D. S. Research-data-statement, G. E. Arnon, S. Collins, and . Mccallum, Data supporting the research in this paper is available from http Cylindrical algebraic decomposition I: The basic algorithm, SIAM J. Comput, vol.13, issue.4, pp.865-877, 1984.

D. J. Bates, J. D. Hauenstein, A. J. Sommese, and C. W. Wampler, Bertini: Software for numerical algebraic geometry, pp.10-7274

U. S. Bhalla and R. Iyengar, Emergent Properties of Networks of Biological Signaling Pathways, Science, vol.283, issue.5400, pp.381-387, 1999.
DOI : 10.1126/science.283.5400.381

C. Chen, J. Davenport, J. May, M. Moreno-maza, B. Xia et al., Triangular decomposition of semi-algebraic systems, Journal of Symbolic Computation, vol.49, pp.3-26, 2013.
DOI : 10.1016/j.jsc.2011.12.014

C. Chen, M. Moreno-maza, B. Xia, and L. Yang, Computing cylindrical algebraic decomposition via triangular decomposition, Proceedings of the 2009 international symposium on Symbolic and algebraic computation, ISSAC '09, pp.95-102, 2009.
DOI : 10.1145/1576702.1576718

URL : http://www.csd.uwo.ca/~moreno//Publications/Chen.Moreno-Maza.Xia.Yang-ISSAC-2009.pdf

C. Conradi, E. Feliu, M. Mincheva, and C. Wiuf, Identifying parameter regions for multistationarity, PLOS Computational Biology, vol.24, issue.2, 2017.
DOI : 10.1371/journal.pcbi.1005751.s001

URL : https://doi.org/10.1371/journal.pcbi.1005751

C. Conradi, D. Flockerzi, and J. Raisch, Multistationarity in the activation of a MAPK: Parametrizing the relevant region in parameter space, Mathematical Biosciences, vol.211, issue.1, pp.105-136, 2008.
DOI : 10.1016/j.mbs.2007.10.004

C. Conradi and M. Mincheva, Catalytic constants enable the emergence of bistability in dual phosphorylation, Journal of The Royal Society Interface, vol.276, issue.12, p.2014
DOI : 10.1111/j.1742-4658.2009.07027.x

G. Craciun, A. Dickenstein, A. Shiu, and B. Sturmfels, Toric dynamical systems, Journal of Symbolic Computation, vol.44, issue.11, pp.1551-1565, 2009.
DOI : 10.1016/j.jsc.2008.08.006

URL : https://doi.org/10.1016/j.jsc.2008.08.006

A. Dolzmann and T. Sturm, REDLOG, ACM SIGSAM Bulletin, vol.31, issue.2, pp.2-9, 1997.
DOI : 10.1145/261320.261324

M. England, R. Bradford, and J. Davenport, Improving the Use of Equational Constraints in Cylindrical Algebraic Decomposition, Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '15, pp.165-172, 2015.
DOI : 10.1109/SYNASC.2014.15

M. England and J. Davenport, The complexity of cylindrical algebraic decomposition with respect to polynomial degre, Proceedings of the CASC 2016, pp.172-192, 2016.

M. Feinberg, Chemical reaction network structure and the stability of complex isothermal reactors???I. The deficiency zero and deficiency one theorems, Chemical Engineering Science, vol.42, issue.10, pp.2229-226837, 1987.
DOI : 10.1016/0009-2509(87)80099-4

E. Gross, H. A. Harrington, Z. Rosen, and B. Sturmfels, Algebraic Systems Biology: A Case Study for the Wnt Pathway, Bulletin of Mathematical Biology, vol.25, issue.1, pp.21-51, 2016.
DOI : 10.1145/317275.317286

H. Hong, R. Liska, and S. Steinberg, Testing Stability by Quantifier Elimination, Journal of Symbolic Computation, vol.24, issue.2, pp.161-187, 1997.
DOI : 10.1006/jsco.1997.0121

M. D. Johnston, A note on " MAPK networks and their capacity for multistationarity due to toric steady states, 2014.

B. Joshi and A. Shiu, A Survey of Methods for Deciding Whether a Reaction Network is Multistationary, Mathematical Modelling of Natural Phenomena, vol.12, issue.1, pp.47-67, 2015.
DOI : 10.1137/120873388

C. Li, M. Donizelli, N. Rodriguez, H. Dharuri, L. Endler et al., BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models, BMC Systems Biology, vol.4, issue.1, p.92, 2010.
DOI : 10.1186/1752-0509-4-92

URL : https://bmcsystbiol.biomedcentral.com/track/pdf/10.1186/1752-0509-4-92?site=bmcsystbiol.biomedcentral.com

N. I. Markevich, J. B. Hoek, and B. N. Kholodenko, Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades, The Journal of Cell Biology, vol.71, issue.3, pp.353-359, 2004.
DOI : 10.1074/jbc.M103369200

URL : http://jcb.rupress.org/content/jcb/164/3/353.full.pdf

M. , P. Millán, and A. Dickenstein, The structure of MESSI biological systems, 2016.

M. , P. Millán, and A. G. Turjanski, MAPK's networks and their capacity for multistationarity due to toric steady states, Math. Biosci, vol.262, pp.125-162, 2015.

S. Schuster and T. Höfer, Determining all extreme semi-positive conservation relations in chemical reaction systems: a test criterion for conservativity, J. Chem. Soc., Faraday Trans., vol.22, issue.16, pp.2561-2566, 1991.
DOI : 10.1016/0303-2647(88)90047-0

A. J. Sommese, J. Verschelde, and C. W. Wampler, Introduction to numerical algebraic geometry, Solving Polynomial Equations: Foundations, Algorithms, and Applications, pp.301-337, 2005.
DOI : 10.1007/3-540-27357-3_8

URL : http://www.math.tamu.edu/%7Ejhauenst/preprints/hauenstein_thesis.pdf

D. Wang, Elimination Methods, 2000.
DOI : 10.1007/978-3-7091-6202-6

URL : https://hal.archives-ouvertes.fr/hal-01573183

D. Wang and B. Xia, Stability analysis of biological systems with real solution classification, Proceedings of the 2005 international symposium on Symbolic and algebraic computation , ISSAC '05, pp.354-361, 2005.
DOI : 10.1145/1073884.1073933

URL : https://hal.archives-ouvertes.fr/hal-01486880

V. Weispfenning, Quantifier Elimination for Real Algebra -- the Quadratic Case and Beyond, Applicable Algebra in Engineering, Communication and Computing, vol.8, issue.2, pp.85-101, 1997.
DOI : 10.1007/s002000050055

URL : http://www.fmi.uni-passau.de/~redlog/paper/quadqe1.ps.Z

G. Weng, U. S. Bhalla, and R. Iyengar, Complexity in Biological Signaling Systems, Science, vol.284, issue.5411, pp.92-98, 1999.
DOI : 10.1126/science.284.5411.92

URL : https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3773983/pdf