3f:null 40:["$","title",null,{"children":"linear & Fourier math (WIP) | Riley | Observable"}] 46:T47a,wrapHeading(htl.html.fragment`rectangle: rect / ${tex`\Pi`}`, 3, htl.html`

${plotAdjust(Plot.plot({ height: 128, marks: [...plotAxisRules, Plot.line([ [-1, 0], [-0.5, 0] ]), Plot.line([ [-0.5, 1], [0.5, 1] ]), Plot.dot([ [-0.5, 0.5], [0.5, 0.5] ], {symbol: "circle", fill: "currentColor"}), Plot.line([ [1, 0], [0.5, 0] ]), Plot.dot([ [-0.5, 0], [-0.5, 1], [0.5, 1], [0.5, 0] ], {symbol: "circle", stroke: "currentColor", fill: "#FFF"}) ], x: { label: "x", ticks: 5, tickFormat: fracFormat, grid: true }, y: { label: "y", ticks: 3, tickFormat: fracFormat, domain: [0, 1], grid: true }, style: { background: "transparent" } }))} ${texCB`${texFn`RECT``x`}\overset{\text{def}}{=}\begin{cases} 1, && ${texAbs`x`} < ${texFrac(1)(2)} \\ ${texFrac(1)(2)}, && ${texAbs`x`} = ${texFrac(1)(2)} \\ 0, && ${texAbs`x`} > ${texFrac(1)(2)} \end{cases}`}

` )47:T41a,wrapHeading(htl.html.fragment`sinc`, 3, htl.html`

${(() => { let pairData = (x, y) => x.map((xv, i) => [xv, y[i]]); let Xs = plotXs.map(x => x * 6); let sincYs = Xs.map(x => Math.sin(x = x * Math.PI) / x); let cosYs = Xs.map(x => Math.cos(x * Math.PI)); let extremas = Xs.flatMap((x, i) => (x == 0 || (Math.abs(x) > 1 && (Math.abs(sincYs[i] - cosYs[i]) < 0.01))) ? [[x, sincYs[i]]] : [] ); return plotAdjust(Plot.plot({ marks: [...plotAxisRules, Plot.line(pairData(Xs, sincYs)), Plot.line(pairData(Xs, cosYs), {opacity: 0.25}), Plot.dot(extremas, {fill: "currentColor"}), Plot.dot([[0, 1]], {fill: "#FFF", stroke: "currentColor"}) ], x: { label: "x", ticks: 9, tickFormat: fracFormat, nice: true, grid: true }, y: { label: "y", ticks: 4, nice: true, tickFormat: fracFormat, // domain: [-1, 1], grid: true }, style: { background: "transparent" } })) })()} ${texCB`${texFn`SINC``x`}${texEqDef}${texFrac(texFn.sin`\pi x`)`\pi x`}`}

` )48:T452,wrapHeading(htl.html.fragment`sinc²`, 3, htl.html`

${(() => { let pairData = (x, y) => x.map((xv, i) => [xv, y[i]]); let Xs = plotXs.map(x => x * 4); let sincYs = Xs.map(x => Math.sin(x = x * Math.PI) / x); let sinc2Ys = sincYs.map(y => y * y); let cosYs = Xs.map(x => Math.cos(x * Math.PI)); let extremas = Xs.flatMap((x, i) => (x == 0 || (Math.abs(x) > 1 && (Math.abs(sincYs[i] - cosYs[i]) < 0.01))) ? [[x, sinc2Ys[i]]] : [] ); return plotAdjust(Plot.plot({ marks: [ Plot.ruleX([0], {opacity: 0.5}), Plot.ruleY([0], {opacity: 0.5}), Plot.line(pairData(Xs, sinc2Ys)), Plot.dot(extremas, {fill: "currentColor"}), Plot.dot([[0, 1]], {fill: "#FFF", stroke: "currentColor"}) ], x: { label: "x", ticks: 9, tickFormat: fracFormat, nice: true, grid: true }, y: { label: "y", ticks: 3, nice: true, tickFormat: fracFormat, // domain: [-1, 1], grid: true }, style: { background: "transparent" } })) })()} ${texCB`${texFn`SINC``x`}${texEqDef}${texFrac(texFn.sin`\pi x`)`\pi x`}`}

` )49:T676,htl.html`

${plotAdjust(Plot.plot({ marks: [...plotAxisRules, ...(besselN == 0 ? [ Plot.line(plotXs.map(x => [x = (x + 1) * 4, Cephes.j0(Math.PI * x)])) ] : [ Plot.line(plotXs.map(x => [x = (x + 1) * 4, Cephes.j0(Math.PI * x)]), { opacity: 0.25 }), Plot.line(plotXs.map(x => [x = (x + 1) * 4, besselFn(x)])) ]) ], x: { label: "x", ticks: 9, tickFormat: fracFormat, grid: true }, y: { label: "y", ticks: 3, tickFormat: fracFormat, grid: true }, style: { background: "transparent" } }))} ${ Number.isInteger(besselN) ? texCB`${texMat("", [String.raw`${texFn`J_n``x`}=`, String.raw`${texSum(String.raw`\mathscr{l}`,0,Infinity)`${texFrac`${texBracket["("](-1)}^\mathscr{l}``\mathscr{l}!${texBracket["("]`n+\mathscr{l}`}!`}${texBracket["("](texFrac`x`(2))}^{n+2\mathscr{l}}`}`], [String.raw`\operatorname{J}_{${fracFormatTex(besselN)}}${texBracket["["]`x`}=`, besselN == 0 ? String.raw`${texSum(String.raw`\mathscr{l}`,0,Infinity)`${texFrac`${texBracket["("](-1)}^\mathscr{l}``${texBracket["("]`\mathscr{l}!`}^2`}${texBracket["("](texFrac`x`(2))}^{2\mathscr{l}}`}` : String.raw`${texSum(String.raw`\mathscr{l}`,0,Infinity)`${texFrac`${texBracket["("](-1)}^\mathscr{l}``\mathscr{l}!${texBracket["("]`${fracFormatTex(besselN)}+\mathscr{l}`}!`}${texBracket["("](texFrac`x`(2))}^{${fracFormatTex(besselN)}+2\mathscr{l}}`}`] )}` : texCB`${texFn`J_n``x`}=${texSum(String.raw`\mathscr{l}`,0,Infinity)`${texFrac`${texBracket["("](-1)}^\mathscr{l}``\mathscr{l}!${texBracket["("]`n+\mathscr{l}`}!`}${texBracket["("](texFrac`x`(2))}^{n+2\mathscr{l}}`}` }

`4a:T505,ʘtrigonometryހcircular = makeTable("circular relationships", 3, { headers: [ "name", texC`\bold{f(\theta)}`, texC`\bold{\frac{\mathrm{\bold{d}} }{\mathrm{\bold{d}} \theta} ${texBracket["["]`f(\theta)`}}`, texC`\bold{\frac{\mathrm{\bold{d}} }{\mathrm{\bold{d}} \theta} ${texBracket["["]`f^{-1}(\theta)`}}` ], rows: [ [ // sine "sine", texCB`\sin(\theta)`, texCB`\cos(\theta)`, texCB`\frac{1}{\sqrt{1-\theta^2}}` ], [ // cosine "cosine", texCB`\cos(\theta)`, texCB`-\sin(\theta)`, texCB`-\frac{1}{\sqrt{1-\theta^2}}` ], [ // tangent "tangent", texCB`\tan(\theta)`, texCB`\sec(\theta)^2`, texCB`\frac{1}{1+\theta^2}` ], [ // cotangent "cotangent", texCB`\cot(\theta)`, texCB`-\csc(\theta)^2`, texCB`-\frac{1}{1+\theta^2}` ], [ // secant "secant", texCB`\sec(\theta)`, texCB`\tan(\theta)\sec(\theta)`, texCB`\frac{1}{${texAbs`\theta`}\sqrt{\theta^2-1}}` ], [ // cosecant "cosecant", texCB`\csc(\theta)`, texCB`-\cot(\theta)\csc(\theta)`, texCB`-\frac{1}{${texAbs`\theta`}\sqrt{\theta^2-1}}` ] ] })4b:T736,ʘtrigonometryހhyperbolic = makeTable("hyperbolic relationships", 3, { headers: [ "name", texC`\bold{f(\theta)}`, texC`\bold{\frac{\mathrm{\bold{d}} }{\mathrm{\bold{d}} \theta} ${texBracket["["]`f(\theta)`}}`, texC`\bold{\frac{\mathrm{\bold{d}} }{\mathrm{\bold{d}} \theta} ${texBracket["["]`f^{-1}(\theta)`}}` ], rows: [ [ // hyperbolic sine "hyperbolic sine", texCB`\sinh{(\theta)} = \frac{e^\theta-e^{-\theta}}{2}`, texCB`\cosh{(\theta)}`, texCB`\frac{1}{\sqrt{\theta^2+1}}` ], [ // hyperbolic cosine "hyperbolic cosine", texCB`\cosh{(\theta)} = \frac{e^\theta+e^{-\theta}}{2}`, texCB`\sinh{(\theta)}`, texCB`\frac{1}{\sqrt{\theta^2-1}}` ], [ // hyperbolic tangent "hyperbolic tangent", // texCB`\tanh{(\theta)} = \frac{\sinh{(\theta)}}{\cosh{(\theta)}} = \frac{e^\theta-e^{-\theta}}{e^\theta+e^{-\theta}}`, texCB`\tanh{(\theta)} = \frac{\sinh{(\theta)}}{\cosh{(\theta)}}`, texCB`${texFn("sech", 2)`\theta`}`, [{[makeTable.attr]: true, rowspan: 2}, texCB`\frac{1}{1-\theta^2}`] ], [ // hyperbolic cotangent "hyperbolic cotangent", texCB`\coth{(\theta)}`, texCB`-\operatorname{csch}{(\theta)}^2`, // texCB`\frac{1}{1-\theta^2}` ], [ // hyperbolic secant "hyperbolic secant", texCB`${texFn.sech`\theta`} = \frac{1}{\cosh{(\theta)}}`, texCB`-${texFn.sech`\theta`} \cdot \tanh{(\theta)}`, texCB`\frac{-1}{\theta\sqrt{1-\theta^2}}` ], [ // hyperbolic cosecant "hyperbolic cosecant", texCB`\operatorname{csch}{(\theta)}`, texCB`-\operatorname{csch}{(\theta)} \cdot \coth{(\theta)}`, texCB`\frac{-1}{${texBracket["|"]`\theta`}\sqrt{1+\theta^2}}` ] ] })4c:Tbeb,textAutoColors = { const wrapElement = document.createElement("div"); const styleElement = document.createElement("style"); const dispElement = document.createElement("ol"); dispElement.classList.add("variable-color-palette", "katex"); const stringCompare = Intl.Collator(undefined, { sensitivity: "case", numeric: true, caseFirst: "upper" }); const delimitElm = document.createElement("span"); delimitElm.append("|"); delimitElm.classList.add("symbol-delimiter"); wrapElement.append(dispElement, styleElement); let docRoot = document.body.querySelector(".observablehq-root"); let recolor = () => { let symbols = [...docRoot.querySelectorAll(texAutoColorClasses.query)].map(e => symbolInfo(e)); symbols.sort((a, b) => stringCompare.compare(a.group, b.group) || stringCompare.compare(a.raw, b.raw)); symbols = unique(symbols, (a, b) => (a.raw == b.raw) && (a.style.sort().join(" ") == b.style.sort().join(" "))); let groups = new Map(); for (let sym of symbols) { if (groups.has(sym.group)) { groups.get(sym.group).push(sym); } else { let a = [sym]; a.lang = sym.lang; groups.set(sym.group, a); } } let colors = []; for (let i = 0; i < symbols.length; i++) { colors[i] = d3.lch(50, 75, (360 * i / symbols.length)).formatHex().toUpperCase(); } let newDisp = []; let newStyle = []; for (let [group, syms] of groups) { let c = (colors.length % 2) ? colors.shift() : colors.pop(); let dispItem = document.createElement("li"); dispItem.append(...syms.flatMap(({raw, style}) => { let e = document.createElement("span"); e.append(raw); e.classList.add(...style); return [delimitElm.cloneNode(Infinity), e]; }).slice(1)); syms.lang == "Greek" && greekAlphabet.has(syms[0].base) && (dispItem.title = greekAlphabet.get(syms[0].base)); dispItem.style.backgroundColor = c; newDisp.push(dispItem); newStyle.push(`.katex .mord[data-symbol-group="${group}"] { color: ${c}; }`); } dispElement.replaceChildren(...newDisp); styleElement.innerText = newStyle.join("\n\n"); groups.clear(); newStyle.length = newDisp.length = 0; }; recolor(); { let watcher = new MutationObserver(records => { for (let r of records) { if (r.type == "attributes") { return recolor(); } else { for (let collection of [r.addedNodes, r.removedNodes]) { for (let n of collection) { if (!(n instanceof Element)) { continue; } if (n.matches(texAutoColorClasses.query) || n.querySelector(texAutoColorClasses.query)) { return recolor(); } } } } } }); watcher.observe(docRoot, { subtree: true, childList: true }); invalidation.then(() => { watcher.disconnect(); styleElement.replaceChildren(); styleElement.remove(); }); } return wrapElement; }4d:T4be,viewof texAutoColorClasses = { const wrap = document.createElement("div"); Object.defineProperty(wrap, "value", { enumerable: true, configurable: true, get: function value() { let v = new Set(this.firstElementChild.value.sort()); return Object.defineProperties(v, { query: { enumerable: true, value: [...v].map(cls => `.katex .katex-html .mord.${cls}`).join(", ") }, queryBase: { enumerable: true, value: [...v].map(cls => `.mord.${cls}`).join(", ") } }); } }); wrap.append(Inputs.checkbox(new Map(Object.entries({ mathdefault: "normal", mathscr: "script", mathbf: "bold", boldsymbol: "bold symbol", mathcal: "calligraphic", mathfrak: "Fraktur", mathsf: "sans-serif", mathbb: "blackboard", mathtt: "monospace" }).map(e => e.reverse()).sort(([nameA], [nameB]) => nameA == nameB ? 0 : nameA < nameB ? -1 : +1)), { label: "symbol styles to color", format: ([name, cls]) => htl.html`${name}`, value: ["mathdefault", "mathscr"] })); invalidation.then(() => { delete wrap.value; wrap.replaceChildren(); wrap.remove(); }); return wrap; }4e:T8e0,license = { const logo = htl.svg``; logo.style.height = "1em"; logo.style.verticalAlign = "baseline"; return htl.html`

license

Use this notebook how you want. I make no guarantees of the accuracy of these formulae; if you find an error, please comment on it! Where applicable, the contents of this notebook are licensed under the WTFPL ${logo}, except where otherwise noted. The static diagram of the unit circle is from Wikimedia Commons and is a colored version of Gustavb’s original work from 2006.

`; }4f:Ta9f,texStyle = html``50:T456,function texAutoColor(texOutput) { if (typeof texOutput == "string" || texOutput instanceof String) { return texOutput; } if (!(texOutput instanceof Node) && Symbol.iterator in texOutput) { for (let e of texOutput) { texAutoColor(e); } return texOutput; } for (let e of texOutput.querySelectorAll(texAutoColorClasses.query)) { let name = e.innerText.trim(); if (!name) { continue; } symbolInfo(e, true); // e.dataset.symbolRaw = name; // if (name.match(/[A-Za-z]/)) { // e.dataset.symbolLang = "Latin"; // texAutoColorCase.Latin || (name = name.toLowerCase()); // } else if (name.length > 1 ? [...name].some(l => greekAlphabet.has(l)) : greekAlphabet.has(name)) { // e.dataset.symbolLang = "Greek"; // texAutoColorCase.Greek || (name = name.toLowerCase()); // e.dataset.symbolLang = "other"; // } else if (!texAutoColorCase.other) { // name = name.toLowerCase(); // } // e.dataset.symbol = name; // e.dataset.symbolStyle = [...e.classList].filter(cls => classes.has(cls)).join(" "); } return texOutput; }51:T507,texDispError = { function texDisplayError() { return String.raw`\fcolorbox{red}{null}{ ${takeTag.concat.raw(...arguments)} }`; } Object.defineProperties(texDisplayError, { apply: { value: function applyDisplayError(text, ...objects) { if (!text) { } else if (typeof text != "string" && !(text instanceof String)) { objects.unshift(text); } for (let o of objects) { Object.defineProperty(o, "toString", { value: texDisplayError.make(text || o), enumerable: true }); } return objects.length == 1 ? objects[0] : objects; } }, make: { value: function makeDisplayError() { let text; switch (arguments.length) { case 0: text = "error"; break; case 1: { text = arguments[0]; if (typeof text == "function" || text instanceof Function) { text = text.displayName || text.name || text[Symbol.toStringTag] || text; } text = text.toString(); break; } default: text = takeTag.concat.raw(...arguments); } return () => this(text); } } }) return texDisplayError; }52:Tc0b,texFn = { const defaultBracket = "[", legal = new Set(), // names allowed in shorthand (like ‘\sin’) known = new Map(), // names registered in texFn bSlash = "\\", primeChars = new Map(Object.entries({ "\\prime": ["'′ʹ", '"″ʺ〞', "‴", "⁗"], "\\backprime": ["`‵", "‶〝", "‷"] }) .flatMap(([base, items]) => items.flatMap((chars = "", count) => { let currentBase = base.repeat(++count); return [...chars].map(c => [c, currentBase]); }) )), convertPrimes = s => { for (let [find, replace] of primeChars) { s = s.replaceAll(find, replace); } return s; }; invalidation.then(() => { legal.clear(); known.clear(); primeChars.clear(); }); function texFunction(name, power = 1, decorator) { if (!name) { throw new TypeError("no name"); } name = String(name); let fn; let basic = (power == 1 || power == "") && !decorator; if (decorator && decorator.toString().trimStart().match(/^[-−]/)) { decorator = decorator.toString().trimStart(); decorator = String.raw`{}^{-} ${decorator.slice(1)}`; } let allowed; if (basic && (fn = known.get(name))) { return fn; } allowed = legal.has(name); if (!allowed) { try { tex`${bSlash}${name}`; allowed = true; } catch { allowed = false; } } // potentially escape function name allowed = allowed ? String.raw`${bSlash}${name}` : name.length == 1 ? `{ ${name} }` : String.raw`\operatorname{${name}}`; if (basic) { // define basic function fn = (...contents) => String.raw`${allowed}{${texBracket[defaultBracket]`${takeTag.concat.raw(...contents)}`}}`; // define inverse function fn.i = (...contents) => String.raw`${allowed}^{{}^{-}1}{${texBracket[defaultBracket]`${takeTag.concat.raw(...contents)}`}}`; // cache function known.set(name, fn); } else { power = (power == 1 || power == "") ? "" : String.raw`^{ ${power} }`; if (!decorator) { decorator = ""; } else { if ([...decorator.toString()].every(c => c == " " || primeChars.has(c))) { decorator = String.raw`^{ ${convertPrimes(decorator)} }`; } else { decorator = String.raw`^{ ${decorator} }`; } } // single-use function fn = (...contents) => String.raw`${allowed}${decorator}{ ${texBracket["["]`${takeTag.concat.raw(...contents)}`} }${power}`; } return nullToString(fn); } Object.defineProperty(texFunction, "log", { value: ((...sub) => (...contents) => String.raw`\log_{${takeTag.concat.raw(...sub)}}{ \left ( ${takeTag.concat.raw(...contents)} \right )}`), enumerable: true }); for (let name of "ln sin cos tan cot sec csc sinh cosh tanh coth sech csch".trim().split(/\s+/)) { let f = texFunction(name); name in texFunction || Object.defineProperty(texFunction, name, { value: f, enumerable: true }); } return texFunction; }53:T6da,texBracket = { const known = Object.freeze({ pairs: new Map([ ...[..."‘’“”()<>[]||".matchAll(/[\s\S]{2}/g)].flat().map(pair => [...pair]), ["\\{", "\\}"], ["\\|", "\\|"], ...["floor", "ceil", "angle"].map(name => [`\\l${name}`, `\\r${name}`]) ].sort(([a], [b]) => a < b ? -1 : +1).flatMap(pair => [pair, [...pair].reverse()])), fromUnicode: new Map(Object.entries({ "{": "\\{", "}": "\\}", "⌊": "\\lfloor", "⌋": "\\rfloor", "⌈": "\\lceil", "⌉": "\\rceil", "<": "\\langle", "〈": "\\langle", "❬": "\\langle", "⟨": "\\langle", "〈": "\\langle", ">": "\\rangle", "〉": "\\rangle", "❭": "\\rangle", "⟩": "\\rangle", "〉": "\\rangle", "||": "\\|", "‖": "\\|", "\u23F8": "\\|" })) }); const sizes = ["big", "Big", "bigg", "Bigg"].map(s => `\\${s}`); invalidation.then(() => { known.pairs.clear(); known.fromUnicode.clear(); sizes.length = 0; }); const fun = function texBracket(left = "(", size) { for (let [u, t] of known.fromUnicode) { left = left.replaceAll(u, t); } let right = known.pairs.get(left) ?? left; if (size === undefined || size === null) { left = String.raw`\left ${left}`; right = String.raw`\right ${right}`; } else if ((--size) in sizes) { left = `${sizes[size]}${left}`; right = `${sizes[size]}${right}`; } return nullToString(((...contents) => String.raw`${left} ${takeTag.concat.raw(...contents)} ${right}`)); }; for (let left of known.pairs.keys()) { Object.defineProperty(fun, left, { value: fun(left), enumerable: true }); } return fun; }54:T482,texMaybeInfinity = { const infPos = String.raw`\infty`, infNeg = String.raw`-\infty`, setPos = new Set([Infinity, "+", ...["infty", "infinity", "∞"].flatMap(s => [s, `+${s}`]) ]), setNeg = new Set([-Infinity, "-", "−", ...["infty", "infinity", "∞"].flatMap(s => [`-${s}`, `−${s}`]) ]); function texMaybeInfinity(n, bias = 0) { (typeof bias == "string" || bias instanceof String) && ((bias = bias.valueOf()) === "+" ? 1 : (bias === "-" || bias === "−") ? -1 : 0); bias = (typeof bias == "number" || bias instanceof Number) ? bias.valueOf() : 0; (n instanceof String || n instanceof Number) && (n = n.valueOf()); if (typeof n == "number" && Number.isNaN(n)) { return bias == 0 ? 0 : bias > 0 ? infNeg : infPos; } if (n === undefined || n === null) { return bias == 0 ? 0 : bias > 0 ? infPos : infNeg; } return setPos.has(n) ? infPos : setNeg.has(n) ? infNeg : n; } Object.defineProperty(texMaybeInfinity, "range", { value: function texMaybeInfiniteRange(from, to) { return [texMaybeInfinity(from, -1), texMaybeInfinity(to, +1)]; } }) return texMaybeInfinity; }55:T1624,texNumberInput = { function rand(length) { return new Array(length).fill().map(() => Math.floor(Math.random() * 10).toFixed(0)).join(""); } function innerText(node, trim = false) { if (node instanceof CharacterData) { return (node instanceof Text) ? node.textContent : ""; } return [...node.childNodes].map(c => innerText(c, false)).join(""); } function matchMord(mord, text) { if (text == null) { throw new TypeError("no match string provided"); } if (!(mord?.classList?.contains?.("mord"))) { return false; } text = text.trim(); let part = mord.innerText.trim(); if (part == text) { return mord; } if (part == text.slice(0, part.length)) { let matches = matchMord(mord.nextElementSibling, text.slice(part.length)); if (matches) { if (Array.isArray(matches)) { matches.unshift(mord); return matches; } return [mord, matches]; } } return false; } return function texNumberInput(generator = n => `n=${n}`, [min, max] = [], {value = 0, step, validate, invalidation, keyLength = 64} = {}) { const rnd = rand(keyLength); const whole = tex`${generator(rnd)}`; whole.normalize(); const semantic = [...whole.querySelector(".katex-mathml math semantics").querySelectorAll("mn")].find(n => innerText(n, true) == rnd); if (!semantic) { throw new SyntaxError("semantic tag not found"); } const setSemantic = v => semantic.replaceChildren(v); const annotation = [...whole.querySelector(".katex-mathml math semantics").querySelectorAll("annotation")].find(n => innerText(n).includes(rnd)); if (!annotation) { throw new SyntaxError("annotation tag not found"); } let setAnnotation; { let text = innerText(annotation); let pre = text.slice(0, text.indexOf(rnd)); let post = text.slice(text.indexOf(rnd) + rnd.length); setAnnotation = v => semantic.replaceChildren(`${pre}${v}${post}`); } let texInput = [...whole.querySelector(".katex-html").querySelectorAll(".mord")].find(n => matchMord(n, rnd)); if (!texInput) { throw new SyntaxError("TeX tag not found"); } texInput = matchMord(texInput, rnd); if (Array.isArray(texInput)) { for (let mord of texInput.slice(1)) { mord.remove(); } texInput = texInput.shift(); } texInput.contentEditable = true; texInput.classList.add("tex-number-input"); const testInput = document.createElement("input"); testInput.type = "number"; min == null || min === -Infinity || (testInput.min = min); max == null || max === Infinity || (testInput.max = max); step == null || (testInput.step = step); const refresh = (v = whole.value) => { setSemantic(v); setAnnotation(v); testInput.value = v; }; inputListener: { let listener = ["input", event => { testInput.value = innerText(texInput).trim(); if (!whole.checkValidity()) { event.stopImmediatePropagation(); } }, { passive: true }]; texInput.addEventListener(...listener); invalidation?.then(() => texInput.removeEventListener(...listener)); } upDownListener: if (testInput.hasAttribute("step")) { let listener = ["keydown", e => { if (e.ctrlKey || e.altKey || e.isComposing || e.metaKey) { return; } let direction; switch (e.code) { case "ArrowUp": direction = +1; break; case "ArrowDown": direction = -1; break; default: return; } let v = whole.value; if (is.number(v, {NaN: false, infinity: false})) { let step = testInput.step; step = direction * (step ? Number.parseFloat(step) : 1); e.shiftKey && (step *= 10); if (direction < 0) { // down if (testInput.min) { let min = Number.parseFloat(testInput.min); testInput.valueAsNumber = Math.max(min, v + step); } else { testInput.valueAsNumber = v + step; } } else { // up if (testInput.max) { let min = Number.parseFloat(testInput.max); testInput.valueAsNumber = Math.min(max, v + step); } else { testInput.valueAsNumber = v + step; } } if (v != testInput.valueAsNumber) { e.preventDefault(); refresh(texInput.innerText = testInput.valueAsNumber); texInput.dispatchEvent(new Event("input", {bubbles: true, cancelable: true})); } } }, { passive: false }]; texInput.addEventListener(...listener); invalidation?.then(() => texInput.removeEventListener(...listener)); } Object.defineProperties(whole, { value: { get: function value() { return Number.parseFloat(innerText(texInput).trim()); }, set: function value(v) { texInput.replaceChildren(v); return refresh(v); }, enumerable: true }, disabled: { get: function disabled() { return !texInput.contentEditable; }, set: function disabled(d) { return texInput.contentEditable = !d; }, enumerable: true }, checkValidity: { value: function checkValidity() { refresh(); return testInput.checkValidity() && validate ? validate.call(testInput, testInput.valueAsNumber ?? testInput.value) : true; }, enumerable: true } }); whole.value = value ?? min ?? max ?? 0; return whole; } }56:T878,unique = { unique.merge = mergeSame; return unique; function transformOutput(o) { if (o === null || o === undefined || (typeof o === "number" && Number.isNaN(o))) { return 0; } try { o = o.valueOf(); } catch { return o; } if (o === 0 || o === true) { return 0; } if (o === false) { return 1; } return o; } function unique(items, ...comparators) { if (!comparators.length) { return new Set(items); } if (comparators.length == 1 && comparators[0] == "JSON") { return [...new Set((Array.isArray(items) ? items : [...items]).map(e => JSON.stringify(e, undefined, "\t")))] .map(e => JSON.parse(e)); } let out = []; inputs: for (let a of items) { tests: for (let b of out) { comps: for (let comp of comparators) { if (transformOutput(comp(a, b)) != 0) { continue tests; // If this comparator finds a difference, go to the next test element. } continue inputs; // If none of the comparators found a difference, then this test element is identical to the input element, so go to the next input element. } } out.push(a); } return out; } function mergeSame(items, merger, ...comparators) { if (!comparators.length) { return new Set(items); } if (comparators.length == 1 && comparators[0] == "JSON") { return [...new Set((Array.isArray(items) ? items : [...items]).map(e => JSON.stringify(e, undefined, "\t")))] .map(e => JSON.parse(e)); } let out = []; inputs: for (let a of items) { tests: for (let bi = 0; bi < out.length; ++bi) { comps: for (let comp of comparators) { if (transformOutput(comp(a, out[bi])) != 0) { continue tests; // If this comparator finds a difference, go to the next test element. } out[bi] = merger(a, out[bi]); continue inputs; // If none of the comparators found a difference, then this test element is identical to the input element, so go to the next input element. } } out.push(a); } return out; } }57:Tc65,makeTable = { const symAttr = Symbol("table cell attributes"); function makeCell(cell, contents) { (cell instanceof Element) ? (cell.cloneNode(Infinity)) : (cell = document.createElement(cell)); for (let c of to.multi(contents)) { if (c == null || c === "") { continue; } if (is.in(c, symAttr)) { for (let [attr, value] of Object.entries(c)) { cell.setAttribute(attr, value); } } else { cell.append(c); } } return cell; } function makeRow({row = "tr", cell = "td"} = {}, contents) { (row instanceof Element) ? (row.cloneNode(Infinity)) : (row = document.createElement(row)); for (let c of to.multi(contents)) { row.append(makeCell(cell, c)); } return row; } function makeTable(title, { multiHead = false, headers = [], rows }) { let level = 2; if (title && isHeadingNumber(arguments[1])) { level = arguments[1]; ({ headers = [], rows } = arguments[2]); } let table = document.createElement("table"); table.classList.add("katex-inline-block"); if (multiHead) { let thead = document.createElement("thead"); for (let contents of to.multi(headers)) { thead.append(makeRow({row: "tr", cell: "th"}, contents)); } table.append(thead); } else { makeHeader: { let thead = document.createElement("thead"); thead.append((Array.isArray(headers) ? headers : [...headers]) .map(header => { let elm = document.createElement("th"); header instanceof HTMLElement && texAutoColor(header); for (let h of to.multi(header)) { if (is.in(h, symAttr)) { for (let [attr, value] of Object.entries(h)) { elm.setAttribute(attr, value); } } else { elm.append(h); // h instanceof Element && texAutoColor(h); } } return elm; }).reduce((row, header) => { row.append(header); return row; }, document.createElement("tr"))); table.append(thead); } } makeBody: { table.append((Array.isArray(rows) ? rows : [...rows]) .map(row => row.map(cell => { let cellElm = document.createElement("td"); cellElm.style.verticalAlign = "middle"; for (let c of to.multi(cell)) { if (is.in(c, symAttr)) { for (let [attr, value] of Object.entries(c)) { cellElm.setAttribute(attr, value); } } else { cellElm.append(c); // c instanceof Element && texAutoColor(c); } } return cellElm; }).reduce((rowElm, cell) => { rowElm.append(cell); return rowElm; }, document.createElement("tr"))) .reduce((tbody, row) => { tbody.append(row); return tbody; }, document.createElement("tbody"))); } return title ? wrapHeading(title, level, table) : table; } Object.defineProperty(makeTable, "attr", { value: symAttr, enumerable: true }); return makeTable; }58:T1348,wrapElm = { let BS = String.fromCodePoint(0x5C); let kebab = import("//CDN.SkyPack.dev/lodash.kebabcase@4.1.1?min"); let CSSExt = "$"; function toCSSKebab(name) { let prefix = name.slice(0, Math.max(name.indexOf(CSSExt), 0)); return `${prefix ? `-${prefix}-` : ""}${kebab(name.slice(prefix.length))}`; } function setProps(element, properties) { for (let [name, value] of is.multi(properties) ? properties : Object.entries(properties)) { element[name] = value; } } function append(element, children) { for (let c of children) { (!is.a(c, Node) && is.multi(c)) ? append(element, c) : element.append(c); } } function wrapElement(...args) { let tag, // tag name (potentially with CSS-style ID & class selectors) [default: "div"] keep, // whether to make copies of the element to re-use the output function [default: false] raw, // whether to accept string contents just like String.raw [default: true] normalize, // whether to normalize the resulting element (Node.prototype.normalize) [default: true] then, // callback called for every element returned (this = element) (signature: (element) => {}) invalidation, // promise after which the saved element is forgotten attr, // attributes (as an array of pairs or an object with own enumerable properties) prop, // properties (as an array/object) propD, // property descriptors (as property descriptor object) style, // inline CSS properties (as an array/object) styleC; // inline CSS properties in camelCase (with the form ‘moz$appearance’ for prefixed or custom properties) (as an array/object) if (is.string(args[0])) { tag = args.shift(); } if (is.object(args[0]) && !is.a(args[0], Node) && !is.a(args[0], String)) { ({tag = tag, attr, prop, propD, style, styleC, keep, raw = true, normalize = true, invalidation} = args.shift()); } let e; if (tag && tag != "div") { if (tag.includes("#") || tag.includes(".")) { let tagName = tag.slice(0, Math.max(tag.indexOf("#"), tag.indexOf("."))); tag = tag.slice(tagName.length); e = document.createElement(tagName); for (let [, type, value] of tag.matchAll(/([#.])([^#.]+)/g)) { switch (type) { case "#": e.id = value; break; case ".": e.classList.add(value); } } tag = tagName; } } e ??= document.createElement(tag ||= "div"); if (attr) { for (let a of is.multi(attr) ? attr : Object.entries(attr)) { e.setAttribute(...a); }} if (style) { for (let s of is.multi(style) ? style : Object.entries(style)) { e.style.setProperty(...s); }} if (styleC) { for (let s of is.multi(styleC) ? styleC : Object.entries(styleC)) { s = [...s]; e.style.setProperty(toCSSKebab(s.shift()), ...s); s.length = 0; }} prop && (is.multi(prop) || (prop = Object.entries(prop))); if (args.length) { append(e, args); normalize && e.normalize(); } args.length = 0; if (keep) { !invalidation && (keep instanceof Promise) && (invalidation = keep); keep = e; invalidation?.then(() => { used = true; keep = true; e = undefined; }); } else if (invalidation) { invalidation.then(() => e = undefined); } const takeTagMode = raw ? takeTag.array.raw : takeTag.array; let used; return Object.defineProperty((...children) => { if (keep) { e = keep.cloneNode(Infinity); } else if (used) { throw new ReferenceError("element already used"); } else { used = true; queueMicrotask(() => e = undefined); } prop && setProps(e, prop); propD && Object.defineProperties(e, propD); if (children.length) { append(e, takeTagMode(...children)); normalize && e.normalize(); } then && then.call(e, e); return e; }, "toString", { value: () => { throw new SyntaxError(`${wrapElement.name}: broken callback chain on <${tag}${elmShorthand(e)}> element`); }, enumerable: true, configurable: true }); } Object.defineProperty(wrapElement, "CSSExt", { enumerable: true, get: (() => CSSExt), set: v => CSSExt = String(v) }); function elmShorthand(e) { const out = [e.tagName.toLowerCase()]; e.id && out.push(`#${e.id}`); if (e.classList.length) { for (let c of e.classList) { out.push(`.${c}`); }} let name; if (name = e.getAttribute("name")) { let q = name.includes('"') ? "'" : '"'; name.endsWith(BS) && (name = `${name.slice(0, -1)}${BS.repeat(2)}`); name.replaceAll(q, `${BS}${q}`); out.push(`[name=${q}${name}${q}]`); } return out.join(""); }; kebab = (await kebab).default; return wrapElement; }59:T2a14,/** * adapted from https://GitHub.com/balint42/diff.js/blob/master/diff.js * ⓒ2014 Balint Morvai * MIT license */ class diffJS { /** * Calculate differences of a vector. * * Takes an object or array Y with m numbers and returns an array * dY with m-1 numbers that constitutes the differences: * dY = [Y(2)-Y(1) Y(3)-Y(2) ... Y(m)-Y(m-1)] * If Y are function values f(1), f(2), ... with a step size of 1, * then dY constitutes the approximate derivative of f. For a different * step size use diffXY. * NOTE: For a step size other than 1, the differences do NOT constitute * the approximate derivative and thus in those cases use diffXY if you * want to get the derivative. * * If as second parameter a number n is given, the returned array * dY will be the n-th differential, thus above step applied n-times. * * @author Balint Morvai * @license http://en.wikipedia.org/wiki/MIT_License MIT License * @param values * @param n * @returns Array */ static diff(values, n) { // make y enumerated and define x = 1, 2, 3, ... var x, y; y = this.enumerate(values); x = Object.keys(y).map(Math.floor); // call diffXY version return this.diffXY(x, y, n); } /** * Calculate approximate derivative of a vector Y, assuming * that Y=f(X) with given vector X. * * Takes objects or arrays X and Y with m numbers and returns * an array dY with m-1 numbers that constitutes the approximate * derivative: * dY = [(Y(2)-Y(1))/(X(2)-X(1)) (Y(3)-Y(2)/(X(3)-X(2)) ... * (Y(m)-Y(m-1))/((X(m)-X(m-1))] * * If as second parameter a number n is given, the returned array * dY will be the n-th differential, thus above step applied n-times. * * @author Balint Morvai * @license http://en.wikipedia.org/wiki/MIT_License MIT License * @param x * @param y * @param n * @returns Array */ static diffXY(x, y, n) { // recursive calls to get n-th diff if(n > 1) { y = this.diffXY(x, y, n-1); x.pop(); } // loop through 1,...,m-1 entries of values to get diff var keysX = Object.keys(x); var keysY = Object.keys(y); var len = Math.min(keysX.length-1, keysY.length-1); for (var k = 0; k < len; k++) { y[k] = (y[keysY[k+1]]-y[keysY[k]]) / (x[keysX[k+1]]-x[keysX[k]]); } y.pop(); // last element is old value, delete it return y; } /** * Calculate reverse differences of a vector. * * Takes an object or array Y with m numbers and returns an array * IY with m numbers that constitutes the reverse differences: * [ ... -Y(m)-Y(m-1)-Y(m-2) -Y(m)-Y(m-1) -Y(m)] * If Y are function values f(1), f(2), ... with a step size of 1, * then IY constitutes the approximate integral of f. For a different * step size use integralXY. * * If as second parameter a number n is given, the returned array * Y will be the n-th integral, thus above step applied n-times. * * NOTE: the integral cannot determine the original set of values * before "diff" was applied, thus "integral(diff(values)) != values" * due to the nature of integration and differentiation. However the * shape of the result will be the same, the curve will only be * shifted by a constant value. ("translation") * * @author Balint Morvai * @license http://en.wikipedia.org/wiki/MIT_License MIT License * @param values * @param n * @returns Array */ static integral(values, n) { // make y enumerated and define x = 1, 2, 3, ... var x, y; y = this.enumerate(values); x = Object.keys(y).map(Math.floor); // call integralXY version return this.integralXY(x, y, n); } /** * Calculate approximate integral of a vector, assuming * that Y=f(X) with given vector X. * * Takes an object or array Y with m numbers and returns an array * X with m numbers that constitutes the integral: * [ ... * -Y(m)*(X(m)-X(m-1)-Y(m-1)*(X(m)-X(m-1)-Y(m-2)*(X(m-1)-X(m-2)-Y(m-3)*(X(m-2)-X(m-3) * -Y(m)*(X(m)-X(m-1)-Y(m-1)*(X(m)-X(m-1)-Y(m-2)*(X(m-1)-X(m-2) * -Y(m)*(X(m)-X(m-1)-Y(m-1)*(X(m)-X(m-1) * -Y(m)*(X(m)-X(m-1)) * ] * * If as second parameter a number n is given, the returned array * X will be the n-th integral, thus above step applied n-times. * * NOTE: the integral cannot determine the original set of values * before "diff" was applied, thus "integral(diff(values)) != values" * due to the nature of integration and differentiation. However the * shape of the result will be the same, the curve will only be * shifted by a constant value. ("translation") * * @author Balint Morvai * @license http://en.wikipedia.org/wiki/MIT_License MIT License * @param x * @param y * @param n * @returns Array */ static integralXY(x, y, n) { // recursive calls to get n-th diff if(n > 1) { y = this.integral(x, y, n-1); } // loop through m,...,1 entries of values to get integral var keysX = Object.keys(x); var keysY = Object.keys(y); var len = Math.min(keysX.length-1, keysY.length-1); // NOTE: below we would need X(len+1) & Y(len+1) but both are missing; // thus we assume "X(len+1)-X(len)=X(len)-X(len-1)" and "Y(len+1)=0" y[len] = -y[len]*(x[keysX[len]]-x[keysX[len-1]]); for (var k = len-1; k >= 0; k--) { y[k] = -y[keysY[k]]*(x[keysX[k+1]]-x[keysX[k]])+y[keysY[k+1]]; } return y; } /** * Find local maxima and minima in a list of values. * * Javascript implementation of: * "A Linear-Time Algorithm That Locates Local Extrema * of a Function of One Variable From Interval Measurement * Results" - Karen Villaverde, Vladik Kreinovich * (Interval Computations 01/1993; 1993(4)) * * Takes an object or array with numbers and returns an object * with two lists of indices: 'minlist' with indices of values * that are local minima and 'maxlist' with indices of values that * are local maxima. Indices can be of any type. * Takes numbers as first parameter and an accuracy > 0 (epsilon) * as second parameter. The accuracy has to be chosen depending * on the fluctuations in the data: smaller values mean greater * reliability in finding extrema but also greater chance of * confusing noise with a local minimum or maximum. * * @author Balint Morvai * @license http://en.wikipedia.org/wiki/MIT_License MIT License * @param values * @param eps * @returns {minlist: Array, maxlist: Array} */ static extrema(values, eps) { // make y enumerated and define x = 1, 2, 3, ... var x, y; y = this.enumerate(values); x = Object.keys(y).map(Math.floor); // call extremaXY version var res = this.extremaXY(x, y, eps); res.minlist = res.minlist.map(function(val) { var index = Math.floor((val[1] + val[0]) / 2); return Object.keys(values)[index]; }); res.maxlist = res.maxlist.map(function(val) { var index = Math.floor((val[1] + val[0]) / 2); return Object.keys(values)[index]; }); return {minlist: res.minlist, maxlist: res.maxlist}; } /** * Alternative version that takes vectors [x] and [y] instead of * [values] as input and returns intervals that contain local minima * and local maxima. [x] elements can be of any type. * * @author Balint Morvai * @license http://en.wikipedia.org/wiki/MIT_License MIT License * @param x * @param y * @param eps * @returns {minlist: Array, maxlist: Array} */ static extremaXY(x, y, eps) { // declare local vars var n, s, m, M, maxlist, minlist, i, j; // define x & y enumerated arrays var enumerate = function(obj) { var arr = []; var keys = Object.keys(obj); for (var k = 0; k < keys.length; k++) { arr[k] = obj[keys[k]]; } return arr; } y = enumerate(y); x = enumerate(x); // set initial values n = y.length; s = 0; m = y[0]; M = y[0]; maxlist = []; minlist = []; i = 1; if (typeof eps == "undefined") { eps = 0.1; } // the algorithm while (i < n) { if (s == 0) { if (!(M - eps <= y[i] && y[i] <= m + eps)) { if (M - eps > y[i]) { s = -1; } if (m + eps < y[i]) { s = 1; } } M = Math.max(M, y[i]); m = Math.min(m, y[i]); } else { if (s == 1) { if (M - eps <= y[i]) { M = Math.max(M, y[i]); } else { j = i - 1; while(y[j] >= M - eps) { j--; } maxlist.push( [x[j], x[i]] ); s = -1; m = y[i]; } } else { if(s == -1) { if(m + eps >= y[i]) { m = Math.min(m, y[i]); } else { j = i - 1; while(y[j] <= m + eps) { j--; } minlist.push( [x[j], x[i]] ); s = 1; M = y[i]; } } } } i++; } return {minlist: minlist, maxlist: maxlist}; } // helper to make an array or object an enumerated array static enumerate(obj) { var arr = []; var keys = Object.keys(obj); for (var k = 0; k < keys.length; k++) { arr[k] = obj[keys[k]]; } return arr; } }5a:[{"id":"c9dfc237e469ea75298e9efabc69ff41136533d927549826e8987df035bcf53be1d45783ed54c514cc61b733f7503f92ef1d6193bb117d170538dc6d71f7082b","href":"https://static.observableusercontent.com/files/c9dfc237e469ea75298e9efabc69ff41136533d927549826e8987df035bcf53be1d45783ed54c514cc61b733f7503f92ef1d6193bb117d170538dc6d71f7082b","name":"unit circle@1.svg","type":"image/svg+xml","lastModified":1674142323139.147,"size":172617}] 44:{"id":"c38bedcfd25d9d08","slug":"linear-fourier","title":"linear & Fourier math (WIP)","thumbnail":"a6ad63b6559f6ab9a02db567a74ce6f7f0d4510392452bb43d5e0f3c0d22869f","access_level":"public","create_time":"$D2023-01-19T15:32:03.139Z","update_time":"$D2023-02-28T16:36:37.036Z","view_time":null,"first_public_time":"$D2023-01-19T15:32:03.139Z","has_unpublished_edits":null,"fork":{"id":"af2e374f9b420294","slug":"calculus","title":"calculus","owner":{"id":"d2b7afa3a61febdf","login":"rmw4269","name":"Riley"}},"stars":2,"starred":false,"owner":{"type":"team","id":"d2b7afa3a61febdf","login":"rmw4269","name":"Riley","avatar_url":"https://avatars-next.observableusercontent.com/839ad38e4ca0e32eaad7be29b5bc0c3a7f4304d5f91dd0f3642acf08015b6530","tier":"starter_2024","bio":"I enjoy spreadsheets and JavaScript way too much.","following":false},"version":3988,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"817e538440b46e8a","login":"rmw4269","name":"Riley","avatar_url":"https://avatars-next.observableusercontent.com/839ad38e4ca0e32eaad7be29b5bc0c3a7f4304d5f91dd0f3642acf08015b6530","tier":null,"bio":"I enjoy spreadsheets and JavaScript way too much.\n\ntrust://Riley.science!","following":false}],"members":[{"type":"individual","id":"817e538440b46e8a","login":"rmw4269","name":"Riley","avatar_url":"https://avatars-next.observableusercontent.com/839ad38e4ca0e32eaad7be29b5bc0c3a7f4304d5f91dd0f3642acf08015b6530","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":3,"collection":null,"type":"notebook","body":{"titling":"auto","title":"linear & Fourier math (WIP)","cells":[{"id":0,"value":"md`# linear & Fourier math (WIP)\n\nThis is my personal study guide for the linear & Fourier math college course that I ${Date.now() > new Date(2023, 4, 15) ? \"took in 2023 spring\" : \"am taking this spring\"}. If you want to use this code, please pin the version or copy it; I make no stability guarantees.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":796,"value":"{\n const list = ToC({ headers: [\"h2\"], filter: [\"appendix\", \"license\", \"other resources\", \"symbols\"], invalidation });\n list.style.columns = 3;\n return list;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1608,"value":"## other resources\nI have found the [Desmos graphing calculator](//Desmos.com/calculator) extremely useful. For more calculus-oriented stuff, check out the [corresponding notebook](/@rmw4269/calculus)!","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":599,"value":"{\n let e = document.createElement(\"div\");\n {\n let header = document.createElement(\"h2\");\n header.append(\"symbols\");\n e.append(header);\n }\n e.append(...[\n [\"abcdenxyθ\", \"variables\"],\n [\"fghuv\", \"functions\"]\n ]\n .map(([symbols, type]) => {\n let paragraph = document.createElement(\"p\");\n paragraph.append(\n symbols.length == 1 ? \"The symbol \" : \"The symbols \",\n ...[...symbols].sort().flatMap((symbol, index, array) => {\n let t = tex`${symbol}`;\n switch (array.length) {\n case 1: return t;\n case 2: return (index == 0) ? [t, \" & \"] : [t];\n default: return (index == 0) ? [t] : (index == array.length - 1) ? [\", & \", t] : [\", \", t];\n }\n }),\n symbols.length == 1 ? \" represents \" : \" represent \",\n type,\n \".\"\n );\n paragraph.normalize();\n return texAutoColor(paragraph);\n }));\n return e;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2781,"value":"ʘimaging_model = wrapHeading(\"imaging model\", 2,\n wrapElm(\"h3\")`imaging tasks`,\n wrapElm(\"p\")(texC`${texFn(\"f\")`x`}=g`),\n wrapElm(\"dl\")(...[\n \"forward task\",\n takeTag.array`find ${texC`g`} given ${texC`f`} & ${texC`x`}`,\n \"reverse task\",\n takeTag.array`find ${texC`x`} given ${texC`f`} & ${texC`g`}`,\n \"system analysis\",\n takeTag.array`find ${texC`f`} given ${texC`x`} & ${texC`g`}`\n ].map((e, i) => wrapElm((i % 2) ? \"dd\" : \"dt\")(e)))\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2903,"value":"wrapHeading(\"Euler relation\",\n (e => (e.style.fontSize = \"150%\", e))(texCIB`e^{i\\theta}=${texFn.cos`\\theta`}+i\\cdot${texFn.sin`\\theta`}`)\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3774,"value":"wrapHeading(\"Euler’s identity\",\n (e => (e.style.fontSize = \"150%\", e))(texCIB`e^{i\\pi}=-1`)\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3498,"value":"wrapHeading(\"Fourier transform\",\n(e => (e.style.fontSize = \"150%\", e))(texCB`${texFn`F``\\xi`}=${texAbs`${texFn`F``\\xi`}`}e^{i\\Phi${texBracket(\"{\")`${texFn`F``\\xi`}`}}`)\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2797,"value":"wrapHeading(\"sine & cosine parameter addition\", 2,\ntexCB`${texFn.cos`a \\pm b`}=${texFn.cos`a`}${texFn.cos`b`} \\mp ${texFn.sin`a`}${texFn.sin`b`}`,\ntexCB`${texFn.sin`a \\pm b`}=${texFn.sin`a`}${texFn.cos`b`} \\pm ${texFn.cos`a`}${texFn.sin`b`}`\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2810,"value":"wrapHeading(\"even & odd components\", 2,\ntexCB`${texFn`f_{even}``x`}=${texFrac`${texFn`f``x`}+${texFn`f``-x`}`(2)}`,\ntexCB`${texFn`f_{odd}``x`}=${texFrac`${texFn`f``x`}-${texFn`f``-x`}`(2)}`\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2909,"value":"ʘ1D_special_functions = wrapHeading(htl.html.fragment`1D special functions`, 2)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2940,"value":"$46","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3881,"value":"wrapHeading(htl.html.fragment`point source: ${tex`\\delta`}`, 3,\nhtl.html`\n

\n${plotAdjust(Plot.plot({\n marks: [...plotAxisRules,\n Plot.dot([\n [0, 1]\n ], {symbol: \"circle\", fill: \"currentColor\"})\n ],\n height: 128,\n x: {\n label: \"x\",\n ticks: 2,\n tickFormat: fracFormat,\n domain: [-1, 1],\n grid: true\n },\n y: {\n label: \"y\",\n ticks: 1,\n tickFormat: fracFormat,\n domain: [0, 1],\n grid: true\n },\n style: {\n background: \"transparent\"\n }\n}))}\n${texCB`${texFn`\\delta``x`}\\overset{\\text{def}}{=}\\begin{cases}\n1, && x = 0\n\\end{cases}`}\n

\n${plotAdjust(Plot.plot({\n height: 128,\n marks: [...plotAxisRules,\n Plot.line([\n [-2, 0],\n [-1, 0],\n [0, 1],\n [1, 0],\n [2, 0]\n ])\n ],\n x: {\n label: \"x\",\n ticks: 5,\n tickFormat: fracFormat,\n grid: true\n },\n y: {\n label: \"y\",\n ticks: 3,\n tickFormat: fracFormat,\n domain: [0, 1],\n grid: true\n },\n style: {\n background: \"transparent\"\n }\n}))}\n${texCB`${texMat(\"\",\n[String.raw`${texFn`TRI``x`}\\overset{\\text{def}}{=}`,\nString.raw`\\begin{cases}\n1 - ${texAbs`x`}, && ${texAbs`x`} < 1 \\\\\n0, && ${texAbs`x`} \\ge 1\n\\end{cases}`],\n[String.raw`${texFn`TRI``x`}=`, String.raw`${texBracket[\"(\"]`1-${texAbs`x`}`}\\cdot ${texFn`RECT`(texFrac`x`(2))}`]\n)}`}\n

\n${plotAdjust(Plot.plot({\n height: 128,\n marks: [...plotAxisRules,\n Plot.line([\n [-1, -1],\n [0, -1]\n ]),\n Plot.line([\n [0, 1],\n [1, 1]\n ]),\n Plot.dot([\n [0, -1],\n [0, 1]\n ], {stroke: \"currentColor\", fill: \"#FFF\"}),\n Plot.dot([[0, 0]], {fill: \"currentColor\"})\n ],\n x: {\n label: \"x\",\n ticks: 2,\n tickFormat: fracFormat,\n grid: true\n },\n y: {\n label: \"y\",\n ticks: 2,\n tickFormat: fracFormat,\n domain: [-1, 1],\n grid: true\n },\n style: {\n background: \"transparent\"\n }\n}))}\n${texCB`${texFn`SGN``x`}\\overset{\\text{def}}{=}\\begin{cases}\n-1, && x < 0 \\\\\n0, && x = 0 \\\\\n1, && x > 0\n\\end{cases}`}\n

\n${plotAdjust(Plot.plot({\n height: 128,\n marks: [...plotAxisRules,\n Plot.line([\n [-1, 0],\n [0, 0]\n ]),\n Plot.line([\n [0, 1],\n [1, 1]\n ]),\n Plot.dot([\n [0, 0],\n [0, 1]\n ], {stroke: \"currentColor\", fill: \"#FFF\"}),\n Plot.dot([[0, 0.5]], {fill: \"currentColor\"})\n ],\n x: {\n label: \"x\",\n ticks: 2,\n tickFormat: fracFormat,\n grid: true\n },\n y: {\n label: \"y\",\n ticks: 2,\n tickFormat: fracFormat,\n domain: [0, 1],\n grid: true\n },\n style: {\n background: \"transparent\"\n }\n}))}\n${texCB`${texFn`STEP``x`}\\overset{\\text{def}}{=}\\begin{cases}\n0, && x < 0 \\\\\n${texFrac(1)(2)}, && x = 0 \\\\\n1, && x > 0\n\\end{cases}`}\n

\n${plotAdjust(Plot.plot({\n marks: [\n Plot.ruleX([0], {opacity: 0.5}),\n Plot.ruleY([0], {opacity: 0.5}),\n Plot.line(plotXs.map(x => [x, Math.sin(x * Math.PI)]))\n ],\n x: {\n label: \"x\",\n ticks: 5,\n tickFormat: x => x == 0 ? 0 : `${x == 1 ? \"\" : x == -1 ? \"−\" : fracFormat(x)}π`,\n grid: true\n },\n y: {\n label: \"y\",\n ticks: 3,\n tickFormat: fracFormat,\n domain: [-1, 1],\n grid: true\n },\n style: {\n background: \"transparent\"\n }\n}))}\n

\n${plotAdjust(Plot.plot({\n marks: [...plotAxisRules,\n Plot.line(plotXs.map(x => [x, Math.cos(x * Math.PI)]))\n ],\n x: {\n label: \"x\",\n ticks: 5,\n tickFormat: x => x == 0 ? 0 : `${x == 1 ? \"\" : x == -1 ? \"−\" : fracFormat(x)}π`,\n grid: true\n },\n y: {\n label: \"y\",\n ticks: 3,\n tickFormat: fracFormat,\n domain: [-1, 1],\n grid: true\n },\n style: {\n background: \"transparent\"\n }\n}))}\n

\n`\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3200,"value":"$47","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3335,"value":"$48","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3362,"value":"wrapHeading(htl.html.fragment`quadratic-phase sinusoid (‘chirp’)`, 3,\nhtl.html`\n

sine

\n${plotAdjust(Plot.plot({\n height: 128,\n marks: [...plotAxisRules,\n Plot.line(plotXs.map(x => [x *= 4, Math.sin(x * x * Math.PI)]))\n ],\n x: {\n label: \"x\",\n ticks: 9,\n tickFormat: fracFormat,\n grid: true\n },\n y: {\n label: \"y\",\n ticks: 2,\n tickFormat: fracFormat,\n domain: [-1, 1],\n grid: true\n },\n style: {\n background: \"transparent\"\n }\n}))}\n${texCB`${texFn.sin`\\pi x^2`}`}\n

\n\n

cosine

\n${plotAdjust(Plot.plot({\n height: 128,\n marks: [...plotAxisRules,\n Plot.line(plotXs.map(x => [x *= 4, Math.cos(x * x * Math.PI)]))\n ],\n x: {\n label: \"x\",\n ticks: 9,\n tickFormat: fracFormat,\n grid: true\n },\n y: {\n label: \"y\",\n ticks: 2,\n tickFormat: fracFormat,\n domain: [-1, 1],\n grid: true\n },\n style: {\n background: \"transparent\"\n }\n}))}\n${texCB`${texFn.cos`\\pi x^2`}`}\n

\n${plotAdjust(Plot.plot({\n height: 256,\n marks: [...plotAxisRules,\n Plot.line(plotXs.map(x => [x *= 2, Math.exp(-Math.PI * x * x)]))\n ],\n x: {\n label: \"x\",\n ticks: 9,\n tickFormat: fracFormat,\n grid: true\n },\n y: {\n label: \"y\",\n ticks: 3,\n tickFormat: fracFormat,\n grid: true\n },\n style: {\n background: \"transparent\"\n }\n}))}\n${texCB`${texFn`GAUS``x`}${texEqDef}e^{-\\pi x^{2}}`}\n

superGauss

\n${plotAdjust(Plot.plot({\n height: 256,\n marks: [...plotAxisRules,\n Plot.line(plotXs.map(x => [x *= 2, Math.exp(-Math.PI * x * x)]), {opacity: 0.25}),\n Plot.line(plotXs.map(x => [x *= 2, Math.exp(-Math.PI * Math.pow(Math.abs(x), superGaussN))]))\n ],\n x: {\n label: \"x\",\n ticks: 9,\n tickFormat: fracFormat,\n grid: true,\n nice: true,\n zero: true\n },\n y: {\n label: \"y\",\n ticks: 3,\n tickFormat: fracFormat,\n grid: true,\n nice: true,\n zero: true\n },\n style: {\n background: \"transparent\"\n }\n}))}\n${texCB`${texMat(\"\",\n[String.raw`${texFn`GAUS``x; n`}${texEqDef}`, String.raw`e^{-\\pi ${texAbs`x`}^{n}}`],\n[String.raw`${texFn`f``x`}=`, String.raw`e^{-\\pi ${superGaussN % 2 ? texAbs`x` : \"x\"}${superGaussN == 1 ? \"\" : `^{${fracFormatTex(superGaussN)}}`}}`],\n)}`}\n

Bessel

trigonometry

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":338,"value":"$4a","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":630,"value":"$4b","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1853,"value":"### integrating powers","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1849,"value":"texAutoColor(wrapHeading(\"Pythagorean identities\", 4,\n \"For odd powers of sine or cosine and for powers of tangent or cotangent greater than two, substitute one of the powers with a Pythagoeran identity.\",\n tex.block`${texFn.sin`x`}^2+${texFn.cos`x`}^2=1`,\n tex.block`${texFn(\"sec\", 2)`x`}=${texFn(\"tan\", 2)`x`}+1`,\n tex.block`${texFn(\"csc\", 2)`x`}=${texFn(\"cot\", 2)`x`}+1`)\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1856,"value":"texAutoColor(wrapHeading(\"even powers of sine & cosine\", 4,\n \"Reduce the power with one of the half-angle formulae.\",\n tex.block`${texFn.sin`\\theta`}^2=\\frac{1-${texFn.cos`2\\theta`}}{2}`,\n tex.block`${texFn.cos`\\theta`}^2=\\frac{1+${texFn.cos`2\\theta`}}{2}`)\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1864,"value":"texAutoColor(wrapHeading(\"secant & tangent power reduction\", 4,\n tex.block`${texInt.x(texFn(\"sec\", \"n\")`x`)}=${texFrac`${texFn(\"sec\", \"n-2\")`x`}\\cdot${texFn.tan`x`}+${texBracket[\"(\"]`n-2`}\\cdot${texInt.x(texFn(\"sec\", \"n-2\")`x`)}``n-1`}`,\n tex.block`${texInt.x(texFn(\"tan\", \"n\")`x`)}=${texFrac(texFn(\"tan\", \"n-1\")`x`)`n-1`}-${texInt.x(texFn(\"tan\", \"n-2\")`x`)}`\n))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1860,"value":"texAutoColor(wrapHeading(\"different arguments\", 4,\n \"When two multiplied trigonometric functions have different arguments, substitute.\",\n tex.block`${texFn.sin`ax`}\\cdot${texFn.sin`bx`}=${texFrac`${texFn.cos`x${texBracket[\"(\"]`a-b`}`}-${texFn.cos`x${texBracket[\"(\"]`a+b`}`}``2`}`,\n tex.block`${texFn.sin`ax`}\\cdot${texFn.cos`bx`}=${texFrac`${texFn.sin`x${texBracket[\"(\"]`a-b`}`}+${texFn.sin`x${texBracket[\"(\"]`a+b`}`}``2`}`,\n tex.block`${texFn.cos`ax`}\\cdot${texFn.cos`bx`}=${texFrac`${texFn.cos`x${texBracket[\"(\"]`a-b`}`}+${texFn.cos`x${texBracket[\"(\"]`a+b`}`}``2`}`)\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":505,"value":"makeSectionCluster(\"inverse trigonometric integrals\",\n tex.block`\\int${texBracket[\"[\"]`\\frac{1}{\\sqrt{a^2-u^2}}`}\\textrm{d}u=\\sin^{-1}${texBracket[\"(\"]`\\frac{u}{a}`}+C`,\n tex.block`\\int${texBracket[\"[\"]`\\frac{1}{a^2+u^2}`}\\textrm{d}u=${texBracket[\"(\"]`\\frac{1}{a}`}\\cdot\\tan^{-1}${texBracket[\"(\"]`\\frac{u}{a}`}+C`,\n tex.block`\\int${texBracket[\"[\"]`\\frac{1}{u\\sqrt{u^2-a^2}}`}\\textrm{d}u=${texBracket[\"(\"]`\\frac{1}{a}`}\\cdot\\sec^{-1}${texBracket[\"(\"]`\\frac{${texBracket[\"|\"]`u`}}{a}`}+C`\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":457,"value":"makeSectionCluster(\"logarithms\",\n tex.block`${texDeriv(\"\", \"x\", \"[\")(texFn.ln`u`)}=\\frac{\\mathrm{d} u}{u}`,\n tex.block`${texDeriv(\"\", \"x\", \"[\")(texFn.log`b``u`)}=\\frac{\\mathrm{d}u}{u\\cdot \\ln(b)}`,\n tex.block`\\int{${texBracket[\"[\"](texFrac(1)`x`)}\\mathrm{d}x = \\ln{${texBracket[\"(\"]`|x|`}}}+C`,\n tex.block`\\int{${texBracket[\"[\"](texFn.ln`x`)}}\\mathrm{d}x = x ${texBracket[\"(\"]`\\ln{(x)}-1`}+C`,\n tex.block`\\int{${texBracket[\"[\"](texFn.log`b``x`)}}\\mathrm{d}x = \\frac{x ${texBracket[\"(\"]`\\ln{(x)}-1`}}{\\ln{(b)}}+C`\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":203,"value":"makeSectionCluster(\"miscellaneous relationships\",\n [tex.block`${texDeriv(\"\", \"x\", \"[\")`a^x`}=a^x\\ln(a)`, \", when \", tex`a>0`],\n tex.block`${texDeriv(\"\", \"x\", \"[\")`e^x`}=e^x`,\n tex.block`${texInt.x`a^x`}=\\frac{a^x}{\\ln{(a)}}+C`,\n tex.block`\\int{${texBracket(\"[\")`e^{kx}`}}\\mathrm{d}x=\\frac{e^{kx}}{k}+C`,\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":525,"value":"ʘunitCircle = {\n const wrap = document.createElement(\"div\");\n const header = document.createElement(\"h2\");\n const image = new DOMParser().parseFromString(await FileAttachment(\"unit circle@1.svg\").text(), \"image/svg+xml\").documentElement;\n image.style.maxWidth = \"var(--cell-width)\";\n image.style.maxHeight = `${(screen.availHeight ?? (screen.height - 64)) * 0.75}px`;\n header.append(\"unit circle\");\n wrap.append(header, image, html`

This diagram is from Wikimedia Commons and is a colored version of Gustavb’s original work from 2006.

`);\n if (wrap.children.length == 1) {\n const element = wrap.firstChild;\n element.remove();\n return element;\n }\n return wrap;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3627,"value":"## configuration","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":3067,"value":"viewof figureFontSize = Inputs.range([0.125, 4], {label: \"figure font multiplier\", step: 0.125, value: 2})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3615,"value":"### variable color palette","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":136,"value":"$4c","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3619,"value":"viewof texAutoColorCase = {\n const keys = [\"Latin\", \"Greek\", \"other\"];\n const wrap = document.createElement(\"div\");\n Object.defineProperty(wrap, \"value\", {\n enumerable: true,\n configurable: true,\n get: function value() {\n let v = this.firstElementChild.value;\n return Object.fromEntries(keys.map(k => [k, v.includes(k)]));\n }\n });\n wrap.append(Inputs.checkbox(keys, {\n label: \"case sensitivity\",\n value: [\"Latin\", \"Greek\", \"other\"]\n }));\n invalidation.then(() => {\n delete wrap.value;\n wrap.replaceChildren();\n wrap.remove();\n });\n return wrap;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3647,"value":"viewof texAutoColorStyle = Inputs.toggle({\n label: \"style sensitivity\",\n value: true\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3569,"value":"$4d","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":833,"value":"$4e","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":279,"value":"## appendix","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":18,"value":"$4f","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3522,"value":"","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":3781,"value":"Cephes = {\n let Cephes = require(\"//bundle.run/cephes@1.2.0\");\n await Cephes.compiled;\n return Cephes;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3715,"value":"function symbolInfo(elm, attrs = false) {\n let out = {};\n let sym = elm.innerText.trim();\n out.raw = sym;\n attrs && (elm.dataset.symbolRaw = out.raw);\n if (sym.match(/[A-Za-z]/)) {\n out.lang = \"Latin\";\n texAutoColorCase.Latin || (sym = sym.toLowerCase());\n } else if (sym.length > 1 ? [...sym].some(l => greekAlphabet.has(l)) : greekAlphabet.has(sym)) {\n out.lang = \"Greek\";\n texAutoColorCase.Greek || (sym = sym.toLowerCase());\n out.lang = \"other\";\n } else if (!texAutoColorCase.other) {\n sym = sym.toLowerCase();\n }\n attrs && (elm.dataset.symbolLang = out.lang);\n out.base = sym;\n attrs && (elm.dataset.symbolBase = out.base);\n out.style = [...elm.classList].filter(cls => texAutoColorClasses.has(cls));\n attrs && (elm.dataset.symbolStyle = out.style.join(\" \"));\n out.group = texAutoColorStyle\n ? `${sym}-${out.style.join(\"|\")}`\n : sym;\n attrs && (elm.dataset.symbolGroup = out.group);\n return out;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":121,"value":"$50","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3516,"value":"greekAlphabet = new Map([\n \"Αα alpha\",\n \"Ββ\tbeta\",\n \"Γγ gamma\",\n \"Δδ delta\",\n \"Εε epsilon\",\n \"Ζζ zeta\",\n \"Ηη eta\",\n \"Θθ theta\",\n \"Ιι iota\",\n \"Κκ kappa\",\n \"Λλ lambda\",\n \"Μμ mu\",\n \"Νν nu\",\n \"Ξξ xi\",\n \"Οο omicron\",\n \"Ππ pi\",\n \"Ρρ rho\",\n \"Σσς sigma\",\n \"Ττ tau\",\n \"Υυ upsilon\",\n \"Φφ phi\",\n \"Χχ chi\",\n \"Ψψ psi\",\n \"Ωω omega\"\n].map(s => s.split(/\\s+/)).flatMap(([letters, name]) => [...letters].map(letter => [letter, name])))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1199,"value":"texSum = {\n function texSummation(variable = \"n\", start = \"1\", end) {\n start = texMaybeInfinity(start, 0);\n end = texMaybeInfinity(end, 1);\n return nullToString((...contents) => String.raw`\\sum_{${variable} = ${start}}^{${end}}${texBracket[\"[\"](...contents)}`);\n }\n for (let v of \"iknux\") {\n Object.defineProperty(texSummation, v, {\n value: texSummation(v),\n enumerable: true\n });\n }\n return texSummation;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1173,"value":"texLim = {\n function texLimit(variable = \"n\", end) {\n end = texMaybeInfinity(end, 1);\n return nullToString((...contents) => String.raw`\\lim\\limits_{ ${variable} \\to ${end} } ${texBracket[\"[\"](...contents)}`);\n }\n for (let v of \"iknux\") {\n Object.defineProperty(texLimit, v, {\n value: texLimit(v), enumerable: true\n })\n }\n return texLimit;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":968,"value":"texParseError = {\n try {\n tex`\\csch`;\n } catch (e) {\n e = Object.getPrototypeOf(e);\n e.name ?? Object.defineProperty(e, \"name\", {\n value: \"ParseError\",\n enumerable: true,\n configurable: true\n });\n return e;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1701,"value":"$51","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":962,"value":"$52","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2830,"value":"texMat = {\n const brackEnvis = new Map([[null, \"\"], [NaN, \"smallmatrix\"], ...Object.entries({\n \"\": \"matrix\",\n \"(\": \"pmatrix\",\n \"[\": \"bmatrix\",\n \"|\": \"vmatrix\",\n \"||\": \"Vmatrix\",\n \"{\": \"Bmatrix\"\n })]);\n\n return function texMat(bracket = \"[\", ...rows) {\n rows = rows.map(row => (!isString(row) && (Symbol.iterator in row)) ? (\n (Array.isArray(row) ? row : [...row]).join(\" & \")\n ) : row).join(\" \\\\\\\\\\n\");\n if (brackEnvis.has(bracket)) {\n bracket = brackEnvis.get(bracket);\n return `\\\\begin{${bracket}}\\n${rows}\\n\\\\end{${bracket}}`;\n } else {\n return `${texBracket(bracket)(`\\\\begin{matrix}\\n${rows}\\n\\\\end{matrix}`)}`;\n }\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":49,"value":"function texDeriv(numerator = \"\", denominator = \"\", bracket, bracketSize) {\n if (bracket || (bracketSize != null)) {\n return nullToString((...contents) => `${texDeriv(numerator, denominator)} ${texBracket(bracket, bracketSize)(...contents)}`);\n }\n return String.raw`\\frac{\\mathrm{d} ${numerator}}{\\mathrm{d} ${denominator}}`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":944,"value":"texAbs = texBracket[\"|\"]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1689,"value":"texFrac = Object.defineProperties(function texFraction() {\n return nullToString((...contents) =>\n String.raw`\\frac{ ${takeTag.concat.raw(...arguments)} }{ ${takeTag.concat.raw(...contents)} }`\n );\n}, {\n \"(\": {\n value: function texFractionWithParentheses() {\n return nullToString((...contents) =>\n texBracket[\"(\"]`\\frac{ ${takeTag.concat.raw(...arguments)} }{ ${takeTag.concat.raw(...contents)} }`\n );\n },\n enumerable: true\n },\n \"[\": {\n value: function texFractionWithBrackets() {\n return nullToString((...contents) =>\n texBracket[\"[\"]`\\frac{ ${takeTag.concat.raw(...arguments)} }{ ${takeTag.concat.raw(...contents)} }`\n );\n },\n enumerable: true\n }\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":72,"value":"$53","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1445,"value":"function texDifEval(from, to, ...contents) {\n [from, to] = texMaybeInfinity.range(from, to);\n return contents.length\n ? String.raw`{ ${texBracket[\"[\"]`${contents.join(\"\")}`} } \\right |_{ ${from} }^{ ${to} }`\n : nullToString((...contents) => String.raw`\\left . { ${texBracket[\"[\"]`${takeTag.concat.raw(...contents)}`} } \\right |_{ ${from} }^{ ${to} }`);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":915,"value":"texInt = {\n function texIntegral(variable = \"x\", bracket = \"[\") {\n return (...contents) =>\n String.raw`\\int{${texBracket(bracket)(...contents)}}\\mathrm{d}${variable}`;\n }\n function texDefiniteIntegral(variable = \"x\", from = 1, to = Infinity, bracket = \"[\") {\n [from, to] = texMaybeInfinity.range(from, to);\n // return {variable, from, to, bracket};\n return (...contents) => String.raw`\\int_{${from}}^{${to}}{${texBracket(bracket)(...contents)}}\\mathrm{d}${variable}`;\n }\n Object.defineProperty(texIntegral, \"def\", {\n value: texDefiniteIntegral,\n enumerable: true\n });\n for (let v of \"nuxyvθ\") {\n Object.defineProperty(texIntegral, v, {\n value: texIntegral(v),\n enumerable: true\n });\n Object.defineProperty(texDefiniteIntegral, v, {\n value: ((...args) => texDefiniteIntegral(v, ...args)),\n enumerable: true\n });\n }\n return texIntegral;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1236,"value":"texIBlock = function texInlineBlock (...args) {\n let e = tex.block(...args);\n if (!(e instanceof Element)) {\n let wrap = document.createElement(\"span\");\n wrap.append(e);\n e = wrap;\n }\n e.classList.add(\"katex-inline-block\");\n return e;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3299,"value":"texEqDef = String.raw`\\overset{\\text{def}}{=}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2590,"value":"texCIB = function texColoredInlineBlock(...args) {\n let out = texAutoColor(tex.block(...args));\n out.classList.add(\"katex-inline-block\");\n return out;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2588,"value":"texCB = function texColoredBlock(...args) {\n return texAutoColor(tex.block(...args));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2586,"value":"texC = function texColored(...args) {\n return texAutoColor(tex(...args));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1252,"value":"$54","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1738,"value":"nullToString = {\n const descriptor = Object.freeze({\n toString: {\n value: function toString() {\n return this();\n },\n enumerable: true\n }\n });\n return function nullToString() {\n for (let o of arguments) {\n if (typeof o == \"function\" || o instanceof Function) {\n Object.defineProperties(o, descriptor);\n } else {\n throw new TypeError(\"argument not a function\");\n }\n }\n return arguments.length == 1 ? arguments[0] : arguments;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1998,"value":"$55","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3654,"value":"$56","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":31,"value":"import {cellWidth} from \"@rmw4269/css-cell-width\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":446,"value":"cellWidth","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":638,"value":"function makeSectionCluster(title, ...items) {\n let level = 2;\n if (title && isHeadingNumber(items[0])) {\n level = items.shift();\n }\n let list = items\n .map(item => {\n let elm = document.createElement(\"li\");\n item && (\n (typeof item == \"object\" && !(item instanceof String) && Symbol.iterator in item)\n ? elm.append(...item)\n : elm.append(item));\n texAutoColor(elm);\n return elm;\n })\n .reduce((list, item) => {\n list.append(item);\n return list;\n }, document.createElement(\"ul\"));\n list.classList.add(\"sectionCluster\", \"katex-inline-block\");\n return title ? wrapHeading(title, level, list) : list;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2752,"value":"makeTable(\"nested inverses\", 3, {\n multiHead: true,\n headers: [\n [\"outer\"],\n [\"sine\", \"cosine\", \"tangent\"]\n ],\n rows: [\n [\n \"sine\",\n texCIB`${texFn.sin(texFn.sin.i`\\theta`)}`,\n texCIB`${texFn.sin(texFn.cos.i`\\theta`)}`,\n texCIB`${texFn.sin(texFn.tan.i`\\theta`)}`\n ]\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":646,"value":"$57","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":654,"value":"function makeSectionGrid(title, ...sections) {\n let level = 2;\n if (isHeadingNumber(sections[0])) {\n level = sections.shift();\n }\n let sublevel = level + (title ? 1 : 0);\n let grid = document.createElement(\"ul\");\n grid.classList.add(\"sectionGrid\");\n grid.append(...sections\n .map(({title: subtitle = \"section\", equations = []}) => {\n let listItem = document.createElement(\"li\");\n let heading = document.createElement(`h${sublevel}`);\n heading.append(subtitle);\n listItem.append(heading, ...equations.map(e => {\n if (!(e instanceof Node) && !(typeof e == \"string\" || e instanceof String) && e !== null && e instanceof Object && Symbol.iterator in e) {\n let wrap = document.createElement(\"div\");\n wrap.append(...e);\n e = wrap;\n }\n return texAutoColor(e);\n }));\n return listItem;\n }));\n return title ? wrapHeading(title, level, grid) : grid;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2473,"value":"function wrapFrag(...children) {\n children = takeTag.array.raw(...children);\n for (let i = children.length - 1; i >= 0; i--) {\n let child = children[i];\n if (!(child instanceof Node) && is.multi(child)) {\n Array.isArray(child) || (child = [...child]);\n children.splice(i, 1, ...child);\n i += child.length;\n }\n }\n const frag = document.createDocumentFragment();\n frag.append(...children);\n return frag;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":662,"value":"function wrapHeading(title, level, ...children) {\n if (!isHeadingNumber(level)) {\n children.unshift(level);\n level = 2;\n }\n if (!title && children.length <= 1) { return children.shift(); }\n let wrap = document.createElement(\"div\");\n if (title) {\n let header = document.createElement(`h${level.toFixed(0)}`);\n header.append(title);\n wrap.append(header);\n }\n wrap.append(...children);\n return wrap;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2207,"value":"$58","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2572,"value":"kwd = {\n const kwd = wrapElm(\"span.theorem-kwd\", {keep: invalidation});\n Object.defineProperties(kwd, Object.fromEntries(\"where let be for is if then else but and\".split(/\\s+/).sort().map(word => {\n let e = wrapElm(\"span.theorem-kwd\", {keep: invalidation})(word);\n invalidation.then(() => e = undefined);\n return [word, {\n get: (() => e.cloneNode(Infinity)),\n enumerable: true\n }];\n })));\n return kwd;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3076,"value":"plotAdjust = {\n plotAdjust.class = \"a-plot\";\n return plotAdjust;\n function plotAdjust(e) {\n (figureFontSize == 1) || e.setAttribute(\"font-size\", Number(e.getAttribute(\"font-size\", 16) || 12) * figureFontSize);\n e.classList.add(plotAdjust.class);\n return e;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3352,"value":"plotAxisRules = [\n Plot.ruleX([0], {opacity: 0.5}),\n Plot.ruleY([0], {opacity: 0.5})\n]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":701,"value":"function isHeadingNumber(n) {\n return typeof n == \"number\" || (n instanceof Number && (n = n.valueOf())) && Number.isInteger(n) && n >= 1 && n <= 6;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2832,"value":"function isString(str) {\n switch (typeof str) {\n case \"string\": return true;\n case \"object\": return str instanceof String;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":792,"value":"import {ToC} from \"@rmw4269/contents\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1044,"value":"import {takeTag} from \"@rmw4269/utilities\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1425,"value":"import {debug, is, to} from \"@rmw4269/utilities\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3043,"value":"import {fracFormat} from \"@rmw4269/fractional-selector\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3840,"value":"function fracFormatTex(exact, options = {}) {\n options.rich = \"wrap\";\n let out = fracFormat(exact, options);\n let outTex = [];\n let sup, sub;\n if (typeof out == \"object\") {\n if (out instanceof HTMLElement) {\n out.normalize();\n if (out.firstChild && !(out.firstChild instanceof Element)) {\n outTex.push(out.firstChild.textContent.replaceAll(\"\\u2212\", \"-\").replaceAll(\"\\u00A0\", \"\").trim());\n }\n if ((sup = out.querySelector(\"sup\")) && (sub = out.querySelector(\"sub\"))) {\n outTex.push(texFrac(sup.innerText.trim().replaceAll(\"\\u2212\", \"-\"))(sub.innerText.trim().replaceAll(\"\\u2212\", \"-\")));\n }\n return outTex = outTex.join(\"\\\\,\");\n } else if (out instanceof Node) {\n out.normalize();\n return out.textContent.replaceAll(\"\\u2212\", \"-\").replaceAll(\"\\u00A0\", \"\").trim();\n }\n }\n return out.toString();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3039,"value":"Plot = require(\"@observablehq/plot@0.6\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3063,"value":"Inputs = require(\"@observablehq/inputs@0.10\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3258,"value":"plotXs = {\n let Xs = [];\n for (let i = -width2; i <= width2; i++) {\n Xs.push(i / width2);\n }\n return Xs;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3969,"value":"$59","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3985,"value":"licenseSym = Symbol(\"license\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3213,"value":"viewof width2 = {\n let e = document.createElement(\"span\");\n e.append(new Text(\"width to the largest power of two\"));\n let r;\n let p = new Promise(ret => r = ret);\n p.resolve = r;\n e.value = p;\n r = p = undefined;\n return e;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3227,"value":"{\n let w2 = Math.pow(2, Math.ceil(Math.log2(width)));\n if (typeof (viewof width2).value !== \"number\") {\n (viewof width2).value.resolve(w2);\n (viewof width2).value = w2;\n } else if ((viewof width2).value !== w2) {\n (viewof width2).value = w2;\n (viewof width2).dispatchEvent(new Event(\"input\"));\n }\n return w2;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W5a","stdlib":"1"}} 45:"$44:body"