feat: Add derivatives, incl. high-order and mixed partial

docs/support_table.md

@@ -360,6 +360,7 @@ use `\ce` instead|
 |\downharpoonleft|$\downharpoonleft$||
 |\downharpoonright|$\downharpoonright$||
 |{drcases}|$\begin{drcases}a&\text{if }b\\c&\text{if }d\end{drcases}$|`\begin{drcases}`<br>&nbsp;&nbsp;&nbsp;`a &\text{if } b  \\`<br>&nbsp;&nbsp;&nbsp;`c &\text{if } d`<br>`\end{drcases}`|
+|\dv|$\dv{f}{t} \dv[2]{y}{x}$|`\dv{f}{t} \dv[2]{y}{x}`|
 
 ## E
 
@@ -791,6 +792,7 @@ use `\ce` instead|
 |\O|$\text{\O}$|`\text{\O}`|
 |\o|$\text{\o}$|`\text{\o}`|
 |\odot|$\odot$||
+|\odv|$\odv{f}{t} \odv[2]{y}{x}$|`\odv{f}{t} \odv[2]{y}{x}`|
 |\OE|$\text{\OE}$|`\text{\OE}`|
 |\oe|$\text{\oe}$|`\text{\oe}`|
 |\officialeuro|<span style="color:firebrick;">Not supported</span>||
@@ -837,6 +839,7 @@ use `\ce` instead|
 |\parallel|$\parallel$||
 |\part|<span style="color:firebrick;">Not supported</span>|[Deprecated](https://en.wikipedia.org/wiki/Help:Displaying_a_formula#Deprecated_syntax)|
 |\partial|$\partial$||
+|\pdv|$\pdv{f}{t} \pdv[2,2][4]{\psi}{x, y}$|`\pdv{f}{t} \pdv[2,2][4]{\psi}{x, y}`|
 |\perp|$\perp$||
 |\phantom|$\Gamma^{\phantom{i}j}_{i\phantom{j}k}$|`\Gamma^{\phantom{i}j}_{i\phantom{j}k}`|
 |\phase|$\phase{-78^\circ}$|`\phase{-78^\circ}`|

docs/supported.md

@@ -559,6 +559,40 @@ Direct Input: $← ↑ → ↓ ↔ ↕ ↖ ↗ ↘ ↙ ↚ ↛ ↞ ↠ ↢ ↣ 
 
 Extensible arrows all can take an optional argument in the same manner<br>as `\xrightarrow[under]{over}`.
 
+## Derivatives
+
+The syntax closely emulates popular $LaTeX$ packages that provide derivatives,
+such as `physics`, `diffcoef`, and `derivative`.
+
+|||
+|:----------|:----------|
+|$\odv{}{t}$ `\odv{}{t}`   |$\odv[2]{}{x}$ `\odv[2]{}{x}`  |
+|$\odv{f}{t}$ `\odv{f}{t}` |$\odv[2]{y}{x}$ `\odv[2]{y}{x}`|
+|$\pdv{}{t}$ `\pdv{}{t}`   |$\pdv[2]{}{x}$ `\pdv[2]{}{x}`  |
+|$\pdv{f}{t}$ `\pdv{f}{t}` |$\pdv[2]{y}{x}$ `\pdv[2]{y}{x}`|
+|$\pdv[1,1][2]{}{x,y}$ `\pdv[1,1][2]{}{x,y}`  |$\pdv[1,n][1+n]{}{x,y}$ `\pdv[1,n][1+n]{}{x,y}`  |
+|$\pdv[1,1][2]{z}{x,y}$ `\pdv[1,1][2]{z}{x,y}`|$\pdv[1,n][1+n]{z}{x,y}$ `\pdv[1,n][1+n]{z}{x,y}`|
+|$\pdv[1,N-1][N]{z}{x_{\mu,\sigma},y_\xi}$ `\pdv[1,N-1][N]{z}{x_{\mu,\sigma},y_\xi}`||
+
+Ordinary derivative `\odv[order]{f}{x}`:
+* The first required brace `{f}` holds the function to take derivative of. This
+  brace can be left empty.
+* The second required brace `{x}` holds the variable.
+* `[order]` holds the derivative order. If the order is 1, you may omit this
+    bracket.
+
+Partial derivative `\pdv[var_orders][total_order]{f}{vars}`:
+* The first required brace `{f}` holds the function to take derivative of. This
+  brace can be left empty.
+* The second required brace `{vars}` holds the comma-separated variables, e.g.
+  `{x}`, `{x, y, z_k}`.
+* The first optional braket `[var_orders]` holds the list of derivative orders
+  corresponding to the variables, e.g. `[2]`, `[1, n, m+1]`. If there is only
+  one variable and its order is 1, you may omit this bracket.
+* The second optional braket `[total_order]` holds the total order of the
+  derivative. If there is only one variable order and that is the same as the
+  total order, you may omit this bracket.
+
 ## Special Notation
 
 **Bra-ket Notation**

src/functions/genfrac.js

@@ -11,6 +11,8 @@ import * as html from "../buildHTML";
 import * as mml from "../buildMathML";
 import {calculateSize, makeEm} from "../units";
 
+import {derivativeHandler} from './utils/assembleDerivative';
+
 const adjustStyle = (size, originalStyle) => {
     // Figure out what style this fraction should be in based on the
     // function used
@@ -508,3 +510,18 @@ defineFunction({
     htmlBuilder,
     mathmlBuilder,
 });
+
+defineFunction({
+    type: "genfrac",
+    names: [
+        "\\dv", "\\odv", // Ordinary derivative.
+        "\\pdv",         // Partial derivative.
+    ],
+    props: {
+        numArgs: 2,  // Function, variable(s).
+        numOptionalArgs: 2,  // Lower index(es), upper index.
+    },
+    handler: derivativeHandler,
+    htmlBuilder,
+    mathmlBuilder,
+});

src/functions/utils/assembleDerivative.js

@@ -0,0 +1,137 @@
+// @flow
+
+import {assertNodeType} from "../../parseNode";
+
+import type {AnyParseNode, ParseNode} from "../../parseNode";
+import type {FunctionContext} from "../../defineFunction";
+
+const groupByComma = (node: AnyParseNode): AnyParseNode[][] => {
+    if (node.type !== "ordgroup") {
+        return [[node]];
+    }
+
+    // Dives into the body list of this ParseNode<"ordgroup">, then groups the
+    // member nodes using comma as the delimiter:
+    // ["1", "+", "a", ",", "n"] => [ ["1", "+", "a" ], ["n"] ]
+    const nodesArr = assertNodeType(node, "ordgroup").body;
+    const res = [];
+    let currentChunk: AnyParseNode[] = [];
+    for (let i = 0; i < nodesArr.length; ++i) {
+        const e: AnyParseNode = nodesArr[i];
+        const isDelimiter = e.type === "atom" && e.text === ",";
+        if (!isDelimiter) {
+            currentChunk.push(e);
+        }
+        if (isDelimiter || i === nodesArr.length - 1) {
+            res.push(currentChunk);
+            currentChunk = [];
+        }
+    }
+    return res;
+};
+
+const MATH_ONE: ParseNode<"textord"> = {
+    type: "textord",
+    mode: "math",
+    text: "1",
+};
+const PLACEHOLDER: ParseNode<"textord"> = {
+    type: "textord",
+    mode: "math",
+    text: "\\square",
+};
+
+export function derivativeHandler(
+    {parser, funcName}: FunctionContext,
+    args: AnyParseNode[],
+    optArgs: (?AnyParseNode)[],
+): ParseNode<"genfrac"> {
+    const makeOrdGroup =
+        (bodyArr: AnyParseNode[]): ParseNode<"ordgroup"> => ({
+            type: "ordgroup",
+            mode: parser.mode,
+            body: bodyArr,
+        });
+
+    const func = args[0];
+    const vars = args[1];
+
+    const lowerDiffOrder: AnyParseNode =
+        optArgs[0] ?? makeOrdGroup([MATH_ONE]);
+    const totalDiffOrder: AnyParseNode =
+        optArgs[1] ?? lowerDiffOrder;
+
+    let symbol;
+    switch (funcName) {
+        case "\\dv":
+        case "\\odv":
+            symbol = "d";
+            break;
+        case "\\pdv":
+            symbol = "\\partial";
+            break;
+        default:
+            throw new Error("Unrecognized differential command");
+    }
+
+    const dVars = groupByComma(vars);
+    const numVar = dVars.length;
+    const dIndices = groupByComma(lowerDiffOrder);
+    const numIndices = dIndices.length;
+
+    if (numVar < numIndices) {
+        dVars.push(...Array(numIndices - numVar).fill([PLACEHOLDER]));
+    } else if (numVar > numIndices) {
+        dIndices.push(...Array(numVar - numIndices).fill([PLACEHOLDER]));
+    }
+
+    const makeDGroup = (base, sup) => {
+        if (!sup) {
+            return base;
+        }
+        if (sup.type === "ordgroup") {
+            const supBody = ((sup: any): ParseNode<"ordgroup">).body;
+            if (supBody.length === 0) {
+                supBody.push(PLACEHOLDER);
+            } else if (supBody.length === 1
+                && supBody[0].mode === "math"
+                && supBody[0].text === "1") {
+                return base;  // Omit the index if derivative order is 1.
+            }
+        }
+        return {
+            type: "supsub",
+            mode: parser.mode,
+            base,
+            sup,
+        };
+    };
+    const d = {
+        type: "textord",
+        mode: parser.mode,
+        text: symbol,
+    };
+
+    const numer = makeOrdGroup([
+        makeDGroup(d, totalDiffOrder), func]);
+    const denom = makeOrdGroup(dVars.map((variable: AnyParseNode[], i) => {
+        const index: AnyParseNode[] = dIndices[i];
+        return makeDGroup(
+            makeOrdGroup([d].concat(makeOrdGroup(variable))),
+            makeOrdGroup(index),
+        );
+    }));
+
+    return {
+        type: "genfrac",
+        mode: parser.mode,
+        continued: false,
+        numer,
+        denom,
+        hasBarLine: true,
+        leftDelim: null,
+        rightDelim: null,
+        size: "auto",
+        barSize: null,
+    };
+}

test/screenshotter/ss_data.yaml

@@ -125,6 +125,16 @@ DelimiterSizing: |
         a & b & c\\
         a & b & c\\
     \end{pmatrix}\; \Braket{ ϕ | \frac{∂^2}{∂ t^2} | ψ } \\
+Derivatives: |
+    \dv{}{x},\odv{y}{x},\odv[2]{}{x},\odv[n+1]{y}{x} \\
+    \pdv{}{x},\pdv{y}{x},\pdv[2]{}{x},\pdv[n+1]{y}{x} \\
+    \pdv[1,1][2]{z}{x,y},\pdv[2,2][4]{z}{x,y}, \pdv[1,a][1+a]{z}{x,y} \\
+    \pdv[1+2^n,{(1,2)},k,1][N_k+1]{\begin{pmatrix}\psi&0\\0&\phi\end{pmatrix}} {x,y,z_{\mu,\sigma},\tau} \\
+DerivativesFallbacks: |
+    \square = \text{placeholder} \\
+    \odv[]{y}{x}, \pdv[]{y}{x} \\
+    \pdv[2][4]{z}{x,y}, \pdv[2,2][]{z}{x,y}, \pdv[2,2][4]{z}{x} \\
+    \pdv[2][6]{\psi}{x,y,z}, \pdv[2,2][]{\psi}{x,y,z}, \pdv[2,2,2][6]{\psi}{x} \\
 DisplayMode:
     tex: \sum_{i=0}^\infty \frac{1}{i}
     pre: pre