Gen html, small md-LaTeX fixes

blogo-input/posts/kzg-batch-proof.md

@@ -20,6 +20,7 @@ where \space\space\space l_j(x) = \prod\_{0\leq m \leq k} \frac{x-x_m}{x_j - x_m
 $$
 
 And the $x-z$, which was to ensure that $q(x)$ had a root at $z$, now, as we want to ensure that $q(x)$ has roots at all the points of the commitment, we will use the *zero polynomial*:
+
 $$
 Z(x) = \prod_{i=0}^{k} x-z_i =\newline
 =(x-z_0)(x-z_1)...(x-z_k)
@@ -30,16 +31,19 @@ This polynomial ensures that when $x=z_i$ ($z_i$ being one of our points), the p
 Now we can put $I(x)$ and $Z(x)$ in place, obtaining $q(x)=\frac{p(x)-I(x)}{Z(x)}$. And the batch proof evaluation is obtained by $\pi=[q(\tau)]_1$.
 
 The verification is quite similar than what we did for single proofs, but using the mentioned $z(x)$ and $I(x)$:
+
 $$
 \hat{e}(\pi, [Z(\tau)]_2) == \hat{e}(c - [I(\tau)]_1, H)
 $$
 
 Which, as we did with the single proofs in the previous post, we can unroll it and see that:
+
 $$
 \hat{e}(\pi, [Z(\tau)]_2) == \hat{e}(c - [I(\tau)]_1, H)\newline
 \Rightarrow \hat{e}([q(\tau)]_1, [Z(\tau)]_2) == \hat{e}([p(\tau)]_1 - [I(\tau)]_1, H)\newline
 \Rightarrow [q(\tau) \cdot Z(\tau)]_T == [p(\tau) - I(\tau)]_T
 $$
+
 From where we see that is the equation $q(x)\cdot Z(x)=p(x)-I(x)$, which can be expressed as $q(x) = \frac{p(x) - I(x)}{Z(x)}$, evaluated at $\tau$ from the trusted setup, which is not known: $q(\tau) = \frac{p(\tau) - I(\tau)}{Z(\tau)}$.
 
 #### Vector commitments

blogo-input/posts/kzg-commitments.md

@@ -32,6 +32,7 @@ $$
 $$
 
 Which in additive representation is:
+
 $$
 (G, \tau G, \tau^2 G, ..., \tau^{n-1} G) \in \mathbb{G}_1\newline
 (H, \tau H, \tau^2 H, ..., \tau^{n-1} H) \in \mathbb{G}_2

blogo-input/posts/shamir-secret-sharing.md

@@ -53,6 +53,7 @@ We will work over a finite field of size $p$, where $p$ is a prime number. For o
 Let our secret be $s=14$. We now generate our polynomial of degree $n-1=2$, where $s$ will be the constant coefficient: $p(x)= s + \alpha_1 x^1 + \alpha_2 x^2$. We can set $\alpha_1$ and $\alpha_2$ into any random value, as example $\alpha_1=4$ and $\alpha_2=6$. So we have our polynomial: $p(x) = 14 + 4 x + 6 x^2$.
 
 Now that we have the polynomial, we can pick $k$ points from it, using incremental indexes for the $x$ coordinate: $P_1=(1, p(1)), P_2=(2, p(2)), \space\ldots\space, P_k=(k, p(k))$. With the numbers of our example this is (remember, we work over $\mathbb{F}\_{19}$):
+
 $$
 p(x) = 14 + 4 x + 6 x^2,\newline
 p(1)=14 + 4 \cdot 1 + 6 \cdot 1^2 = 24 \space (mod \space 19) = 5\newline
@@ -61,6 +62,7 @@ p(3)=14 + 4 \cdot 3 + 6 \cdot 3^2 = 80 \space (mod \space 19) = 4\newline
 p(4)=14 + 4 \cdot 4 + 6 \cdot 4^2 = 126 \space (mod \space 19) = 12\newline
 p(5)=14 + 4 \cdot 5 + 6 \cdot 5^2 = 184 \space (mod \space 19) = 13
 $$
+
 So our $k$ points are: $(1,5), (2,8), (3,4), (4,12), (5,13)$. We can distribute these points as our 'secret parts'.
 In order to recover the secret, we need at least $n=3$ points, for example $P_1$, $P_3$, $P_5$, and we compute the *Lagrange polynomial interpolation* to recover the original polynomial (remember, we work over $\mathbb{F}\_{19}$):
 
@@ -68,11 +70,13 @@ $$
 I(x) = \sum_{i=0}^n y_i l_i(x) \space\space
 where \space\space\space l_i(x) = \prod\_{0 \leq j \leq n \\ j\neq i} \frac{x-x_j}{x_i - x_j}
 $$
+
 $$
 l_1(x) = \frac{x-3}{1-3} \cdot \frac{x-5}{1-5} = \frac{x-3}{17} \cdot \frac{x-5}{15}=\frac{x^2+11x+15}{8}\newline
 l_3(x) = \frac{x-1}{3-1} \cdot \frac{x-5}{3-5} = \frac{x-1}{2} \cdot \frac{x-5}{17} =\frac{x^2+13x+5}{15}\newline
 l_5(x) = \frac{x-1}{5-1} \cdot \frac{x-3}{5-3} = \frac{x-1}{4} \cdot \frac{x-3}{2} = \frac{x^2 + 15x + 3}{8}\newline
 $$
+
 $$
 I(x) = y_2 \cdot l_2(x) + y_4 \cdot l_4(x) + y_5 \cdot l_5(x)\newline
 = 5 \cdot (\frac{x^2+11x+15}{8}) + 4 \cdot (\frac{x^2+13x+5}{15}) + 13 \cdot (\frac{x^2 +15x + 3}{8})\newline

public/blind-signatures-ec.html

@@ -21,7 +21,7 @@
 
     <meta name="viewport" content="width=device-width, initial-scale=1">
 
-    <link href="https://cdn.jsdelivr.net/npm/bootstrap@5.0.2/dist/css/bootstrap.min.css" rel="stylesheet" integrity="sha384-EVSTQN3/azprG1Anm3QDgpJLIm9Nao0Yz1ztcQTwFspd3yD65VohhpuuCOmLASjC" crossorigin="anonymous">
+    <link href="css/bootstrap.min.css" rel="stylesheet">
     <link rel="stylesheet" href="css/style.css">
 
     <!-- highlightjs -->
@@ -30,7 +30,7 @@
     <script src="js/highlightjs/highlight.pack.js"></script>
 
     <!-- katex -->
-    <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.13.11/dist/katex.min.css" integrity="sha384-Um5gpz1odJg5Z4HAmzPtgZKdTBHZdw8S29IecapCSB31ligYPhHQZMIlWLYQGVoc" crossorigin="anonymous">
+    <link rel="stylesheet" href="js/katex/katex.min.css">
   </head>
 
   <body>
@@ -82,18 +82,18 @@ The main idea is that one party has a message and blinds it, then sends the blin
 
 <p>In this notes, we will cover the scheme proposed at <em>&ldquo;<a href="https://sci-hub.do/10.1109/ICCKE.2013.6682844">New Blind Signature Schemes Based on the (Elliptic Curve) Discrete Logarithm Problem</a>&rdquo;</em> paper by Hamid Mala &amp; Nafiseh Nezhadansari (thanks to <a href="https://twitter.com/feministPLT">Daira Hopwood</a> who mentioned this paper in a Telegram group).</p>
 
-<p>First of all, the <em>signer</em> generates their key pair by generating a random scalar $d \in \mathbb{Z}_n$ (where $\mathbb{Z}_n$ is the elliptic curve field), which will be the <em>private key</em>. From $d$ they can compute the <em>public key</em> by $Q = dG$, where $G$ is the generator point of $\mathbb{G}$ (the elliptic curve group).</p>
+<p>First of all, the <em>signer</em> generates their key pair by generating a random scalar <span class="math inline">\(d \in \mathbb{Z}_n\)</span> (where <span class="math inline">\(\mathbb{Z}_n\)</span> is the elliptic curve field), which will be the <em>private key</em>. From <span class="math inline">\(d\)</span> they can compute the <em>public key</em> by <span class="math inline">\(Q = dG\)</span>, where <span class="math inline">\(G\)</span> is the generator point of <span class="math inline">\(\mathbb{G}\)</span> (the elliptic curve group).</p>
 
-<p>Appart from their key pair, the <em>signer</em> will generate for each request of signature another random value $k \in \mathbb{Z}_n$, and its respective $R&rsquo;=kG$.</p>
+<p>Appart from their key pair, the <em>signer</em> will generate for each request of signature another random value <span class="math inline">\(k \in \mathbb{Z}_n\)</span>, and its respective <span class="math inline">\(R'=kG\)</span>.</p>
 
-<p>The <em>user</em> has a message <em>m</em> that which they want to get signed by the <em>signer</em> (without the <em>signer</em> knowing the content of <em>m</em>). In order to achieve that, the user will generate a coupe of random values $a, b \in \mathbb{Z}_n$, and from these parameters will compute the <em>blinding factor</em> $R=aR&rsquo; + bG = (ak + b)G$, and as $R$ is a point we can get $R = (x, y)$.
-The user can <em>blind</em> the message by computing $m&rsquo; = a^{-1} \cdot x \cdot h(m)$, where $h(m)$ is the hash of the message.</p>
+<p>The <em>user</em> has a message <em>m</em> that which they want to get signed by the <em>signer</em> (without the <em>signer</em> knowing the content of <em>m</em>). In order to achieve that, the user will generate a coupe of random values <span class="math inline">\(a, b \in \mathbb{Z}_n\)</span>, and from these parameters will compute the <em>blinding factor</em> <span class="math inline">\(R=aR' + bG = (ak + b)G\)</span>, and as <span class="math inline">\(R\)</span> is a point we can get <span class="math inline">\(R = (x, y)\)</span>.
+The user can <em>blind</em> the message by computing <span class="math inline">\(m' = a^{-1} \cdot x \cdot h(m)\)</span>, where <span class="math inline">\(h(m)\)</span> is the hash of the message.</p>
 
-<p>Then, the <em>user</em> sends the <em>blinded message</em> ($m&rsquo;$) to the <em>signer</em>, who will perform the <em>blind signature</em> by computing $s&rsquo; = d m&rsquo; + k$, which is sent back to the <em>user</em>.</p>
+<p>Then, the <em>user</em> sends the <em>blinded message</em> (<span class="math inline">\(m'\)</span>) to the <em>signer</em>, who will perform the <em>blind signature</em> by computing <span class="math inline">\(s' = d m' + k\)</span>, which is sent back to the <em>user</em>.</p>
 
-<p>The <em>user</em> can unblind the signature by $s = a s&rsquo; + b$, and the complete signature will be $(R, s)$.</p>
+<p>The <em>user</em> can unblind the signature by <span class="math inline">\(s = a s' + b\)</span>, and the complete signature will be <span class="math inline">\((R, s)\)</span>.</p>
 
-<p>And now, we are in a point where the signature can be verified by a third party for the <em>signer</em>&rsquo;s public key by checking $sG == R + x h(m) Q$.</p>
+<p>And now, we are in a point where the signature can be verified by a third party for the <em>signer</em>&rsquo;s public key by checking <span class="math inline">\(sG == R + x h(m) Q\)</span>.</p>
 
 <p><div style="text-align:center; font-size:80%;">
     <img style="padding:50px;max-width:100%;" src="img/posts/blind-signatures-ec/flow1.png" />
@@ -101,15 +101,13 @@ The user can blind the message by computing $m’ = a^{-1} \cdot x
 </div>
 <br></p>
 
-<p>From the verification $sG == R + x h(m) Q$, we can unroll it and check that:</p>
-
-<p>$$
-\fbox{sG} = (a s&rsquo; + b) G = (a (d m&rsquo; + k) + b) G\newline
-= (a d m&rsquo; + ak + b) G = ((a d (a^{-1} x h(m))) + ak + b) G\newline
+<p>From the verification <span class="math inline">\(sG == R + x h(m) Q\)</span>, we can unroll it and check that:</p>
+<p><span class="math display">\[
+\fbox{sG} = (a s' + b) G = (a (d m' + k) + b) G\newline
+= (a d m' + ak + b) G = ((a d (a^{-1} x h(m))) + ak + b) G\newline
 = (d x h(m) + ak + b) G\newline
 = dG x h(m) + (ak + b)G = \fbox{R + x h(m) Q}
-$$</p>
-
+\]</span></p>
 <h4>Code</h4>
 
 <p>Here is an example of how this scheme on the <a href="https://en.bitcoin.it/wiki/Secp256k1">secp256k1</a> curve could be used using the implementation from <a href="https://github.com/arnaucube/go-blindsecp256k1">go-blindsecp256k1</a>.</p>
@@ -189,8 +187,8 @@ func main() {
     </script>
     <script src="js/external-links.js"></script>
     <script>hljs.initHighlightingOnLoad();</script>
-    <script defer src="https://cdn.jsdelivr.net/npm/katex@0.13.11/dist/katex.min.js" integrity="sha384-YNHdsYkH6gMx9y3mRkmcJ2mFUjTd0qNQQvY9VYZgQd7DcN7env35GzlmFaZ23JGp" crossorigin="anonymous"></script>
-    <script defer src="https://cdn.jsdelivr.net/npm/katex@0.13.11/dist/contrib/auto-render.min.js" integrity="sha384-vZTG03m+2yp6N6BNi5iM4rW4oIwk5DfcNdFfxkk9ZWpDriOkXX8voJBFrAO7MpVl" crossorigin="anonymous"></script>
+    <script defer src="js/katex/katex.min.js"></script>
+    <script defer src="js/katex/auto-render.min.js"></script>
     <script>
       document.addEventListener("DOMContentLoaded", function() {
         renderMathInElement(document.body, {
@@ -200,6 +198,8 @@ func main() {
           delimiters: [
             {left: '$$', right: '$$', display: true},
             {left: '$', right: '$', display: false},
+            {left: "\\[", right: "\\]", display: true},
+            {left: "\\(", right: "\\)", display: false},
           ],
           // • rendering keys, e.g.:
           throwOnError : true
@@ -249,7 +249,7 @@ func main() {
     tagLinks("h4");
     tagLinks("h5");
     </script>
-    <script src="https://cdn.jsdelivr.net/npm/mermaid/dist/mermaid.min.js"></script>
+    <script src="js/mermaid.min.js"></script>
 
 
   </body>

public/blogo.html

@@ -21,7 +21,7 @@
 
     <meta name="viewport" content="width=device-width, initial-scale=1">
 
-    <link href="https://cdn.jsdelivr.net/npm/bootstrap@5.0.2/dist/css/bootstrap.min.css" rel="stylesheet" integrity="sha384-EVSTQN3/azprG1Anm3QDgpJLIm9Nao0Yz1ztcQTwFspd3yD65VohhpuuCOmLASjC" crossorigin="anonymous">
+    <link href="css/bootstrap.min.css" rel="stylesheet">
     <link rel="stylesheet" href="css/style.css">
 
     <!-- highlightjs -->
@@ -30,7 +30,7 @@
     <script src="js/highlightjs/highlight.pack.js"></script>
 
     <!-- katex -->
-    <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.13.11/dist/katex.min.css" integrity="sha384-Um5gpz1odJg5Z4HAmzPtgZKdTBHZdw8S29IecapCSB31ligYPhHQZMIlWLYQGVoc" crossorigin="anonymous">
+    <link rel="stylesheet" href="js/katex/katex.min.css">
   </head>
 
   <body>
@@ -436,8 +436,8 @@ func putHTMLToTemplate(template string, m map[string]string) string {
     </script>
     <script src="js/external-links.js"></script>
     <script>hljs.initHighlightingOnLoad();</script>
-    <script defer src="https://cdn.jsdelivr.net/npm/katex@0.13.11/dist/katex.min.js" integrity="sha384-YNHdsYkH6gMx9y3mRkmcJ2mFUjTd0qNQQvY9VYZgQd7DcN7env35GzlmFaZ23JGp" crossorigin="anonymous"></script>
-    <script defer src="https://cdn.jsdelivr.net/npm/katex@0.13.11/dist/contrib/auto-render.min.js" integrity="sha384-vZTG03m+2yp6N6BNi5iM4rW4oIwk5DfcNdFfxkk9ZWpDriOkXX8voJBFrAO7MpVl" crossorigin="anonymous"></script>
+    <script defer src="js/katex/katex.min.js"></script>
+    <script defer src="js/katex/auto-render.min.js"></script>
     <script>
       document.addEventListener("DOMContentLoaded", function() {
         renderMathInElement(document.body, {
@@ -447,6 +447,8 @@ func putHTMLToTemplate(template string, m map[string]string) string {
           delimiters: [
             {left: '$$', right: '$$', display: true},
             {left: '$', right: '$', display: false},
+            {left: "\\[", right: "\\]", display: true},
+            {left: "\\(", right: "\\)", display: false},
           ],
           // • rendering keys, e.g.:
           throwOnError : true
@@ -496,7 +498,7 @@ func putHTMLToTemplate(template string, m map[string]string) string {
     tagLinks("h4");
     tagLinks("h5");
     </script>
-    <script src="https://cdn.jsdelivr.net/npm/mermaid/dist/mermaid.min.js"></script>
+    <script src="js/mermaid.min.js"></script>
 
 
   </body>

public/coffeeminer-hacking-wifi-cryptocurrency-miner.html

@@ -21,7 +21,7 @@
 
     <meta name="viewport" content="width=device-width, initial-scale=1">
 
-    <link href="https://cdn.jsdelivr.net/npm/bootstrap@5.0.2/dist/css/bootstrap.min.css" rel="stylesheet" integrity="sha384-EVSTQN3/azprG1Anm3QDgpJLIm9Nao0Yz1ztcQTwFspd3yD65VohhpuuCOmLASjC" crossorigin="anonymous">
+    <link href="css/bootstrap.min.css" rel="stylesheet">
     <link rel="stylesheet" href="css/style.css">
 
     <!-- highlightjs -->
@@ -30,7 +30,7 @@
     <script src="js/highlightjs/highlight.pack.js"></script>
 
     <!-- katex -->
-    <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.13.11/dist/katex.min.css" integrity="sha384-Um5gpz1odJg5Z4HAmzPtgZKdTBHZdw8S29IecapCSB31ligYPhHQZMIlWLYQGVoc" crossorigin="anonymous">
+    <link rel="stylesheet" href="js/katex/katex.min.css">
   </head>
 
   <body>
@@ -575,8 +575,8 @@ def start():
     </script>
     <script src="js/external-links.js"></script>
     <script>hljs.initHighlightingOnLoad();</script>
-    <script defer src="https://cdn.jsdelivr.net/npm/katex@0.13.11/dist/katex.min.js" integrity="sha384-YNHdsYkH6gMx9y3mRkmcJ2mFUjTd0qNQQvY9VYZgQd7DcN7env35GzlmFaZ23JGp" crossorigin="anonymous"></script>
-    <script defer src="https://cdn.jsdelivr.net/npm/katex@0.13.11/dist/contrib/auto-render.min.js" integrity="sha384-vZTG03m+2yp6N6BNi5iM4rW4oIwk5DfcNdFfxkk9ZWpDriOkXX8voJBFrAO7MpVl" crossorigin="anonymous"></script>
+    <script defer src="js/katex/katex.min.js"></script>
+    <script defer src="js/katex/auto-render.min.js"></script>
     <script>
       document.addEventListener("DOMContentLoaded", function() {
         renderMathInElement(document.body, {
@@ -586,6 +586,8 @@ def start():
           delimiters: [
             {left: '$$', right: '$$', display: true},
             {left: '$', right: '$', display: false},
+            {left: "\\[", right: "\\]", display: true},
+            {left: "\\(", right: "\\)", display: false},
           ],
           // • rendering keys, e.g.:
           throwOnError : true
@@ -635,7 +637,7 @@ def start():
     tagLinks("h4");
     tagLinks("h5");
     </script>
-    <script src="https://cdn.jsdelivr.net/npm/mermaid/dist/mermaid.min.js"></script>
+    <script src="js/mermaid.min.js"></script>
 
 
   </body>

public/flock-botnet.html

@@ -21,7 +21,7 @@
 
     <meta name="viewport" content="width=device-width, initial-scale=1">
 
-    <link href="https://cdn.jsdelivr.net/npm/bootstrap@5.0.2/dist/css/bootstrap.min.css" rel="stylesheet" integrity="sha384-EVSTQN3/azprG1Anm3QDgpJLIm9Nao0Yz1ztcQTwFspd3yD65VohhpuuCOmLASjC" crossorigin="anonymous">
+    <link href="css/bootstrap.min.css" rel="stylesheet">
     <link rel="stylesheet" href="css/style.css">
 
     <!-- highlightjs -->
@@ -30,7 +30,7 @@
     <script src="js/highlightjs/highlight.pack.js"></script>
 
     <!-- katex -->
-    <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.13.11/dist/katex.min.css" integrity="sha384-Um5gpz1odJg5Z4HAmzPtgZKdTBHZdw8S29IecapCSB31ligYPhHQZMIlWLYQGVoc" crossorigin="anonymous">
+    <link rel="stylesheet" href="js/katex/katex.min.css">
   </head>
 
   <body>
@@ -361,8 +361,8 @@
     </script>
     <script src="js/external-links.js"></script>
     <script>hljs.initHighlightingOnLoad();</script>
-    <script defer src="https://cdn.jsdelivr.net/npm/katex@0.13.11/dist/katex.min.js" integrity="sha384-YNHdsYkH6gMx9y3mRkmcJ2mFUjTd0qNQQvY9VYZgQd7DcN7env35GzlmFaZ23JGp" crossorigin="anonymous"></script>
-    <script defer src="https://cdn.jsdelivr.net/npm/katex@0.13.11/dist/contrib/auto-render.min.js" integrity="sha384-vZTG03m+2yp6N6BNi5iM4rW4oIwk5DfcNdFfxkk9ZWpDriOkXX8voJBFrAO7MpVl" crossorigin="anonymous"></script>
+    <script defer src="js/katex/katex.min.js"></script>
+    <script defer src="js/katex/auto-render.min.js"></script>
     <script>
       document.addEventListener("DOMContentLoaded", function() {
         renderMathInElement(document.body, {
@@ -372,6 +372,8 @@
           delimiters: [
             {left: '$$', right: '$$', display: true},
             {left: '$', right: '$', display: false},
+            {left: "\\[", right: "\\]", display: true},
+            {left: "\\(", right: "\\)", display: false},
           ],
           // • rendering keys, e.g.:
           throwOnError : true
@@ -421,7 +423,7 @@
     tagLinks("h4");
     tagLinks("h5");
     </script>
-    <script src="https://cdn.jsdelivr.net/npm/mermaid/dist/mermaid.min.js"></script>
+    <script src="js/mermaid.min.js"></script>
 
 
   </body>

public/index.html

@@ -21,7 +21,7 @@
 
     <meta name="viewport" content="width=device-width, initial-scale=1">
 
-    <link href="https://cdn.jsdelivr.net/npm/bootstrap@5.0.2/dist/css/bootstrap.min.css" rel="stylesheet" integrity="sha384-EVSTQN3/azprG1Anm3QDgpJLIm9Nao0Yz1ztcQTwFspd3yD65VohhpuuCOmLASjC" crossorigin="anonymous">
+    <link href="css/bootstrap.min.css" rel="stylesheet">
     <link rel="stylesheet" href="css/style.css">
 
     <!-- highlightjs -->
@@ -30,7 +30,7 @@
     <script src="js/highlightjs/highlight.pack.js"></script>
 
     <!-- katex -->
-    <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.13.11/dist/katex.min.css" integrity="sha384-Um5gpz1odJg5Z4HAmzPtgZKdTBHZdw8S29IecapCSB31ligYPhHQZMIlWLYQGVoc" crossorigin="anonymous">
+    <link rel="stylesheet" href="js/katex/katex.min.css">
   </head>
 
   <body>
@@ -67,7 +67,7 @@
 </a><a href='/blog/kzg-batch-proof.html'><div class="row postThumb">
         <h3>Batch proof in KZG Commitments</h3>
 
-<p>The benefit of <em>batch proof</em> is that allows us to proof multiple points while the proof size remains constant to one $\mathbb{G}_1$ point.</p>
+<p>The benefit of <em>batch proof</em> is that allows us to proof multiple points while the proof size remains constant to one <span class="math inline">\(\mathbb{G}_1\)</span> point.</p>
 
 <p><em>2021-08-14</em></p>
 
@@ -146,8 +146,8 @@
     </script>
     <script src="js/external-links.js"></script>
     <script>hljs.initHighlightingOnLoad();</script>
-    <script defer src="https://cdn.jsdelivr.net/npm/katex@0.13.11/dist/katex.min.js" integrity="sha384-YNHdsYkH6gMx9y3mRkmcJ2mFUjTd0qNQQvY9VYZgQd7DcN7env35GzlmFaZ23JGp" crossorigin="anonymous"></script>
-    <script defer src="https://cdn.jsdelivr.net/npm/katex@0.13.11/dist/contrib/auto-render.min.js" integrity="sha384-vZTG03m+2yp6N6BNi5iM4rW4oIwk5DfcNdFfxkk9ZWpDriOkXX8voJBFrAO7MpVl" crossorigin="anonymous"></script>
+    <script defer src="js/katex/katex.min.js"></script>
+    <script defer src="js/katex/auto-render.min.js"></script>
     <script>
       document.addEventListener("DOMContentLoaded", function() {
         renderMathInElement(document.body, {
@@ -157,6 +157,8 @@
           delimiters: [
             {left: '$$', right: '$$', display: true},
             {left: '$', right: '$', display: false},
+            {left: "\\[", right: "\\]", display: true},
+            {left: "\\(", right: "\\)", display: false},
           ],
           // • rendering keys, e.g.:
           throwOnError : true
@@ -206,7 +208,7 @@
     tagLinks("h4");
     tagLinks("h5");
     </script>
-    <script src="https://cdn.jsdelivr.net/npm/mermaid/dist/mermaid.min.js"></script>
+    <script src="js/mermaid.min.js"></script>
 
 
   </body>

public/js/katex/README.md

@@ -0,0 +1,119 @@
+# [<img src="https://katex.org/img/katex-logo-black.svg" width="130" alt="KaTeX">](https://katex.org/)
+[![npm](https://img.shields.io/npm/v/katex.svg)](https://www.npmjs.com/package/katex)
+[![semantic-release](https://img.shields.io/badge/%20%20%F0%9F%93%A6%F0%9F%9A%80-semantic--release-e10079.svg)](https://github.com/semantic-release/semantic-release)
+[![CI](https://github.com/KaTeX/KaTeX/workflows/CI/badge.svg?branch=main&event=push)](https://github.com/KaTeX/KaTeX/actions?query=workflow%3ACI)
+[![codecov](https://codecov.io/gh/KaTeX/KaTeX/branch/main/graph/badge.svg)](https://codecov.io/gh/KaTeX/KaTeX)
+[![Discussions](https://img.shields.io/badge/Discussions-join-brightgreen)](https://github.com/KaTeX/KaTeX/discussions)
+[![jsDelivr](https://data.jsdelivr.com/v1/package/npm/katex/badge?style=rounded)](https://www.jsdelivr.com/package/npm/katex)
+![katex.min.js size](https://img.badgesize.io/https://unpkg.com/katex/dist/katex.min.js?compression=gzip)
+[![Gitpod ready-to-code](https://img.shields.io/badge/Gitpod-ready--to--code-blue?logo=gitpod)](https://gitpod.io/#https://github.com/KaTeX/KaTeX)
+[![Financial Contributors on Open Collective](https://opencollective.com/katex/all/badge.svg?label=financial+contributors)](https://opencollective.com/katex)
+
+KaTeX is a fast, easy-to-use JavaScript library for TeX math rendering on the web.
+
+ * **Fast:** KaTeX renders its math synchronously and doesn't need to reflow the page. See how it compares to a competitor in [this speed test](http://www.intmath.com/cg5/katex-mathjax-comparison.php).
+ * **Print quality:** KaTeX's layout is based on Donald Knuth's TeX, the gold standard for math typesetting.
+ * **Self contained:** KaTeX has no dependencies and can easily be bundled with your website resources.
+ * **Server side rendering:** KaTeX produces the same output regardless of browser or environment, so you can pre-render expressions using Node.js and send them as plain HTML.
+
+KaTeX is compatible with all major browsers, including Chrome, Safari, Firefox, Opera, Edge, and IE 11.
+
+KaTeX supports much (but not all) of LaTeX and many LaTeX packages. See the [list of supported functions](https://katex.org/docs/supported.html).
+
+Try out KaTeX [on the demo page](https://katex.org/#demo)!
+
+## Getting started
+
+### Starter template
+
+```html
+<!DOCTYPE html>
+<!-- KaTeX requires the use of the HTML5 doctype. Without it, KaTeX may not render properly -->
+<html>
+  <head>
+    <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.15.3/dist/katex.min.css" integrity="sha384-KiWOvVjnN8qwAZbuQyWDIbfCLFhLXNETzBQjA/92pIowpC0d2O3nppDGQVgwd2nB" crossorigin="anonymous">
+
+    <!-- The loading of KaTeX is deferred to speed up page rendering -->
+    <script defer src="https://cdn.jsdelivr.net/npm/katex@0.15.3/dist/katex.min.js" integrity="sha384-0fdwu/T/EQMsQlrHCCHoH10pkPLlKA1jL5dFyUOvB3lfeT2540/2g6YgSi2BL14p" crossorigin="anonymous"></script>
+
+    <!-- To automatically render math in text elements, include the auto-render extension: -->
+    <script defer src="https://cdn.jsdelivr.net/npm/katex@0.15.3/dist/contrib/auto-render.min.js" integrity="sha384-+XBljXPPiv+OzfbB3cVmLHf4hdUFHlWNZN5spNQ7rmHTXpd7WvJum6fIACpNNfIR" crossorigin="anonymous"
+        onload="renderMathInElement(document.body);"></script>
+  </head>
+  ...
+</html>
+```
+
+You can also [download KaTeX](https://github.com/KaTeX/KaTeX/releases) and host it yourself.
+
+For details on how to configure auto-render extension, refer to [the documentation](https://katex.org/docs/autorender.html).
+
+### API
+
+Call `katex.render` to render a TeX expression directly into a DOM element.
+For example:
+
+```js
+katex.render("c = \\pm\\sqrt{a^2 + b^2}", element, {
+    throwOnError: false
+});
+```
+
+Call `katex.renderToString` to generate an HTML string of the rendered math,
+e.g., for server-side rendering.  For example:
+
+```js
+var html = katex.renderToString("c = \\pm\\sqrt{a^2 + b^2}", {
+    throwOnError: false
+});
+// '<span class="katex">...</span>'
+```
+
+Make sure to include the CSS and font files in both cases.
+If you are doing all rendering on the server, there is no need to include the
+JavaScript on the client.
+
+The examples above use the `throwOnError: false` option, which renders invalid
+inputs as the TeX source code in red (by default), with the error message as
+hover text.  For other available options, see the
+[API documentation](https://katex.org/docs/api.html),
+[options documentation](https://katex.org/docs/options.html), and
+[handling errors documentation](https://katex.org/docs/error.html).
+
+## Demo and Documentation
+
+Learn more about using KaTeX [on the website](https://katex.org)!
+
+## Contributors
+
+### Code Contributors
+
+This project exists thanks to all the people who contribute code. If you'd like to help, see [our guide to contributing code](CONTRIBUTING.md).
+<a href="https://github.com/KaTeX/KaTeX/graphs/contributors"><img src="https://contributors-svg.opencollective.com/katex/contributors.svg?width=890&button=false" alt="Code contributors" /></a>
+
+### Financial Contributors
+
+Become a financial contributor and help us sustain our community.
+
+#### Individuals
+
+<a href="https://opencollective.com/katex"><img src="https://opencollective.com/katex/individuals.svg?width=890" alt="Contribute on Open Collective"></a>
+
+#### Organizations
+
+Support this project with your organization. Your logo will show up here with a link to your website.
+
+<a href="https://opencollective.com/katex/organization/0/website"><img src="https://opencollective.com/katex/organization/0/avatar.svg" alt="Organization 1"></a>
+<a href="https://opencollective.com/katex/organization/1/website"><img src="https://opencollective.com/katex/organization/1/avatar.svg" alt="Organization 2"></a>
+<a href="https://opencollective.com/katex/organization/2/website"><img src="https://opencollective.com/katex/organization/2/avatar.svg" alt="Organization 3"></a>
+<a href="https://opencollective.com/katex/organization/3/website"><img src="https://opencollective.com/katex/organization/3/avatar.svg" alt="Organization 4"></a>
+<a href="https://opencollective.com/katex/organization/4/website"><img src="https://opencollective.com/katex/organization/4/avatar.svg" alt="Organization 5"></a>
+<a href="https://opencollective.com/katex/organization/5/website"><img src="https://opencollective.com/katex/organization/5/avatar.svg" alt="Organization 6"></a>
+<a href="https://opencollective.com/katex/organization/6/website"><img src="https://opencollective.com/katex/organization/6/avatar.svg" alt="Organization 7"></a>
+<a href="https://opencollective.com/katex/organization/7/website"><img src="https://opencollective.com/katex/organization/7/avatar.svg" alt="Organization 8"></a>
+<a href="https://opencollective.com/katex/organization/8/website"><img src="https://opencollective.com/katex/organization/8/avatar.svg" alt="Organization 9"></a>
+<a href="https://opencollective.com/katex/organization/9/website"><img src="https://opencollective.com/katex/organization/9/avatar.svg" alt="Organization 10"></a>
+
+## License
+
+KaTeX is licensed under the [MIT License](http://opensource.org/licenses/MIT).

public/js/katex/auto-render.min.js

@@ -0,0 +1 @@
+!function(e,t){"object"==typeof exports&&"object"==typeof module?module.exports=t(require("katex")):"function"==typeof define&&define.amd?define(["katex"],t):"object"==typeof exports?exports.renderMathInElement=t(require("katex")):e.renderMathInElement=t(e.katex)}("undefined"!=typeof self?self:this,(function(e){return function(){"use strict";var t={974:function(t){t.exports=e}},r={};function n(e){var a=r[e];if(void 0!==a)return a.exports;var i=r[e]={exports:{}};return t[e](i,i.exports,n),i.exports}n.n=function(e){var t=e&&e.__esModule?function(){return e.default}:function(){return e};return n.d(t,{a:t}),t},n.d=function(e,t){for(var r in t)n.o(t,r)&&!n.o(e,r)&&Object.defineProperty(e,r,{enumerable:!0,get:t[r]})},n.o=function(e,t){return Object.prototype.hasOwnProperty.call(e,t)};var a={};return function(){n.d(a,{default:function(){return s}});var e=n(974),t=n.n(e),r=function(e,t,r){for(var n=r,a=0,i=e.length;n<t.length;){var o=t[n];if(a<=0&&t.slice(n,n+i)===e)return n;"\\"===o?n++:"{"===o?a++:"}"===o&&a--,n++}return-1},i=/^\\begin{/,o=function(e,t){for(var n,a=[],o=new RegExp("("+t.map((function(e){return e.left.replace(/[-/\\^$*+?.()|[\]{}]/g,"\\$&")})).join("|")+")");-1!==(n=e.search(o));){n>0&&(a.push({type:"text",data:e.slice(0,n)}),e=e.slice(n));var l=t.findIndex((function(t){return e.startsWith(t.left)}));if(-1===(n=r(t[l].right,e,t[l].left.length)))break;var d=e.slice(0,n+t[l].right.length),s=i.test(d)?d:e.slice(t[l].left.length,n);a.push({type:"math",data:s,rawData:d,display:t[l].display}),e=e.slice(n+t[l].right.length)}return""!==e&&a.push({type:"text",data:e}),a},l=function(e,r){var n=o(e,r.delimiters);if(1===n.length&&"text"===n[0].type)return null;for(var a=document.createDocumentFragment(),i=0;i<n.length;i++)if("text"===n[i].type)a.appendChild(document.createTextNode(n[i].data));else{var l=document.createElement("span"),d=n[i].data;r.displayMode=n[i].display;try{r.preProcess&&(d=r.preProcess(d)),t().render(d,l,r)}catch(e){if(!(e instanceof t().ParseError))throw e;r.errorCallback("KaTeX auto-render: Failed to parse `"+n[i].data+"` with ",e),a.appendChild(document.createTextNode(n[i].rawData));continue}a.appendChild(l)}return a},d=function e(t,r){for(var n=0;n<t.childNodes.length;n++){var a=t.childNodes[n];if(3===a.nodeType){var i=l(a.textContent,r);i&&(n+=i.childNodes.length-1,t.replaceChild(i,a))}else 1===a.nodeType&&function(){var t=" "+a.className+" ";-1===r.ignoredTags.indexOf(a.nodeName.toLowerCase())&&r.ignoredClasses.every((function(e){return-1===t.indexOf(" "+e+" ")}))&&e(a,r)}()}},s=function(e,t){if(!e)throw new Error("No element provided to render");var r={};for(var n in t)t.hasOwnProperty(n)&&(r[n]=t[n]);r.delimiters=r.delimiters||[{left:"$$",right:"$$",display:!0},{left:"\\(",right:"\\)",display:!1},{left:"\\begin{equation}",right:"\\end{equation}",display:!0},{left:"\\begin{align}",right:"\\end{align}",display:!0},{left:"\\begin{alignat}",right:"\\end{alignat}",display:!0},{left:"\\begin{gather}",right:"\\end{gather}",display:!0},{left:"\\begin{CD}",right:"\\end{CD}",display:!0},{left:"\\[",right:"\\]",display:!0}],r.ignoredTags=r.ignoredTags||["script","noscript","style","textarea","pre","code","option"],r.ignoredClasses=r.ignoredClasses||[],r.errorCallback=r.errorCallback||console.error,r.macros=r.macros||{},d(e,r)}}(),a=a.default}()}));

public/js/katex/contrib/auto-render.js

@@ -0,0 +1,327 @@
+(function webpackUniversalModuleDefinition(root, factory) {
+	if(typeof exports === 'object' && typeof module === 'object')
+		module.exports = factory(require("katex"));
+	else if(typeof define === 'function' && define.amd)
+		define(["katex"], factory);
+	else if(typeof exports === 'object')
+		exports["renderMathInElement"] = factory(require("katex"));
+	else
+		root["renderMathInElement"] = factory(root["katex"]);
+})((typeof self !== 'undefined' ? self : this), function(__WEBPACK_EXTERNAL_MODULE__771__) {
+return /******/ (function() { // webpackBootstrap
+/******/ 	"use strict";
+/******/ 	var __webpack_modules__ = ({
+
+/***/ 771:
+/***/ (function(module) {
+
+module.exports = __WEBPACK_EXTERNAL_MODULE__771__;
+
+/***/ })
+
+/******/ 	});
+/************************************************************************/
+/******/ 	// The module cache
+/******/ 	var __webpack_module_cache__ = {};
+/******/ 	
+/******/ 	// The require function
+/******/ 	function __webpack_require__(moduleId) {
+/******/ 		// Check if module is in cache
+/******/ 		var cachedModule = __webpack_module_cache__[moduleId];
+/******/ 		if (cachedModule !== undefined) {
+/******/ 			return cachedModule.exports;
+/******/ 		}
+/******/ 		// Create a new module (and put it into the cache)
+/******/ 		var module = __webpack_module_cache__[moduleId] = {
+/******/ 			// no module.id needed
+/******/ 			// no module.loaded needed
+/******/ 			exports: {}
+/******/ 		};
+/******/ 	
+/******/ 		// Execute the module function
+/******/ 		__webpack_modules__[moduleId](module, module.exports, __webpack_require__);
+/******/ 	
+/******/ 		// Return the exports of the module
+/******/ 		return module.exports;
+/******/ 	}
+/******/ 	
+/************************************************************************/
+/******/ 	/* webpack/runtime/compat get default export */
+/******/ 	!function() {
+/******/ 		// getDefaultExport function for compatibility with non-harmony modules
+/******/ 		__webpack_require__.n = function(module) {
+/******/ 			var getter = module && module.__esModule ?
+/******/ 				function() { return module['default']; } :
+/******/ 				function() { return module; };
+/******/ 			__webpack_require__.d(getter, { a: getter });
+/******/ 			return getter;
+/******/ 		};
+/******/ 	}();
+/******/ 	
+/******/ 	/* webpack/runtime/define property getters */
+/******/ 	!function() {
+/******/ 		// define getter functions for harmony exports
+/******/ 		__webpack_require__.d = function(exports, definition) {
+/******/ 			for(var key in definition) {
+/******/ 				if(__webpack_require__.o(definition, key) && !__webpack_require__.o(exports, key)) {
+/******/ 					Object.defineProperty(exports, key, { enumerable: true, get: definition[key] });
+/******/ 				}
+/******/ 			}
+/******/ 		};
+/******/ 	}();
+/******/ 	
+/******/ 	/* webpack/runtime/hasOwnProperty shorthand */
+/******/ 	!function() {
+/******/ 		__webpack_require__.o = function(obj, prop) { return Object.prototype.hasOwnProperty.call(obj, prop); }
+/******/ 	}();
+/******/ 	
+/************************************************************************/
+var __webpack_exports__ = {};
+// This entry need to be wrapped in an IIFE because it need to be isolated against other modules in the chunk.
+!function() {
+
+// EXPORTS
+__webpack_require__.d(__webpack_exports__, {
+  "default": function() { return /* binding */ auto_render; }
+});
+
+// EXTERNAL MODULE: external "katex"
+var external_katex_ = __webpack_require__(771);
+var external_katex_default = /*#__PURE__*/__webpack_require__.n(external_katex_);
+;// CONCATENATED MODULE: ./contrib/auto-render/splitAtDelimiters.js
+/* eslint no-constant-condition:0 */
+var findEndOfMath = function findEndOfMath(delimiter, text, startIndex) {
+  // Adapted from
+  // https://github.com/Khan/perseus/blob/master/src/perseus-markdown.jsx
+  var index = startIndex;
+  var braceLevel = 0;
+  var delimLength = delimiter.length;
+
+  while (index < text.length) {
+    var character = text[index];
+
+    if (braceLevel <= 0 && text.slice(index, index + delimLength) === delimiter) {
+      return index;
+    } else if (character === "\\") {
+      index++;
+    } else if (character === "{") {
+      braceLevel++;
+    } else if (character === "}") {
+      braceLevel--;
+    }
+
+    index++;
+  }
+
+  return -1;
+};
+
+var escapeRegex = function escapeRegex(string) {
+  return string.replace(/[-/\\^$*+?.()|[\]{}]/g, "\\$&");
+};
+
+var amsRegex = /^\\begin{/;
+
+var splitAtDelimiters = function splitAtDelimiters(text, delimiters) {
+  var index;
+  var data = [];
+  var regexLeft = new RegExp("(" + delimiters.map(function (x) {
+    return escapeRegex(x.left);
+  }).join("|") + ")");
+
+  while (true) {
+    index = text.search(regexLeft);
+
+    if (index === -1) {
+      break;
+    }
+
+    if (index > 0) {
+      data.push({
+        type: "text",
+        data: text.slice(0, index)
+      });
+      text = text.slice(index); // now text starts with delimiter
+    } // ... so this always succeeds:
+
+
+    var i = delimiters.findIndex(function (delim) {
+      return text.startsWith(delim.left);
+    });
+    index = findEndOfMath(delimiters[i].right, text, delimiters[i].left.length);
+
+    if (index === -1) {
+      break;
+    }
+
+    var rawData = text.slice(0, index + delimiters[i].right.length);
+    var math = amsRegex.test(rawData) ? rawData : text.slice(delimiters[i].left.length, index);
+    data.push({
+      type: "math",
+      data: math,
+      rawData: rawData,
+      display: delimiters[i].display
+    });
+    text = text.slice(index + delimiters[i].right.length);
+  }
+
+  if (text !== "") {
+    data.push({
+      type: "text",
+      data: text
+    });
+  }
+
+  return data;
+};
+
+/* harmony default export */ var auto_render_splitAtDelimiters = (splitAtDelimiters);
+;// CONCATENATED MODULE: ./contrib/auto-render/auto-render.js
+/* eslint no-console:0 */
+
+
+/* Note: optionsCopy is mutated by this method. If it is ever exposed in the
+ * API, we should copy it before mutating.
+ */
+
+var renderMathInText = function renderMathInText(text, optionsCopy) {
+  var data = auto_render_splitAtDelimiters(text, optionsCopy.delimiters);
+
+  if (data.length === 1 && data[0].type === 'text') {
+    // There is no formula in the text.
+    // Let's return null which means there is no need to replace
+    // the current text node with a new one.
+    return null;
+  }
+
+  var fragment = document.createDocumentFragment();
+
+  for (var i = 0; i < data.length; i++) {
+    if (data[i].type === "text") {
+      fragment.appendChild(document.createTextNode(data[i].data));
+    } else {
+      var span = document.createElement("span");
+      var math = data[i].data; // Override any display mode defined in the settings with that
+      // defined by the text itself
+
+      optionsCopy.displayMode = data[i].display;
+
+      try {
+        if (optionsCopy.preProcess) {
+          math = optionsCopy.preProcess(math);
+        }
+
+        external_katex_default().render(math, span, optionsCopy);
+      } catch (e) {
+        if (!(e instanceof (external_katex_default()).ParseError)) {
+          throw e;
+        }
+
+        optionsCopy.errorCallback("KaTeX auto-render: Failed to parse `" + data[i].data + "` with ", e);
+        fragment.appendChild(document.createTextNode(data[i].rawData));
+        continue;
+      }
+
+      fragment.appendChild(span);
+    }
+  }
+
+  return fragment;
+};
+
+var renderElem = function renderElem(elem, optionsCopy) {
+  for (var i = 0; i < elem.childNodes.length; i++) {
+    var childNode = elem.childNodes[i];
+
+    if (childNode.nodeType === 3) {
+      // Text node
+      var frag = renderMathInText(childNode.textContent, optionsCopy);
+
+      if (frag) {
+        i += frag.childNodes.length - 1;
+        elem.replaceChild(frag, childNode);
+      }
+    } else if (childNode.nodeType === 1) {
+      (function () {
+        // Element node
+        var className = ' ' + childNode.className + ' ';
+        var shouldRender = optionsCopy.ignoredTags.indexOf(childNode.nodeName.toLowerCase()) === -1 && optionsCopy.ignoredClasses.every(function (x) {
+          return className.indexOf(' ' + x + ' ') === -1;
+        });
+
+        if (shouldRender) {
+          renderElem(childNode, optionsCopy);
+        }
+      })();
+    } // Otherwise, it's something else, and ignore it.
+
+  }
+};
+
+var renderMathInElement = function renderMathInElement(elem, options) {
+  if (!elem) {
+    throw new Error("No element provided to render");
+  }
+
+  var optionsCopy = {}; // Object.assign(optionsCopy, option)
+
+  for (var option in options) {
+    if (options.hasOwnProperty(option)) {
+      optionsCopy[option] = options[option];
+    }
+  } // default options
+
+
+  optionsCopy.delimiters = optionsCopy.delimiters || [{
+    left: "$$",
+    right: "$$",
+    display: true
+  }, {
+    left: "\\(",
+    right: "\\)",
+    display: false
+  }, // LaTeX uses $…$, but it ruins the display of normal `$` in text:
+  // {left: "$", right: "$", display: false},
+  // $ must come after $$
+  // Render AMS environments even if outside $$…$$ delimiters.
+  {
+    left: "\\begin{equation}",
+    right: "\\end{equation}",
+    display: true
+  }, {
+    left: "\\begin{align}",
+    right: "\\end{align}",
+    display: true
+  }, {
+    left: "\\begin{alignat}",
+    right: "\\end{alignat}",
+    display: true
+  }, {
+    left: "\\begin{gather}",
+    right: "\\end{gather}",
+    display: true
+  }, {
+    left: "\\begin{CD}",
+    right: "\\end{CD}",
+    display: true
+  }, {
+    left: "\\[",
+    right: "\\]",
+    display: true
+  }];
+  optionsCopy.ignoredTags = optionsCopy.ignoredTags || ["script", "noscript", "style", "textarea", "pre", "code", "option"];
+  optionsCopy.ignoredClasses = optionsCopy.ignoredClasses || [];
+  optionsCopy.errorCallback = optionsCopy.errorCallback || console.error; // Enable sharing of global macros defined via `\gdef` between different
+  // math elements within a single call to `renderMathInElement`.
+
+  optionsCopy.macros = optionsCopy.macros || {};
+  renderElem(elem, optionsCopy);
+};
+
+/* harmony default export */ var auto_render = (renderMathInElement);
+}();
+__webpack_exports__ = __webpack_exports__["default"];
+/******/ 	return __webpack_exports__;
+/******/ })()
+;
+});

public/js/katex/contrib/auto-render.min.js

@@ -0,0 +1 @@
+!function(e,t){"object"==typeof exports&&"object"==typeof module?module.exports=t(require("katex")):"function"==typeof define&&define.amd?define(["katex"],t):"object"==typeof exports?exports.renderMathInElement=t(require("katex")):e.renderMathInElement=t(e.katex)}("undefined"!=typeof self?self:this,(function(e){return function(){"use strict";var t={771:function(t){t.exports=e}},r={};function n(e){var a=r[e];if(void 0!==a)return a.exports;var i=r[e]={exports:{}};return t[e](i,i.exports,n),i.exports}n.n=function(e){var t=e&&e.__esModule?function(){return e.default}:function(){return e};return n.d(t,{a:t}),t},n.d=function(e,t){for(var r in t)n.o(t,r)&&!n.o(e,r)&&Object.defineProperty(e,r,{enumerable:!0,get:t[r]})},n.o=function(e,t){return Object.prototype.hasOwnProperty.call(e,t)};var a={};return function(){n.d(a,{default:function(){return s}});var e=n(771),t=n.n(e),r=function(e,t,r){for(var n=r,a=0,i=e.length;n<t.length;){var o=t[n];if(a<=0&&t.slice(n,n+i)===e)return n;"\\"===o?n++:"{"===o?a++:"}"===o&&a--,n++}return-1},i=/^\\begin{/,o=function(e,t){for(var n,a=[],o=new RegExp("("+t.map((function(e){return e.left.replace(/[-/\\^$*+?.()|[\]{}]/g,"\\$&")})).join("|")+")");-1!==(n=e.search(o));){n>0&&(a.push({type:"text",data:e.slice(0,n)}),e=e.slice(n));var l=t.findIndex((function(t){return e.startsWith(t.left)}));if(-1===(n=r(t[l].right,e,t[l].left.length)))break;var d=e.slice(0,n+t[l].right.length),s=i.test(d)?d:e.slice(t[l].left.length,n);a.push({type:"math",data:s,rawData:d,display:t[l].display}),e=e.slice(n+t[l].right.length)}return""!==e&&a.push({type:"text",data:e}),a},l=function(e,r){var n=o(e,r.delimiters);if(1===n.length&&"text"===n[0].type)return null;for(var a=document.createDocumentFragment(),i=0;i<n.length;i++)if("text"===n[i].type)a.appendChild(document.createTextNode(n[i].data));else{var l=document.createElement("span"),d=n[i].data;r.displayMode=n[i].display;try{r.preProcess&&(d=r.preProcess(d)),t().render(d,l,r)}catch(e){if(!(e instanceof t().ParseError))throw e;r.errorCallback("KaTeX auto-render: Failed to parse `"+n[i].data+"` with ",e),a.appendChild(document.createTextNode(n[i].rawData));continue}a.appendChild(l)}return a},d=function e(t,r){for(var n=0;n<t.childNodes.length;n++){var a=t.childNodes[n];if(3===a.nodeType){var i=l(a.textContent,r);i&&(n+=i.childNodes.length-1,t.replaceChild(i,a))}else 1===a.nodeType&&function(){var t=" "+a.className+" ";-1===r.ignoredTags.indexOf(a.nodeName.toLowerCase())&&r.ignoredClasses.every((function(e){return-1===t.indexOf(" "+e+" ")}))&&e(a,r)}()}},s=function(e,t){if(!e)throw new Error("No element provided to render");var r={};for(var n in t)t.hasOwnProperty(n)&&(r[n]=t[n]);r.delimiters=r.delimiters||[{left:"$$",right:"$$",display:!0},{left:"\\(",right:"\\)",display:!1},{left:"\\begin{equation}",right:"\\end{equation}",display:!0},{left:"\\begin{align}",right:"\\end{align}",display:!0},{left:"\\begin{alignat}",right:"\\end{alignat}",display:!0},{left:"\\begin{gather}",right:"\\end{gather}",display:!0},{left:"\\begin{CD}",right:"\\end{CD}",display:!0},{left:"\\[",right:"\\]",display:!0}],r.ignoredTags=r.ignoredTags||["script","noscript","style","textarea","pre","code","option"],r.ignoredClasses=r.ignoredClasses||[],r.errorCallback=r.errorCallback||console.error,r.macros=r.macros||{},d(e,r)}}(),a=a.default}()}));

public/js/katex/contrib/auto-render.mjs

@@ -0,0 +1,222 @@
+import katex from '../katex.mjs';
+
+/* eslint no-constant-condition:0 */
+var findEndOfMath = function findEndOfMath(delimiter, text, startIndex) {
+  // Adapted from
+  // https://github.com/Khan/perseus/blob/master/src/perseus-markdown.jsx
+  var index = startIndex;
+  var braceLevel = 0;
+  var delimLength = delimiter.length;
+
+  while (index < text.length) {
+    var character = text[index];
+
+    if (braceLevel <= 0 && text.slice(index, index + delimLength) === delimiter) {
+      return index;
+    } else if (character === "\\") {
+      index++;
+    } else if (character === "{") {
+      braceLevel++;
+    } else if (character === "}") {
+      braceLevel--;
+    }
+
+    index++;
+  }
+
+  return -1;
+};
+
+var escapeRegex = function escapeRegex(string) {
+  return string.replace(/[-/\\^$*+?.()|[\]{}]/g, "\\$&");
+};
+
+var amsRegex = /^\\begin{/;
+
+var splitAtDelimiters = function splitAtDelimiters(text, delimiters) {
+  var index;
+  var data = [];
+  var regexLeft = new RegExp("(" + delimiters.map(x => escapeRegex(x.left)).join("|") + ")");
+
+  while (true) {
+    index = text.search(regexLeft);
+
+    if (index === -1) {
+      break;
+    }
+
+    if (index > 0) {
+      data.push({
+        type: "text",
+        data: text.slice(0, index)
+      });
+      text = text.slice(index); // now text starts with delimiter
+    } // ... so this always succeeds:
+
+
+    var i = delimiters.findIndex(delim => text.startsWith(delim.left));
+    index = findEndOfMath(delimiters[i].right, text, delimiters[i].left.length);
+
+    if (index === -1) {
+      break;
+    }
+
+    var rawData = text.slice(0, index + delimiters[i].right.length);
+    var math = amsRegex.test(rawData) ? rawData : text.slice(delimiters[i].left.length, index);
+    data.push({
+      type: "math",
+      data: math,
+      rawData,
+      display: delimiters[i].display
+    });
+    text = text.slice(index + delimiters[i].right.length);
+  }
+
+  if (text !== "") {
+    data.push({
+      type: "text",
+      data: text
+    });
+  }
+
+  return data;
+};
+
+/* eslint no-console:0 */
+/* Note: optionsCopy is mutated by this method. If it is ever exposed in the
+ * API, we should copy it before mutating.
+ */
+
+var renderMathInText = function renderMathInText(text, optionsCopy) {
+  var data = splitAtDelimiters(text, optionsCopy.delimiters);
+
+  if (data.length === 1 && data[0].type === 'text') {
+    // There is no formula in the text.
+    // Let's return null which means there is no need to replace
+    // the current text node with a new one.
+    return null;
+  }
+
+  var fragment = document.createDocumentFragment();
+
+  for (var i = 0; i < data.length; i++) {
+    if (data[i].type === "text") {
+      fragment.appendChild(document.createTextNode(data[i].data));
+    } else {
+      var span = document.createElement("span");
+      var math = data[i].data; // Override any display mode defined in the settings with that
+      // defined by the text itself
+
+      optionsCopy.displayMode = data[i].display;
+
+      try {
+        if (optionsCopy.preProcess) {
+          math = optionsCopy.preProcess(math);
+        }
+
+        katex.render(math, span, optionsCopy);
+      } catch (e) {
+        if (!(e instanceof katex.ParseError)) {
+          throw e;
+        }
+
+        optionsCopy.errorCallback("KaTeX auto-render: Failed to parse `" + data[i].data + "` with ", e);
+        fragment.appendChild(document.createTextNode(data[i].rawData));
+        continue;
+      }
+
+      fragment.appendChild(span);
+    }
+  }
+
+  return fragment;
+};
+
+var renderElem = function renderElem(elem, optionsCopy) {
+  for (var i = 0; i < elem.childNodes.length; i++) {
+    var childNode = elem.childNodes[i];
+
+    if (childNode.nodeType === 3) {
+      // Text node
+      var frag = renderMathInText(childNode.textContent, optionsCopy);
+
+      if (frag) {
+        i += frag.childNodes.length - 1;
+        elem.replaceChild(frag, childNode);
+      }
+    } else if (childNode.nodeType === 1) {
+      (function () {
+        // Element node
+        var className = ' ' + childNode.className + ' ';
+        var shouldRender = optionsCopy.ignoredTags.indexOf(childNode.nodeName.toLowerCase()) === -1 && optionsCopy.ignoredClasses.every(x => className.indexOf(' ' + x + ' ') === -1);
+
+        if (shouldRender) {
+          renderElem(childNode, optionsCopy);
+        }
+      })();
+    } // Otherwise, it's something else, and ignore it.
+
+  }
+};
+
+var renderMathInElement = function renderMathInElement(elem, options) {
+  if (!elem) {
+    throw new Error("No element provided to render");
+  }
+
+  var optionsCopy = {}; // Object.assign(optionsCopy, option)
+
+  for (var option in options) {
+    if (options.hasOwnProperty(option)) {
+      optionsCopy[option] = options[option];
+    }
+  } // default options
+
+
+  optionsCopy.delimiters = optionsCopy.delimiters || [{
+    left: "$$",
+    right: "$$",
+    display: true
+  }, {
+    left: "\\(",
+    right: "\\)",
+    display: false
+  }, // LaTeX uses $…$, but it ruins the display of normal `$` in text:
+  // {left: "$", right: "$", display: false},
+  // $ must come after $$
+  // Render AMS environments even if outside $$…$$ delimiters.
+  {
+    left: "\\begin{equation}",
+    right: "\\end{equation}",
+    display: true
+  }, {
+    left: "\\begin{align}",
+    right: "\\end{align}",
+    display: true
+  }, {
+    left: "\\begin{alignat}",
+    right: "\\end{alignat}",
+    display: true
+  }, {
+    left: "\\begin{gather}",
+    right: "\\end{gather}",
+    display: true
+  }, {
+    left: "\\begin{CD}",
+    right: "\\end{CD}",
+    display: true
+  }, {
+    left: "\\[",
+    right: "\\]",
+    display: true
+  }];
+  optionsCopy.ignoredTags = optionsCopy.ignoredTags || ["script", "noscript", "style", "textarea", "pre", "code", "option"];
+  optionsCopy.ignoredClasses = optionsCopy.ignoredClasses || [];
+  optionsCopy.errorCallback = optionsCopy.errorCallback || console.error; // Enable sharing of global macros defined via `\gdef` between different
+  // math elements within a single call to `renderMathInElement`.
+
+  optionsCopy.macros = optionsCopy.macros || {};
+  renderElem(elem, optionsCopy);
+};
+
+export { renderMathInElement as default };

public/js/katex/contrib/copy-tex.css

@@ -0,0 +1,13 @@
+/* Force selection of entire .katex/.katex-display blocks, so that we can
+ * copy/paste the entire source code.  If you omit this CSS, partial
+ * selections of a formula will work, but will copy the ugly HTML
+ * representation instead of the LaTeX source code.  (Full selections will
+ * still produce the LaTeX source code.)
+ */
+.katex,
+.katex-display {
+    -webkit-user-select: all;
+       -moz-user-select: all;
+            user-select: all;
+}
+

public/js/katex/contrib/copy-tex.js

@@ -0,0 +1,116 @@
+(function webpackUniversalModuleDefinition(root, factory) {
+	if(typeof exports === 'object' && typeof module === 'object')
+		module.exports = factory();
+	else if(typeof define === 'function' && define.amd)
+		define([], factory);
+	else {
+		var a = factory();
+		for(var i in a) (typeof exports === 'object' ? exports : root)[i] = a[i];
+	}
+})((typeof self !== 'undefined' ? self : this), function() {
+return /******/ (function() { // webpackBootstrap
+/******/ 	"use strict";
+var __webpack_exports__ = {};
+
+;// CONCATENATED MODULE: ./contrib/copy-tex/katex2tex.js
+// Set these to how you want inline and display math to be delimited.
+var defaultCopyDelimiters = {
+  inline: ['$', '$'],
+  // alternative: ['\(', '\)']
+  display: ['$$', '$$'] // alternative: ['\[', '\]']
+
+}; // Replace .katex elements with their TeX source (<annotation> element).
+// Modifies fragment in-place.  Useful for writing your own 'copy' handler,
+// as in copy-tex.js.
+
+var katexReplaceWithTex = function katexReplaceWithTex(fragment, copyDelimiters) {
+  if (copyDelimiters === void 0) {
+    copyDelimiters = defaultCopyDelimiters;
+  }
+
+  // Remove .katex-html blocks that are preceded by .katex-mathml blocks
+  // (which will get replaced below).
+  var katexHtml = fragment.querySelectorAll('.katex-mathml + .katex-html');
+
+  for (var i = 0; i < katexHtml.length; i++) {
+    var element = katexHtml[i];
+
+    if (element.remove) {
+      element.remove(null);
+    } else {
+      element.parentNode.removeChild(element);
+    }
+  } // Replace .katex-mathml elements with their annotation (TeX source)
+  // descendant, with inline delimiters.
+
+
+  var katexMathml = fragment.querySelectorAll('.katex-mathml');
+
+  for (var _i = 0; _i < katexMathml.length; _i++) {
+    var _element = katexMathml[_i];
+
+    var texSource = _element.querySelector('annotation');
+
+    if (texSource) {
+      if (_element.replaceWith) {
+        _element.replaceWith(texSource);
+      } else {
+        _element.parentNode.replaceChild(texSource, _element);
+      }
+
+      texSource.innerHTML = copyDelimiters.inline[0] + texSource.innerHTML + copyDelimiters.inline[1];
+    }
+  } // Switch display math to display delimiters.
+
+
+  var displays = fragment.querySelectorAll('.katex-display annotation');
+
+  for (var _i2 = 0; _i2 < displays.length; _i2++) {
+    var _element2 = displays[_i2];
+    _element2.innerHTML = copyDelimiters.display[0] + _element2.innerHTML.substr(copyDelimiters.inline[0].length, _element2.innerHTML.length - copyDelimiters.inline[0].length - copyDelimiters.inline[1].length) + copyDelimiters.display[1];
+  }
+
+  return fragment;
+};
+/* harmony default export */ var katex2tex = (katexReplaceWithTex);
+;// CONCATENATED MODULE: ./contrib/copy-tex/copy-tex.js
+ // Global copy handler to modify behavior on .katex elements.
+
+document.addEventListener('copy', function (event) {
+  var selection = window.getSelection();
+
+  if (selection.isCollapsed) {
+    return; // default action OK if selection is empty
+  }
+
+  var fragment = selection.getRangeAt(0).cloneContents();
+
+  if (!fragment.querySelector('.katex-mathml')) {
+    return; // default action OK if no .katex-mathml elements
+  } // Preserve usual HTML copy/paste behavior.
+
+
+  var html = [];
+
+  for (var i = 0; i < fragment.childNodes.length; i++) {
+    html.push(fragment.childNodes[i].outerHTML);
+  }
+
+  event.clipboardData.setData('text/html', html.join('')); // Rewrite plain-text version.
+
+  event.clipboardData.setData('text/plain', katex2tex(fragment).textContent); // Prevent normal copy handling.
+
+  event.preventDefault();
+});
+;// CONCATENATED MODULE: ./contrib/copy-tex/copy-tex.webpack.js
+/**
+ * This is the webpack entry point for KaTeX. As ECMAScript doesn't support
+ * CSS modules natively, a separate entry point is used.
+ */
+
+
+__webpack_exports__ = __webpack_exports__["default"];
+/******/ 	return __webpack_exports__;
+/******/ })()
+;
+});

public/js/katex/contrib/copy-tex.min.css

@@ -0,0 +1 @@
+.katex,.katex-display{-webkit-user-select:all;-moz-user-select:all;user-select:all}

public/js/katex/contrib/copy-tex.min.js

@@ -0,0 +1 @@
+!function(e,t){if("object"==typeof exports&&"object"==typeof module)module.exports=t();else if("function"==typeof define&&define.amd)define([],t);else{var n=t();for(var l in n)("object"==typeof exports?exports:e)[l]=n[l]}}("undefined"!=typeof self?self:this,(function(){return function(){"use strict";var e={},t={inline:["$","$"],display:["$$","$$"]},n=function(e,n){void 0===n&&(n=t);for(var l=e.querySelectorAll(".katex-mathml + .katex-html"),r=0;r<l.length;r++){var i=l[r];i.remove?i.remove(null):i.parentNode.removeChild(i)}for(var o=e.querySelectorAll(".katex-mathml"),a=0;a<o.length;a++){var d=o[a],f=d.querySelector("annotation");f&&(d.replaceWith?d.replaceWith(f):d.parentNode.replaceChild(f,d),f.innerHTML=n.inline[0]+f.innerHTML+n.inline[1])}for(var c=e.querySelectorAll(".katex-display annotation"),s=0;s<c.length;s++){var p=c[s];p.innerHTML=n.display[0]+p.innerHTML.substr(n.inline[0].length,p.innerHTML.length-n.inline[0].length-n.inline[1].length)+n.display[1]}return e};return document.addEventListener("copy",(function(e){var t=window.getSelection();if(!t.isCollapsed){var l=t.getRangeAt(0).cloneContents();if(l.querySelector(".katex-mathml")){for(var r=[],i=0;i<l.childNodes.length;i++)r.push(l.childNodes[i].outerHTML);e.clipboardData.setData("text/html",r.join("")),e.clipboardData.setData("text/plain",n(l).textContent),e.preventDefault()}}})),e=e.default}()}));

public/js/katex/contrib/copy-tex.mjs

@@ -0,0 +1,86 @@
+// Set these to how you want inline and display math to be delimited.
+var defaultCopyDelimiters = {
+  inline: ['$', '$'],
+  // alternative: ['\(', '\)']
+  display: ['$$', '$$'] // alternative: ['\[', '\]']
+
+}; // Replace .katex elements with their TeX source (<annotation> element).
+// Modifies fragment in-place.  Useful for writing your own 'copy' handler,
+// as in copy-tex.js.
+
+var katexReplaceWithTex = function katexReplaceWithTex(fragment, copyDelimiters) {
+  if (copyDelimiters === void 0) {
+    copyDelimiters = defaultCopyDelimiters;
+  }
+
+  // Remove .katex-html blocks that are preceded by .katex-mathml blocks
+  // (which will get replaced below).
+  var katexHtml = fragment.querySelectorAll('.katex-mathml + .katex-html');
+
+  for (var i = 0; i < katexHtml.length; i++) {
+    var element = katexHtml[i];
+
+    if (element.remove) {
+      element.remove(null);
+    } else {
+      element.parentNode.removeChild(element);
+    }
+  } // Replace .katex-mathml elements with their annotation (TeX source)
+  // descendant, with inline delimiters.
+
+
+  var katexMathml = fragment.querySelectorAll('.katex-mathml');
+
+  for (var _i = 0; _i < katexMathml.length; _i++) {
+    var _element = katexMathml[_i];
+
+    var texSource = _element.querySelector('annotation');
+
+    if (texSource) {
+      if (_element.replaceWith) {
+        _element.replaceWith(texSource);
+      } else {
+        _element.parentNode.replaceChild(texSource, _element);
+      }
+
+      texSource.innerHTML = copyDelimiters.inline[0] + texSource.innerHTML + copyDelimiters.inline[1];
+    }
+  } // Switch display math to display delimiters.
+
+
+  var displays = fragment.querySelectorAll('.katex-display annotation');
+
+  for (var _i2 = 0; _i2 < displays.length; _i2++) {
+    var _element2 = displays[_i2];
+    _element2.innerHTML = copyDelimiters.display[0] + _element2.innerHTML.substr(copyDelimiters.inline[0].length, _element2.innerHTML.length - copyDelimiters.inline[0].length - copyDelimiters.inline[1].length) + copyDelimiters.display[1];
+  }
+
+  return fragment;
+};
+
+document.addEventListener('copy', function (event) {
+  var selection = window.getSelection();
+
+  if (selection.isCollapsed) {
+    return; // default action OK if selection is empty
+  }
+
+  var fragment = selection.getRangeAt(0).cloneContents();
+
+  if (!fragment.querySelector('.katex-mathml')) {
+    return; // default action OK if no .katex-mathml elements
+  } // Preserve usual HTML copy/paste behavior.
+
+
+  var html = [];
+
+  for (var i = 0; i < fragment.childNodes.length; i++) {
+    html.push(fragment.childNodes[i].outerHTML);
+  }
+
+  event.clipboardData.setData('text/html', html.join('')); // Rewrite plain-text version.
+
+  event.clipboardData.setData('text/plain', katexReplaceWithTex(fragment).textContent); // Prevent normal copy handling.
+
+  event.preventDefault();
+});

public/js/katex/contrib/mathtex-script-type.js

@@ -0,0 +1,112 @@
+(function webpackUniversalModuleDefinition(root, factory) {
+	if(typeof exports === 'object' && typeof module === 'object')
+		module.exports = factory(require("katex"));
+	else if(typeof define === 'function' && define.amd)
+		define(["katex"], factory);
+	else {
+		var a = typeof exports === 'object' ? factory(require("katex")) : factory(root["katex"]);
+		for(var i in a) (typeof exports === 'object' ? exports : root)[i] = a[i];
+	}
+})((typeof self !== 'undefined' ? self : this), function(__WEBPACK_EXTERNAL_MODULE__771__) {
+return /******/ (function() { // webpackBootstrap
+/******/ 	"use strict";
+/******/ 	var __webpack_modules__ = ({
+
+/***/ 771:
+/***/ (function(module) {
+
+module.exports = __WEBPACK_EXTERNAL_MODULE__771__;
+
+/***/ })
+
+/******/ 	});
+/************************************************************************/
+/******/ 	// The module cache
+/******/ 	var __webpack_module_cache__ = {};
+/******/ 	
+/******/ 	// The require function
+/******/ 	function __webpack_require__(moduleId) {
+/******/ 		// Check if module is in cache
+/******/ 		var cachedModule = __webpack_module_cache__[moduleId];
+/******/ 		if (cachedModule !== undefined) {
+/******/ 			return cachedModule.exports;
+/******/ 		}
+/******/ 		// Create a new module (and put it into the cache)
+/******/ 		var module = __webpack_module_cache__[moduleId] = {
+/******/ 			// no module.id needed
+/******/ 			// no module.loaded needed
+/******/ 			exports: {}
+/******/ 		};
+/******/ 	
+/******/ 		// Execute the module function
+/******/ 		__webpack_modules__[moduleId](module, module.exports, __webpack_require__);
+/******/ 	
+/******/ 		// Return the exports of the module
+/******/ 		return module.exports;
+/******/ 	}
+/******/ 	
+/************************************************************************/
+/******/ 	/* webpack/runtime/compat get default export */
+/******/ 	!function() {
+/******/ 		// getDefaultExport function for compatibility with non-harmony modules
+/******/ 		__webpack_require__.n = function(module) {
+/******/ 			var getter = module && module.__esModule ?
+/******/ 				function() { return module['default']; } :
+/******/ 				function() { return module; };
+/******/ 			__webpack_require__.d(getter, { a: getter });
+/******/ 			return getter;
+/******/ 		};
+/******/ 	}();
+/******/ 	
+/******/ 	/* webpack/runtime/define property getters */
+/******/ 	!function() {
+/******/ 		// define getter functions for harmony exports
+/******/ 		__webpack_require__.d = function(exports, definition) {
+/******/ 			for(var key in definition) {
+/******/ 				if(__webpack_require__.o(definition, key) && !__webpack_require__.o(exports, key)) {
+/******/ 					Object.defineProperty(exports, key, { enumerable: true, get: definition[key] });
+/******/ 				}
+/******/ 			}
+/******/ 		};
+/******/ 	}();
+/******/ 	
+/******/ 	/* webpack/runtime/hasOwnProperty shorthand */
+/******/ 	!function() {
+/******/ 		__webpack_require__.o = function(obj, prop) { return Object.prototype.hasOwnProperty.call(obj, prop); }
+/******/ 	}();
+/******/ 	
+/************************************************************************/
+var __webpack_exports__ = {};
+// This entry need to be wrapped in an IIFE because it need to be isolated against other modules in the chunk.
+!function() {
+/* harmony import */ var katex__WEBPACK_IMPORTED_MODULE_0__ = __webpack_require__(771);
+/* harmony import */ var katex__WEBPACK_IMPORTED_MODULE_0___default = /*#__PURE__*/__webpack_require__.n(katex__WEBPACK_IMPORTED_MODULE_0__);
+
+var scripts = document.body.getElementsByTagName("script");
+scripts = Array.prototype.slice.call(scripts);
+scripts.forEach(function (script) {
+  if (!script.type || !script.type.match(/math\/tex/i)) {
+    return -1;
+  }
+