1993</year>
  <title>Gr&#246;bner bases: a computational approach to commutative algebra</title>
  <series>Graduate texts in mathematics</series>
  <publisher>Springer-Verlag</publisher>
  <doi>10.1007/978-1-4612-0913-3</doi>
 </citation>
 <citation type="inproceedings" key="Buchberger1979">
  <author>B. <surname>Buchberger</surname></author>
  <year>1979</year>
  <title>A criterion for detecting unnecessary reductions in the construction of Gr&#246;bner-bases</title>
  <editor>Edward W. <surname>Ng</surname></editor>
  <booktitle>Symbolic and Algebraic Computation</booktitle>
  <publisher>Springer Berlin Heidelberg</publisher>
  <address>Berlin, Heidelberg</address>
  <pages>3&#8211;21</pages>
  <doi>10.1007/3-540-09519-5_52</doi>
 </citation>
 <citation type="inbook" key="buchberger1985">
  <author>B. <surname>Buchberger</surname></author>
  <year>1985</year>
  <title>Multidimensional Systems Theory &#8211; Progress, Directions and Open Problems in Multidimensional Systems</title>
  <chapter>Gr&#246;bner Bases: An Algorithmic Method in Polynomial Ideal Theory</chapter>
  <pages>184&#8211;232</pages>
  <publisher>Reidel Publishing Company</publisher>
  <doi>10.1007/978-94-017-0275-1_4</doi>
 </citation>
 <citation type="book" key="buchberger1998">
  <author>B. <surname>Buchberger</surname></author>
  <year>1998</year>
  <title>Introduction to Gr&#246;bner Bases</title>
  <series>London Mathematical Society Lectures Notes Series 251</series>
  <publisher>Cambridge University Press</publisher>
  <doi>10.1017/CBO9780511565847</doi>
 </citation>
 <citation type="article" key="theorists">
  <author>Bruno <surname>Buchberger</surname></author>
  <year>2001</year>
  <title>Gr&#246;bner Bases: A Short Introduction for Systems Theorists</title>
  <journal>Research Institute for Symbolic Computation</journal>
  <volume>2178</volume>
  <doi>10.1007/3-540-45654-6_1</doi>
 </citation>
 <citation type="article" key="buchberger1965algorithm">
  <author>Bruno <surname>Buchberger</surname></author>
  <year>2006</year>
  <title>Bruno Buchbergers PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal</title>
  <journal>Journal of Symbolic Computation</journal>
  <volume>41</volume>
  <number>3</number>
  <pages>475 &#8211; 511</pages>
  <doi>10.1016/j.jsc.2005.09.007</doi>
  <note>Logic, Mathematics and Computer Science: Interactions in honor of Bruno Buchberger (60th birthday)</note>
 </citation>
 <citation type="article" key="BuchKauers">
  <author>Bruno <surname>Buchberger</surname></author>
  <author>Manuel <surname>Kauers</surname></author>
  <year>2010</year>
  <title>Gr&#246;bner Basis</title>
  <journal>Scholarpedia</journal>
  <volume>5</volume>
  <number>10</number>
  <doi>10.4249/scholarpedia.7763</doi>
 </citation>
 <citation type="book" key="cox">
  <author>Donal O'Shea <surname>David A. Cox</surname>, John Little</author>
  <year>2015</year>
  <title>Ideals, Varieties, and Algorithms</title>
  <edition>4th</edition>
  <publisher>Springer</publisher>
  <doi>10.1007/978-3-319-16721-3</doi>
 </citation>
 <citation type="article" key="FAUGEREF4">
  <author>Jean-Charles <surname>Faug&#232;re</surname></author>
  <year>1999</year>
  <title>A new efficient algorithm for computing Gr&#246;bner bases (F4)</title>
  <journal>Journal of Pure and Applied Algebra</journal>
  <volume>139</volume>
  <number>1</number>
  <pages>61 &#8211; 88</pages>
  <doi>10.1016/S0022-4049(99)00005-5</doi>
 </citation>
 <citation type="inproceedings" key="FaugereF5">
  <author>Jean Charles <surname>Faug&#232;re</surname></author>
  <year>2002</year>
  <title>A New Efficient Algorithm for Computing Gr&#246;bner Bases Without Reduction to Zero (F5)</title>
  <booktitle>Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation</booktitle>
  <series>ISSAC '02</series>
  <publisher>ACM</publisher>
  <address>New York, NY, USA</address>
  <pages>75&#8211;83</pages>
  <doi>10.1145/780506.780516</doi>
 </citation>
 <citation type="article" key="GERDT1998519">
  <author>Vladimir P. <surname>Gerdt</surname></author>
  <author>Yuri A. <surname>Blinkov</surname></author>
  <year>1998</year>
  <title>Involutive bases of polynomial ideals</title>
  <journal>Mathematics and Computers in Simulation</journal>
  <volume>45</volume>
  <number>5</number>
  <pages>519 &#8211; 541</pages>
  <doi>10.1016/S0378-4754(97)00127-4</doi>
 </citation>
 <citation type="inproceedings" key="Giovini1991">
  <author>Alessandro <surname>Giovini</surname></author>
  <author>Teo <surname>Mora</surname></author>
  <author>Gianfranco <surname>Niesi</surname></author>
  <author>Lorenzo <surname>Robbiano</surname></author>
  <author>Carlo <surname>Traverso</surname></author>
  <year>1991</year>
  <title>"One Sugar Cube, Please"; or Selection Strategies in the Buchberger Algorithm</title>
  <booktitle>Proceedings of the 1991 International Symposium on Symbolic and Algebraic Computation</booktitle>
  <series>ISSAC '91</series>
  <publisher>ACM</publisher>
  <address>New York, NY, USA</address>
  <pages>49&#8211;54</pages>
  <doi>10.1145/120694.120701</doi>
 </citation>
 <citation type="article" key="kredel">
  <author>Heinz <surname>Kredel</surname></author>
  <year>2010</year>
  <title>Parallel and distributed Gr&#246;bner bases computation in JAS</title>
  <journal>CoRR</journal>
  <volume>abs/1008.0011</volume>
 </citation>
 <citation type="article" key="MAYR1982">
  <author>Ernst W <surname>Mayr</surname></author>
  <author>Albert R <surname>Meyer</surname></author>
  <year>1982</year>
  <title>The complexity of the word problems for commutative semigroups and polynomial ideals</title>
  <journal>Advances in Mathematics</journal>
  <volume>46</volume>
  <number>3</number>
  <pages>305 &#8211; 329</pages>
  <doi>10.1016/0001-8708(82)90048-2</doi>
 </citation>
 <citation type="book" key="mora2003solving">
  <author>T. <surname>Mora</surname></author>
  <author>G.C. <surname>Rota</surname></author>
  <author>B. <surname>Doran</surname></author>
  <year>2003</year>
  <title>Solving Polynomial Equation Systems II: Macaulay's Paradigm and Gr&#246;bner Technology</title>
  <series>Encyclopedia of Mathematics and its Applications</series>
  <publisher>Cambridge University Press</publisher>
  <doi>10.1017/CBO9781107340954</doi>
 </citation>
</bibliography>
