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Testing binomiality of chemical reaction networks using comprehensive Gröbner systems. (English) Zbl 1499.13076

Boulier, François (ed.) et al., Computer algebra in scientific computing. 23rd international workshop, CASC 2021, Sochi, Russia, September 13–17, 2021. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12865, 334-352 (2021).
The main subject studied in this paper is the application of parametric binomiality testing in the theory of chemical reaction networks. In biochemical reaction networks, a well-known polynomial model is the the steady state ideal. This model comes from the ordinary differential equations describing change of the concentrations in this kind of reaction networks. The problem of binomiality of steady state ideals is considered when the rate constants are viewed as parameters.
So, to study the binomiality of parametric steady state ideals, we need an effective test for being a binomial ideal. Moreover, one needs some algebraic tools to deal with parametric ideals. The problem of binomiality testing has been considered by several mathematicians and in particular a linear algebra based method has been described to solve this problem which seems to be efficient in practice. Furthermore, to study parametric ideals, the authors apply the concept of comprehensive Grobner bases introduced by Weispfenning. Recently, Montes wrote a book entitled “the Grobner Cover” which is a very good source for the introduction and computation of these bases. Furthermore, with Wibmer, they developed a Singular library called grobcov.lib for computing comprehensive Grobner bases.
Applying this approach, the structure of the steady state ideal of the \(n\)-site phosphorylation (for each natural number \(n\)) has been investigated.
For the entire collection see [Zbl 1482.68009].

MSC:

13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
68W30 Symbolic computation and algebraic computation
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