another try to solve the math rendering

nomad-coe · Oct 28, 2024 · d0ab7df · d0ab7df
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diff --git a/docs/_layouts/default.html b/docs/_layouts/default.html
@@ -14,7 +14,6 @@
     <link rel="stylesheet" href="{{ '/assets/css/style.css?v=' | append: site.github.build_revision | relative_url }}">
     {% include head-custom.html %}
     <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
-    <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
 </head>
 
 <body>

diff --git a/docs/gx_ac.md b/docs/gx_ac.md
@@ -13,7 +13,7 @@ This component of the GreenX library (GX-AC) implements the analytic continuatio
   <img src="./img/Analyticcontinuation_main.svg" width="700">
 </div>
 
-Analytic continuation (AC) is a popular mathematical technique used to extend the domain of a complex analytic (holomorphic) function $f(z)$ beyond its original region of definition. For example, in many applications, a function initially defined on the imaginary axis can be analytically continued to the real axis. Such a continuation can be performed by approximating the function with a rational function, because if two analytic functions match on even a small part of their domain, they must be identical on the entire domain, according to the identity theorem. Two common choices of rational functions that are used in this context are the [two-pole model](https://doi.org/10.1103/PhysRevLett.74.1827) and [Padé approximants](https://books.google.de/books?id=LFCzdo4_20EC&printsec=frontcover&hl=de). Two-pole models are characterized by five parameters and their creation is straight-forward but they prove to be [inaccurate for approximating more complicated functions]((https://doi.org/10.3389/fchem.2019.00377)). In contrast, Padé apoproximants are the [method of choice]((https://doi.org/10.3389/fchem.2019.00377)) for approximating functions with a complicated pole structure due to their flexibility. These functions can take the form
+Analytic continuation (AC) is a popular mathematical technique used to extend the domain of a complex analytic (holomorphic) function \\(f(z)\\) beyond its original region of definition. For example, in many applications, a function initially defined on the imaginary axis can be analytically continued to the real axis. Such a continuation can be performed by approximating the function with a rational function, because if two analytic functions match on even a small part of their domain, they must be identical on the entire domain, according to the identity theorem. Two common choices of rational functions that are used in this context are the [two-pole model](https://doi.org/10.1103/PhysRevLett.74.1827) and [Padé approximants](https://books.google.de/books?id=LFCzdo4_20EC&printsec=frontcover&hl=de). Two-pole models are characterized by five parameters and their creation is straight-forward but they prove to be [inaccurate for approximating more complicated functions]((https://doi.org/10.3389/fchem.2019.00377)). In contrast, Padé apoproximants are the [method of choice]((https://doi.org/10.3389/fchem.2019.00377)) for approximating functions with a complicated pole structure due to their flexibility. These functions can take the form
 
 $$
 f(z) \approx T_{M}(z) = \frac{A_0 + A_1z + \cdots + A_pz^p + \cdots + A_{\frac{M-1}{2}}z^{\frac{M-1}{2}}}{1 + B_1z + \cdots + B_pz^p + \cdots + B_{\frac{M}{2}}z^{\frac{M}{2}}}.
@@ -66,7 +66,8 @@ The three model functions described above were tested with four different config
 We found that the performance of "greedy-128bit" is similar to "plain-128bit". Therefore, the fourth configuration is not reported in Fig. 2.
 
 Figure 2 (left column) shows the real part of the exact model functions and their corresponding Padé approximants, calculated with 128 parameters, for the three different configurations.
-The right column of Figure 2 reports the error of the AC with respect to the number of Padé  parameters.  The error is defined as the residual sum between the values obtained from the Padé model and the exact analytic reference function. 
+The right column of Figure 2 reports the error of the AC with respect to the number of Padé  parameters.  The error is defined as the residual sum between the values obtained from the Padé model and the exact analytic reference function.
+
 $$
 \text{MAE} = \frac{1}{N}\sum_{i=0}^{N} |f(x_i + \eta i) - T(x_i + \eta i)| 
 $$

diff --git a/docs/gx_time_frequency.md b/docs/gx_time_frequency.md
@@ -3,6 +3,7 @@ layout: default
 title: Time-Frequency Component
 tagline: GreenX Time-Frequency
 description: Minimax time and frequency grids for low-scaling RPA and GW
+mathjax: true
 ---
 # General