Merge pull request #619 from isaacsas/fix_networkanalysis_latex

fix broken latex from Katex

Author: isaacsas

docs/src/catalyst_functionality/network_analysis.md

@@ -395,27 +395,26 @@ we find
 \mathbf{x}(t) = \mathbf{x}(0) + \sum_{k=1}^K \left(\int_0^t v_k(\mathbf{x})(s) \, ds\right) \mathbf{N}_k,
 ```
 which demonstrates that ``\mathbf{x}(t) - \mathbf{x}(0)`` is always given by a
-linear combination of the stochiometry vectors, i.e.
+linear combination of the stoichiometry vectors, i.e.
 ```math
-\DeclareMathOperator{\span}{span}
-\mathbf{x}(t) - \mathbf{x}(0) \in \span\{\mathbf{N}_k \}.
+\mathbf{x}(t) - \mathbf{x}(0) \in \operatorname{span}\{\mathbf{N}_k \}.
 ```
 In particular, this says that ``\mathbf{x}(t)`` lives in the translation of the
-``\span\{\mathbf{N}_k \}`` by ``\mathbf{x}(0)`` which we write as
-``(\mathbf{x}(0) + \span\{\mathbf{N}_k\})``. In fact, since the solution should
-stay non-negative, if we let $\bar{\mathbb{R}}_+^{M}$ denote the subset of
-vectors in $\mathbb{R}^{M}$ with non-negative components, the possible physical
-values for the solution, ``\mathbf{x}(t)``, must be in the set
+``\operatorname{span}\{\mathbf{N}_k \}`` by ``\mathbf{x}(0)`` which we write as
+``(\mathbf{x}(0) + \operatorname{span}\{\mathbf{N}_k\})``. In fact, since the
+solution should stay non-negative, if we let $\bar{\mathbb{R}}_+^{M}$ denote the
+subset of vectors in $\mathbb{R}^{M}$ with non-negative components, the possible
+physical values for the solution, ``\mathbf{x}(t)``, must be in the set
 ```math
-(\mathbf{x}(0) + \span\{\mathbf{N}_k\}) \cap \bar{\mathbb{R}}_+^{M}.
+(\mathbf{x}(0) + \operatorname{span}\{\mathbf{N}_k\}) \cap \bar{\mathbb{R}}_+^{M}.
 ```
 This set is called the stoichiometric compatibility class of ``\mathbf{x}(t)``.
 The key property of stoichiometric compatibility classes is that they are
 invariant under the RRE ODE's dynamics, i.e. a solution will always remain
 within the subspace given by the stoichiometric compatibility class. Finally, we
 note that the *positive* stoichiometric compatibility class generated by
-$\mathbf{x}(0)$ is just ``(\mathbf{x}(0) + \span\{\mathbf{N}_k\}) \cap
-\mathbb{R}_+^{M}``, where ``\mathbb{R}_+^{M}`` denotes the vectors in
+$\mathbf{x}(0)$ is just ``(\mathbf{x}(0) + \operatorname{span}\{\mathbf{N}_k\})
+\cap \mathbb{R}_+^{M}``, where ``\mathbb{R}_+^{M}`` denotes the vectors in
 ``\mathbb{R}^M`` with strictly positive components.
 
 With these definitions we can now see how knowing the deficiency and weak