{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T15:25:56Z","timestamp":1777994756394,"version":"3.51.4"},"publisher-location":"Cham","reference-count":15,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031645280","type":"print"},{"value":"9783031645297","type":"electronic"}],"license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024]]},"DOI":"10.1007\/978-3-031-64529-7_17","type":"book-chapter","created":{"date-parts":[[2024,7,16]],"date-time":"2024-07-16T15:21:35Z","timestamp":1721143295000},"page":"155-164","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A SageMath Package for\u00a0Elementary and\u00a0Sign Vectors with\u00a0Applications to\u00a0Chemical Reaction Networks"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-8362-2644","authenticated-orcid":false,"given":"Marcus S.","family":"Aichmayr","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3541-7856","authenticated-orcid":false,"given":"Stefan","family":"M\u00fcller","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7735-3726","authenticated-orcid":false,"given":"Georg","family":"Regensburger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,17]]},"reference":[{"key":"17_CR1","unstructured":"Aichmayr, M.S.: elementary_vectors. https:\/\/github.com\/MarcusAichmayr\/elementary_vectors"},{"key":"17_CR2","unstructured":"Aichmayr, M.S.: sign_vector_conditions. https:\/\/github.com\/MarcusAichmayr\/sign_vector_conditions"},{"key":"17_CR3","unstructured":"Aichmayr, M.S., Regensburger, G.: How to certify solvability of linear inequality systems with elementary vectors (2024, in preparation)"},{"key":"17_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-58152-6","volume-title":"Linear Programming Duality: An Introduction to Oriented Matroids","author":"A Bachem","year":"1992","unstructured":"Bachem, A., Kern, W.: Linear Programming Duality: An Introduction to Oriented Matroids. Springer-Verlag, Berlin (1992). https:\/\/doi.org\/10.1007\/978-3-642-58152-6"},{"key":"17_CR5","doi-asserted-by":"publisher","unstructured":"Bj\u00f6rner, A., Las\u00a0Vergnas, M., Sturmfels, B., White, N., Ziegler, G.: Oriented Matroids, 2nd edn. Cambridge University Press, Cambridge (1999). https:\/\/doi.org\/10.1017\/CBO9780511586507","DOI":"10.1017\/CBO9780511586507"},{"key":"17_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/S0895479892230067","volume":"16","author":"RA Brualdi","year":"1995","unstructured":"Brualdi, R.A., Friedland, S., Pothen, A.: The sparse basis problem and multilinear algebra. SIAM J. Matrix Anal. Appl. 16, 1\u201320 (1995)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"17_CR7","doi-asserted-by":"publisher","first-page":"368","DOI":"10.1007\/BF01585531","volume":"7","author":"GJ Minty","year":"1974","unstructured":"Minty, G.J.: A \u2018from scratch\u2019 proof of a theorem of Rockafellar and Fulkerson. Math. Program. 7, 368\u2013375 (1974)","journal-title":"Math. Program."},{"key":"17_CR8","doi-asserted-by":"publisher","unstructured":"M\u00fcller, S., Feliu, E., Regensburger, G., Conradi, C., Shiu, A., Dickenstein, A.: Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry. Found. Comput. Math. 16, 69\u201397 (2016). https:\/\/doi.org\/10.1007\/s10208-014-9239-3","DOI":"10.1007\/s10208-014-9239-3"},{"key":"17_CR9","doi-asserted-by":"publisher","first-page":"412","DOI":"10.1137\/18M1178153","volume":"3","author":"S M\u00fcller","year":"2019","unstructured":"M\u00fcller, S., Hofbauer, J., Regensburger, G.: On the bijectivity of families of exponential\/generalized polynomial maps. SIAM J. Appl. Algebra Geom. 3, 412\u2013438 (2019). https:\/\/doi.org\/10.1137\/18M1178153","journal-title":"SIAM J. Appl. Algebra Geom."},{"key":"17_CR10","doi-asserted-by":"publisher","first-page":"1926","DOI":"10.1137\/110847056","volume":"72","author":"S M\u00fcller","year":"2012","unstructured":"M\u00fcller, S., Regensburger, G.: Generalized mass action systems: complex balancing equilibria and sign vectors of the stoichiometric and kinetic-order subspaces. SIAM J. Appl. Math. 72, 1926\u20131947 (2012). https:\/\/doi.org\/10.1137\/110847056","journal-title":"SIAM J. Appl. Math."},{"key":"17_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1007\/978-3-319-10515-4_22","volume-title":"Computer Algebra in Scientific Computing","author":"S M\u00fcller","year":"2014","unstructured":"M\u00fcller, S., Regensburger, G.: Generalized mass-action systems and positive solutions of polynomial equations with real and symbolic exponents (invited talk). In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds.) CASC 2014. LNCS, vol. 8660, pp. 302\u2013323. Springer, Cham (2014). https:\/\/doi.org\/10.1007\/978-3-319-10515-4_22"},{"key":"17_CR12","unstructured":"Richter-Gebert, J., Ziegler, G.M.: Oriented matroids. In: Handbook of Discrete and Computational Geometry, pp. 111\u2013132. CRC Press, Boca Raton, FL (1997)"},{"key":"17_CR13","unstructured":"Rockafellar, R.T.: The elementary vectors of a subspace of $${\\mathbb{R}}^n$$. In: Combinatorial Mathematics and Application, Proceedings of Conference on University North Carolina 1967, pp. 104\u2013127 (1969)"},{"key":"17_CR14","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)"},{"key":"17_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8431-1","volume-title":"Lectures on Polytopes","author":"GM Ziegler","year":"1995","unstructured":"Ziegler, G.M.: Lectures on Polytopes. GTM, vol. 152. Springer, New York (1995). https:\/\/doi.org\/10.1007\/978-1-4613-8431-1"}],"container-title":["Lecture Notes in Computer Science","Mathematical Software \u2013 ICMS 2024"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-64529-7_17","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,16]],"date-time":"2024-07-16T15:23:44Z","timestamp":1721143424000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-64529-7_17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"ISBN":["9783031645280","9783031645297"],"references-count":15,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-64529-7_17","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024]]},"assertion":[{"value":"17 July 2024","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors have no competing interests to declare.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"value":"ICMS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Congress on Mathematical Software","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Durham","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"United Kingdom","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 July 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"25 July 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"icms2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/maths.dur.ac.uk\/icms2024\/ICMS2024.html","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}