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Return the negative of the graph Laplacian of the reaction network. The ODE system of a chemical reaction network can be factorized as ``\frac{dx}{dt} = Y A_k Φ(x)``, where Y is the [`complexstoichmat`](@ref) and A_k is the negative of the graph Laplacian, and Φ is the [`massactionvector`](@ref). A_k is an n-by-n matrix, where n is the number of complexes, where ``A_{ij} = k_{ij}`` if a reaction exists between the two complexes and 0 otherwise.
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Return the negative of the graph Laplacian of the reaction network. The ODE system of a chemical reaction network can be factorized as ``\frac{dx}{dt} = Y A_k Φ(x)``, where ``Y`` is the [`complexstoichmat`](@ref) and ``A_k`` is the negative of the graph Laplacian, and ``Φ`` is the [`massactionvector`](@ref). ``A_k`` is an n-by-n matrix, where n is the number of complexes, where ``A_{ij} = k_{ij}`` if a reaction exists between the two complexes and 0 otherwise.
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Returns a symbolic matrix by default, but will return a numerical matrix if parameter values are specified via pmap.
Return an r×c matrix K such that, if complex j is the substrate complex of reaction i, then K_{ij} = k, the rate constant for this reaction. Mostly a helper function for the network Laplacian, [`networklaplacianmat`](@ref). Has the useful property that ``\frac{dx}{dt} = S*K*Φ(x)``, where S is the [`netstoichmat`](@ref) or net stoichiometry matrix and Φ(x) is the [`massactionvector`](@ref).
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Return an r×c matrix ``K`` such that, if complex ``j`` is the substrate complex of reaction ``i``, then ``K_{ij} = k``, the rate constant for this reaction. Mostly a helper function for the network Laplacian, [`laplacianmat`](@ref). Has the useful property that ``\frac{dx}{dt} = S*K*Φ(x)``, where S is the [`netstoichmat`](@ref) or net stoichiometry matrix and ``Φ(x)`` is the [`massactionvector`](@ref).
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Returns a symbolic matrix by default, but will return a numerical matrix if rate constants are specified as a `Tuple`, `Vector`, or `Dict` of symbol-value pairs via `pmap`.
Return the vector whose entries correspond to the "mass action products" of each complex. For example, given the complex A + B, the corresponding entry of the vector would be A*B, and for the complex 2X + Y, the corresponding entry would be X^2*Y. The ODE system of a chemical reaction network can be factorized as ``\frac{dx}{dt} = Y A_k Φ(x)``, where Y is the [`complexstoichmat`](@ref) and A_k is the negative of the [`networklaplacian`](@ref). This utility returns Φ(x).
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Return the vector whose entries correspond to the "mass action products" of each complex. For example, given the complex A + B, the corresponding entry of the vector would be ``A*B``, and for the complex 2X + Y, the corresponding entry would be ``X^2*Y``. The ODE system of a chemical reaction network can be factorized as ``\frac{dx}{dt} = Y A_k Φ(x)``, where ``Y`` is the [`complexstoichmat`](@ref) and ``A_k`` is the negative of the [`laplacianmat`](@ref). This utility returns ``Φ(x)``.
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Returns a symbolic vector by default, but will return a numerical vector if species concentrations are specified as a tuple, vector, or dictionary via scmap.
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If the `combinatoric_ratelaws` option is set, will include prefactors for that (see [introduction to Catalyst's rate laws](@ref introduction_to_catalyst_ratelaws).
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