Enable MathJax for documentation

doc/DaphneDSL/Builtins.md

@@ -74,7 +74,7 @@ DaphneDSL's built-in functions can be categorized as follows:
 
 - **`sample`**`(range:scalar, size:size, withReplacement:bool, seed:si64)`
 
-    Generates a *(`size` x 1)* column-matrix of values drawn from the range *[0, `range` - 1]*.
+    Generates a *(`size` x 1)* column-matrix of values drawn from the range *[0, `range - 1`]*.
     The parameter `withReplacement` determines if a value can be drawn multiple times (`true`) or not (`false`).
     The `seed` can be set to `-1` (randomly chooses a seed), or be provided explicitly to enable reproducible random values.
 
@@ -121,6 +121,7 @@ The following built-in functions all follow the same scheme:
 ### Trigonometric/Hyperbolic
 
 `arg` unit must be radians (conversion: $x^\circ * \frac{\pi}{180^\circ} = y$ radians)
+
 | function | meaning |
 | ----- | ----- |
 | **`sin`** | sine |
@@ -129,9 +130,9 @@ The following built-in functions all follow the same scheme:
 | **`asin`** | arc sine  (inverse of sine) |
 | **`acos`** | arc cosine (inverse of cosine) |
 | **`atan`** | arc tangent (inverse of tangent) |
-| **`sinh`** | hyperbolic sine ($\frac{e^\text{arg}-e^\text{ - arg}}{2}$) |
-| **`cosh`** | hyperbolic cosine ($\frac{e^\text{arg}+e^\text{ - arg}}{2}$) |
-| **`tanh`** | hyperbolic tangent ($\frac{\text{sinh arg}}{\text{cosh arg}}$) |
+| **`sinh`** | hyperbolic sine $\left( \frac{\exp(\text{arg}) \, - \, \exp(\text{ - arg})}{2} \right)$ |
+| **`cosh`** | hyperbolic cosine $\left( \frac{\exp(\text{arg}) \, + \, \exp(\text{ - arg})}{2} \right)$ |
+| **`tanh`** | hyperbolic tangent $\left( \frac{\text{sinh arg}}{\text{cosh arg}} \right)$ |
 
 ### Rounding
 
@@ -401,12 +402,14 @@ Note that most of these operations only have a CUDNN-based kernel for GPU execut
 
     Returns the contingency table of two *(n x 1)* column-matrices `ys` and `xs`.
     The resulting matrix `res` consists of `max(ys) + 1` rows and `max(xs) + 1` columns.
-    More precisely, *`res[x, y]` = |{ k | `ys[k, 0]` = y and `xs[k, 0]` = x, 0 ≤ k ≤ n-1 }| * `weight`*.
+    More precisely,
+    $\text{res}[x, y] = \left| \{ k \bigm| \text{ys}[k, 0] = y \wedge \text{xs}[k, 0] = x, \; 0 \leq k \leq n-1 \} \right| * \text{weight} \quad \forall x \in \text{xs}, y \in \text{ys}$.
 
-    In other words, starting with an all-zero result matrix, `ys` and `xs` can be thought of as lists of `y`/`x`-coordinates which indicate the result matrix's cells whose value shall be increased by `weight`.
+    In other words, starting with an all-zero result matrix, all pairs of values $\{ (\text{xs}[k, 0],\text{ys}[k, 0]) \mid 0 \leq k \leq n-1 \}$
+    are used to index the result matrix and increase the corresponding value by `weight`.  
     Note that `ys` and `xs` must not contain negative numbers.
 
-    The scalar weight is an optional argument and defaults to 1.0.
+    The scalar weight is an optional argument and defaults to `1.0`.
     The weight also determines the value type of the result.
 
     Moreover, optionally, the result shape in terms of the number of rows and columns can be specified.
@@ -566,6 +569,7 @@ These must be provided in a separate [`.meta`-file](/doc/FileMetaDataFormat.md).
     That way, only point predicates are possible on the encoded output.
 
     There are two results:
+
     - The first result is the encoded data, a *(n x 1)* matrix of the codes for each element in the input `arg`.
     - The second result is the decoding dictionary, a *(#distinct(`arg`) x 1)* matrix of the distinct values in `arg`.
         The value at position *i* is the value that is mapped to the code *i*.

doc/DaphneDSL/LanguageRef.md

@@ -329,7 +329,7 @@ So far, this is only supported for addressing columns of frames.
 This is not supported for addressing columns of frames yet.
 
 For each row/column, a single zero/one entry ("bit") must be provided.
-More precisely, a (*r x 1*) matrix is required on data objects with *r* rows, and a (*c x 1*) matrix is required on data objects with *c* columns.
+More precisely, a (*n x 1*) matrix is required on data objects with *n* rows, and a (*m x 1*) matrix is required on data objects with *m* columns.
 Only the rows/columns with a corresponding 1-value in the bit vector are present in the result.
 
 Note that double square brackets (`[[...]]`) must be used to distinguish indexing by bit vector from indexing by an arbitrary sequence of positions.

doc/DaphneLib/Overview.md

@@ -54,7 +54,7 @@ Users can easily mix and match DAPHNE computations with other Python libraries a
 
 ## Introductory Example
 
-The following simple example script generates a *5x3* matrix of random values in *[0, 1)* using numpy, imports the data to DAPHNE, and shifts and scales the data such that each column has a mean of *0* and a standard deviation of *1*.
+The following simple example script generates a *5x3* matrix of random values in $[0, 1)$ using numpy, imports the data to DAPHNE, and shifts and scales the data such that each column has a mean of *0* and a standard deviation of *1*.
 
 ```python
 # (1) Import DaphneLib.

doc/javascripts/mathjax.js

@@ -0,0 +1,12 @@
+window.MathJax = {
+    tex: {
+        inlineMath: [["\\(", "\\)"]],
+        displayMath: [["\\[", "\\]"]],
+        processEscapes: true,
+        processEnvironments: true
+    },
+    options: {
+        ignoreHtmlClass: ".*|",
+        processHtmlClass: "arithmatex"
+    }
+};

mkdocs.yml

@@ -27,6 +27,8 @@ theme:
     - navigation.tabs
     - navigation.tabs.sticky
 markdown_extensions:
+  - pymdownx.arithmatex:
+      generic: true
   - pymdownx.highlight:
       anchor_linenums: true
   - pymdownx.inlinehilite
@@ -35,6 +37,10 @@ markdown_extensions:
   - pymdownx.striphtml
 extra_css:
   - stylesheets/extra.css
+extra_javascript:
+  - javascripts/mathjax.js
+  - https://polyfill.io/v3/polyfill.min.js?features=es6
+  - https://unpkg.com/mathjax@3/es5/tex-mml-chtml.js
 repo_url: https://github.com/daphne-eu/daphne
 repo_name: daphne-eu/daphne
 nav: