mirror of
https://github.com/HananoshikaYomaru/openfreebooks.git
synced 2026-11-12 20:45:52 +00:00
510 lines
15 KiB
TypeScript
510 lines
15 KiB
TypeScript
import { renderLatex } from "@ofb/katex";
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import { createEffect, createMemo, createSignal, For, onCleanup, Show } from "solid-js";
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type Eq = [number, number, number];
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type Method = "substitution" | "elimination";
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type Preset = {
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id: string;
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label: string;
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eq1: Eq;
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eq2: Eq;
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methods: Method[];
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};
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type Step = {
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title: string;
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latex: string;
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};
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const PRESETS: Preset[] = [
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{
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id: "add-y",
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label: "x + y = 5, 2x − y = 1",
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eq1: [1, 1, 5],
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eq2: [2, -1, 1],
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methods: ["elimination", "substitution"],
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},
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{
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id: "sub-y",
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label: "y = 2x + 1, x + y = 7",
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eq1: [-2, 1, 1],
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eq2: [1, 1, 7],
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methods: ["substitution", "elimination"],
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},
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{
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id: "coins",
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label: "x + y = 8, 5x + 2y = 28",
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eq1: [1, 1, 8],
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eq2: [5, 2, 28],
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methods: ["substitution", "elimination"],
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},
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{
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id: "parallel",
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label: "x + y = 5, 2x + 2y = 12 (parallel)",
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eq1: [1, 1, 5],
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eq2: [2, 2, 12],
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methods: ["elimination"],
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},
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];
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function gcd(a: number, b: number): number {
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a = Math.abs(Math.round(a));
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b = Math.abs(Math.round(b));
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while (b) {
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const t = b;
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b = a % b;
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a = t;
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}
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return a || 1;
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}
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function lcm(a: number, b: number): number {
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return (Math.abs(a) * Math.abs(b)) / gcd(a, b);
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}
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function formatTerm(coef: number, variable: string, first: boolean): string {
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if (coef === 0) return "";
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const abs = Math.abs(coef);
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const sign =
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coef < 0 ? (first ? "-" : " - ") : first ? "" : " + ";
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const body = abs === 1 ? variable : `${abs}${variable}`;
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return `${sign}${body}`;
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}
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function formatEqLatex([a, b, c]: Eq): string {
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const xPart = formatTerm(a, "x", true);
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const yPart = formatTerm(b, "y", !xPart);
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const left = (xPart + yPart).trim() || "0";
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return `${left} = ${c}`;
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}
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function determinant(eq1: Eq, eq2: Eq): number {
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const [a1, b1] = eq1;
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const [a2, b2] = eq2;
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return a1 * b2 - a2 * b1;
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}
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function solveSystem(eq1: Eq, eq2: Eq): { x: number; y: number } | null {
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const det = determinant(eq1, eq2);
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if (Math.abs(det) < 1e-9) return null;
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const [a1, b1, c1] = eq1;
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const [a2, b2, c2] = eq2;
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const x = (c1 * b2 - c2 * b1) / det;
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const y = (a1 * c2 - a2 * c1) / det;
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return { x: round(x), y: round(y) };
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}
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function round(n: number, digits = 4) {
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const p = 10 ** digits;
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return Math.round(n * p) / p;
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}
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function formatNum(n: number) {
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if (Number.isInteger(n)) return String(n);
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return round(n, 2).toString();
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}
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function classifySystem(eq1: Eq, eq2: Eq): "unique" | "parallel" | "coincident" {
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const det = determinant(eq1, eq2);
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if (Math.abs(det) > 1e-9) return "unique";
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const [a1, b1, c1] = eq1;
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const [a2, b2, c2] = eq2;
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const ratio =
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Math.abs(a2) > 1e-9
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? a1 / a2
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: Math.abs(b2) > 1e-9
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? b1 / b2
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: 1;
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const same =
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Math.abs(a1 - ratio * a2) < 1e-9 &&
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Math.abs(b1 - ratio * b2) < 1e-9 &&
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Math.abs(c1 - ratio * c2) < 1e-9;
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return same ? "coincident" : "parallel";
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}
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function buildSubstitutionSteps(eq1: Eq, eq2: Eq, solution: { x: number; y: number }): Step[] {
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const [a1, b1, c1] = eq1;
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const steps: Step[] = [
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{
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title: "Write the system",
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latex: `\\begin{cases} ${formatEqLatex(eq1)} \\\\ ${formatEqLatex(eq2)} \\end{cases}`,
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},
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];
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if (b1 === 1 && a1 === 0) {
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steps.push({
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title: "Isolate y from equation (1)",
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latex: `y = ${formatNum(c1)}`,
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});
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steps.push({
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title: "Substitute into equation (2)",
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latex: `${formatTerm(eq2[0], "x", true)}${formatTerm(1, `(${formatNum(c1)})`, false)} = ${eq2[2]}`,
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});
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} else if (b1 === -2 && a1 === 0 && c1 === 1) {
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steps.push({
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title: "Rewrite equation (1) as y = 2x + 1",
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latex: "y = 2x + 1",
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});
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steps.push({
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title: "Substitute into equation (2)",
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latex: "x + (2x + 1) = 7",
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});
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steps.push({
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title: "Collect like terms",
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latex: "3x + 1 = 7",
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});
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steps.push({
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title: "Solve for x",
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latex: `3x = 6 \\Rightarrow x = ${formatNum(solution.x)}`,
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});
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steps.push({
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title: "Find y",
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latex: `y = 2(${formatNum(solution.x)}) + 1 = ${formatNum(solution.y)}`,
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});
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} else if (eq2[1] === 1 && eq2[0] === 1) {
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steps.push({
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title: "Express y from equation (2)",
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latex: `y = ${eq2[2]} - x`,
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});
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steps.push({
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title: "Substitute into equation (1)",
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latex: `${formatTerm(eq1[0], "x", true)}${formatTerm(eq1[1], `(${eq2[2]} - x)`, false)} = ${c1}`,
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});
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const combined = eq1[0] - eq1[1];
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const constant = c1 - eq1[1] * eq2[2];
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steps.push({
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title: "Simplify",
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latex: `${formatTerm(combined, "x", true)} = ${constant}`,
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});
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steps.push({
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title: "Solve for x",
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latex: `x = ${formatNum(solution.x)}`,
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});
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steps.push({
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title: "Find y",
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latex: `y = ${eq2[2]} - ${formatNum(solution.x)} = ${formatNum(solution.y)}`,
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});
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} else {
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steps.push({
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title: "Isolate one unknown, then substitute",
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latex: `\\text{Solve one equation for } x \\text{ or } y, \\text{ substitute into the other.}`,
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});
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steps.push({
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title: "Solution",
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latex: `(x, y) = (${formatNum(solution.x)},\\; ${formatNum(solution.y)})`,
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});
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return steps;
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}
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steps.push({
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title: "Solution",
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latex: `(x, y) = (${formatNum(solution.x)},\\; ${formatNum(solution.y)})`,
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});
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return steps;
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}
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function buildEliminationSteps(eq1: Eq, eq2: Eq, solution: { x: number; y: number }): Step[] {
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const [a1, b1, c1] = eq1;
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const [a2, b2, c2] = eq2;
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const steps: Step[] = [
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{
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title: "Write the system",
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latex: `\\begin{cases} ${formatEqLatex(eq1)} \\quad (1) \\\\ ${formatEqLatex(eq2)} \\quad (2) \\end{cases}`,
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},
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];
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if (b1 !== 0 && b2 !== 0 && b1 === -b2) {
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steps.push({
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title: "Add (1) and (2) to eliminate y",
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latex: `${formatTerm(a1 + a2, "x", true)} = ${c1 + c2}`,
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});
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steps.push({
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title: "Solve for x",
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latex: `x = ${formatNum(solution.x)}`,
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});
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steps.push({
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title: "Substitute into (1)",
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latex: `${formatNum(solution.x)} + y = ${c1} \\Rightarrow y = ${formatNum(solution.y)}`,
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});
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} else if (a1 !== 0 && a2 !== 0 && a1 === -a2) {
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steps.push({
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title: "Add (1) and (2) to eliminate x",
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latex: `${formatTerm(b1 + b2, "y", true)} = ${c1 + c2}`,
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});
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steps.push({
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title: "Solve for y",
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latex: `y = ${formatNum(solution.y)}`,
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});
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steps.push({
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title: "Substitute into (1)",
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latex: `x = ${formatNum(solution.x)}`,
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});
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} else {
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const mult1 = lcm(b1, b2) / Math.abs(b1);
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const mult2 = lcm(b1, b2) / Math.abs(b2);
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const newB1 = b1 * mult1;
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const newB2 = b2 * mult2;
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steps.push({
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title: "Match coefficients of y",
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latex: `\\text{Multiply (1) by } ${mult1}, \\text{ (2) by } ${mult2} \\text{ so y terms cancel.}`,
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});
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const op = newB1 + newB2 === 0 ? "+" : "−";
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steps.push({
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title: `Combine equations (${op})`,
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latex: `${formatTerm(a1 * mult1 + (op === "+" ? a2 * mult2 : -a2 * mult2), "x", true)} = ${op === "+" ? c1 * mult1 + c2 * mult2 : c1 * mult1 - c2 * mult2}`,
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});
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steps.push({
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title: "Solve and back-substitute",
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latex: `x = ${formatNum(solution.x)},\\quad y = ${formatNum(solution.y)}`,
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});
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}
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steps.push({
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title: "Solution",
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latex: `(x, y) = (${formatNum(solution.x)},\\; ${formatNum(solution.y)})`,
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});
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return steps;
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}
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function buildSteps(
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eq1: Eq,
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eq2: Eq,
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method: Method
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): { steps: Step[]; error: string | null } {
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const kind = classifySystem(eq1, eq2);
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if (kind === "parallel") {
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return {
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steps: [],
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error: "These lines are parallel — the system has no solution. Elimination would lead to a false statement such as 0 = 7.",
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};
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}
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if (kind === "coincident") {
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return {
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steps: [],
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error: "The two equations describe the same line — infinitely many solutions. A single (x, y) pair is not enough.",
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};
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}
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const solution = solveSystem(eq1, eq2);
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if (!solution) {
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return { steps: [], error: "Could not solve this system." };
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}
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const steps =
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method === "substitution"
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? buildSubstitutionSteps(eq1, eq2, solution)
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: buildEliminationSteps(eq1, eq2, solution);
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return { steps, error: null };
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}
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function SimultaneousSolverWorkbench() {
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const [presetId, setPresetId] = createSignal(PRESETS[0].id);
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const [method, setMethod] = createSignal<Method>("elimination");
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const [stepIndex, setStepIndex] = createSignal(0);
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const [playing, setPlaying] = createSignal(false);
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const [speed, setSpeed] = createSignal(1200);
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const preset = createMemo(() => PRESETS.find((p) => p.id === presetId()) ?? PRESETS[0]);
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const availableMethods = createMemo(() => preset().methods);
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const result = createMemo(() =>
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buildSteps(preset().eq1, preset().eq2, method())
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);
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const steps = createMemo(() => result().steps);
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const error = createMemo(() => result().error);
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const current = createMemo(() => steps()[stepIndex()] ?? null);
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const progress = createMemo(() =>
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steps().length > 0 ? ((stepIndex() + 1) / steps().length) * 100 : 0
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);
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createEffect(() => {
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presetId();
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method();
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setStepIndex(0);
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setPlaying(false);
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});
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createEffect(() => {
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if (!playing() || error()) return;
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const id = window.setInterval(() => {
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setStepIndex((i) => {
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if (i >= steps().length - 1) {
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setPlaying(false);
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return i;
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}
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return i + 1;
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});
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}, speed());
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onCleanup(() => window.clearInterval(id));
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});
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createEffect(() => {
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if (method() === "substitution" && !availableMethods().includes("substitution")) {
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setMethod(availableMethods()[0]);
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}
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if (method() === "elimination" && !availableMethods().includes("elimination")) {
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setMethod(availableMethods()[0]);
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}
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});
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const eqDisplay = createMemo(() =>
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renderLatex(
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`\\begin{cases} ${formatEqLatex(preset().eq1)} \\\\ ${formatEqLatex(preset().eq2)} \\end{cases}`
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)
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);
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return (
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<section
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class="math-widget sim-solver"
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aria-labelledby="sim-solver-title"
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>
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<h2 id="sim-solver-title" class="math-widget__title">
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Substitution & elimination step-by-step
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</h2>
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<div class="sim-solver__shell">
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<aside class="sim-solver__sidebar">
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<div class="sim-solver__field">
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<span class="sim-solver__label">Preset system</span>
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<select
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class="sim-solver__select"
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value={presetId()}
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onChange={(e) => setPresetId(e.currentTarget.value)}
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>
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<For each={PRESETS}>
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{(p) => <option value={p.id}>{p.label}</option>}
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</For>
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</select>
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</div>
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<div class="sim-solver__field">
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<span class="sim-solver__label">Method</span>
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<div class="sim-solver__method-grid" role="group" aria-label="Solution method">
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<button
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type="button"
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class="sim-solver__method-btn"
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classList={{
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"sim-solver__method-btn--active": method() === "substitution",
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"sim-solver__method-btn--disabled":
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!availableMethods().includes("substitution"),
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}}
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disabled={!availableMethods().includes("substitution")}
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aria-pressed={method() === "substitution"}
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onClick={() => setMethod("substitution")}
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>
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Substitution
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</button>
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<button
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type="button"
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class="sim-solver__method-btn"
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classList={{
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"sim-solver__method-btn--active": method() === "elimination",
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"sim-solver__method-btn--disabled":
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!availableMethods().includes("elimination"),
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}}
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disabled={!availableMethods().includes("elimination")}
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aria-pressed={method() === "elimination"}
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onClick={() => setMethod("elimination")}
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>
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Elimination
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</button>
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</div>
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</div>
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<div class="sim-solver__anim">
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<span class="sim-solver__label">Step controls</span>
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<div class="sim-solver__transport">
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<button
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type="button"
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class="sim-solver__transport-btn"
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aria-label="Previous step"
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disabled={!!error() || stepIndex() === 0}
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onClick={() => setStepIndex((i) => Math.max(0, i - 1))}
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>
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‹
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</button>
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<button
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type="button"
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class="sim-solver__play"
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disabled={!!error() || steps().length === 0}
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onClick={() => setPlaying((p) => !p)}
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>
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{playing() ? "Pause" : "Play"}
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</button>
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<button
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type="button"
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class="sim-solver__transport-btn"
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aria-label="Next step"
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disabled={!!error() || stepIndex() >= steps().length - 1}
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onClick={() => setStepIndex((i) => Math.min(steps().length - 1, i + 1))}
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>
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›
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</button>
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</div>
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<div class="sim-solver__speed">
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<span>Slow</span>
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<input
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type="range"
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class="sim-solver__speed-slider"
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min={600}
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max={2400}
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step={200}
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value={speed()}
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dir="rtl"
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aria-label="Animation speed"
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onInput={(e) => setSpeed(Number(e.currentTarget.value))}
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/>
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<span>Fast</span>
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</div>
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</div>
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</aside>
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<div class="sim-solver__stage">
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<div
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class="sim-solver__message-box"
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classList={{ "sim-solver__message-box--error": !!error() }}
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>
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<Show
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when={error()}
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fallback={
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<p class="sim-solver__message" aria-live="polite">
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Step {stepIndex() + 1} of {steps().length}
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{current() ? `: ${current()!.title}` : ""}
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</p>
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}
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>
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<p class="sim-solver__message" aria-live="polite">
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{error()}
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</p>
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</Show>
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<div class="sim-solver__progress-track">
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<div
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class="sim-solver__progress-fill"
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style={{ width: `${progress()}%` }}
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/>
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</div>
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</div>
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<div class="sim-solver__equation-panel" aria-live="polite">
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<p class="sim-solver__panel-label">System</p>
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<div class="sim-solver__system" innerHTML={eqDisplay()} />
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</div>
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<Show when={current() && !error()}>
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||
<div class="sim-solver__step-panel">
|
||
<h3 class="sim-solver__step-title">{current()!.title}</h3>
|
||
<div class="sim-solver__step-math" innerHTML={renderLatex(current()!.latex)} />
|
||
</div>
|
||
</Show>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
);
|
||
}
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||
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export default SimultaneousSolverWorkbench;
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