Math tools: a library of formulas

AGENTS.md

@@ -19,7 +19,7 @@ generated parser, on netstandard2.0): keep it so, and keep containers and other
 | `src/SharpEquations.Avalonia/` | The controls for Avalonia: `MathEditBox` (the editor), `MathView`; embeds Libertinus Math |
 | `samples/SharpEquations.Avalonia.Demo/` | A window with the editor (`DemoView`, shared with the web demo) |
 | `samples/SharpEquations.Avalonia.Browser.Demo/` | The same demo on WebAssembly (needs the `wasm-tools` workload, so not in the solution; `.github/workflows/demo.yml` publishes it to GitHub Pages) |
-| `samples/SharpEquations.Avalonia.MathTools.Demo/` | A second app, math tools around the editor (`MathToolsView`, a page each: the scientific keypad) |
+| `samples/SharpEquations.Avalonia.MathTools.Demo/` | A second app, math tools around the editor (`MathToolsView`, a page each: the scientific keypad, the library of formulas) |
 | `samples/SharpEquations.Avalonia.Browser.MathTools.Demo/` | The math tools on WebAssembly (as the web demo, not in the solution build; `demo.yml` publishes them under `math/`) |
 | `benchmarks/SharpEquations.Benchmarks/` | BenchmarkDotNet benchmarks of reading, writing and converting the corpora |
 | `tests/SharpEquations.Tests/` | TUnit tests, in folders by subject (PublicApi, MathML, Omml, Mtef, UnicodeMath, LaTeX, Property, Regression) |

README.md

@@ -88,7 +88,8 @@ three projects, so that the core keeps no dependency: `SharpEquations.Editing` (
 UnicodeMath and LaTeX, and `samples/SharpEquations.Avalonia.Browser.Demo` the same demo in the browser, on WebAssembly
 (published to GitHub Pages from `main`; to run it locally: `dotnet workload install wasm-tools`, then
 `dotnet run --project samples/SharpEquations.Avalonia.Browser.Demo`). `samples/SharpEquations.Avalonia.MathTools.Demo` is a
-second app around the editor, a set of math tools (a scientific keypad that types into the editor), with
+second app around the editor, a set of math tools (a scientific keypad that types into the editor, a library of
+formulas), with
 `samples/SharpEquations.Avalonia.Browser.MathTools.Demo` in the browser (published under `math/` of the same site).
 
 ## Architecture

samples/SharpEquations.Avalonia.MathTools.Demo/Formulas.cs

@@ -0,0 +1,94 @@
+namespace SharpEquations.Avalonia.MathTools
+{
+    using System;
+    using System.Collections.Generic;
+    using System.Linq;
+
+    /// <summary>A formula of the library: its subject, its name and the formula in UnicodeMath.</summary>
+    public sealed class Formula
+    {
+        public Formula(string subject, string name, string unicodeMath)
+        {
+            Subject = subject;
+            Name = name;
+            UnicodeMath = unicodeMath;
+        }
+
+        public string Subject { get; }
+
+        public string Name { get; }
+
+        public string UnicodeMath { get; }
+    }
+
+    /// <summary>The library of formulas, by subject.</summary>
+    public static class Formulas
+    {
+        public static IReadOnlyList<Formula> All { get; } = new[]
+        {
+            new Formula("Algebra", "Quadratic formula", "x=(-b±√(b^2-4ac))/2a"),
+            new Formula("Algebra", "Difference of squares", "a^2-b^2=(a+b)(a-b)"),
+            new Formula("Algebra", "Square of a sum", "(a+b)^2=a^2+2ab+b^2"),
+            new Formula("Algebra", "Binomial theorem", "(a+b)^n=∑_(k=0)^n (n¦k) a^k b^(n-k)"),
+            new Formula("Algebra", "Arithmetic series", "∑_(k=1)^n k=(n(n+1))/2"),
+            new Formula("Algebra", "Geometric series", "∑_(k=0)^(n-1) ar^k=a (1-r^n)/(1-r)"),
+            new Formula("Algebra", "Logarithm of a product", "log_b⁡(xy)=log_b⁡x+log_b⁡y"),
+            new Formula("Algebra", "Change of base", "log_b⁡x=(ln⁡x)/(ln⁡b)"),
+            new Formula("Algebra", "Inverse of a 2×2 matrix", "(■(a&b@c&d))^(-1)=1/(ad-bc) (■(d&-b@-c&a))"),
+
+            new Formula("Geometry", "Pythagorean theorem", "a^2+b^2=c^2"),
+            new Formula("Geometry", "Area of a circle", "A=πr^2"),
+            new Formula("Geometry", "Circumference", "C=2πr"),
+            new Formula("Geometry", "Area of a triangle", "A=1/2 bh"),
+            new Formula("Geometry", "Heron's formula", "A=√(s(s-a)(s-b)(s-c))"),
+            new Formula("Geometry", "Volume of a sphere", "V=4/3 πr^3"),
+            new Formula("Geometry", "Surface of a sphere", "S=4πr^2"),
+            new Formula("Geometry", "Volume of a cone", "V=1/3 πr^2 h"),
+            new Formula("Geometry", "Distance between two points", "d=√((x_2-x_1)^2+(y_2-y_1)^2)"),
+
+            new Formula("Trigonometry", "Pythagorean identity", "sin^2⁡θ+cos^2⁡θ=1"),
+            new Formula("Trigonometry", "Tangent", "tan⁡θ=sin⁡θ/cos⁡θ"),
+            new Formula("Trigonometry", "Sine of a sum", "sin⁡(α+β)=sin⁡α cos⁡β+cos⁡α sin⁡β"),
+            new Formula("Trigonometry", "Cosine of a sum", "cos⁡(α+β)=cos⁡α cos⁡β-sin⁡α sin⁡β"),
+            new Formula("Trigonometry", "Double angle", "sin⁡2θ=2 sin⁡θ cos⁡θ"),
+            new Formula("Trigonometry", "Law of sines", "a/sin⁡α=b/sin⁡β=c/sin⁡γ"),
+            new Formula("Trigonometry", "Law of cosines", "c^2=a^2+b^2-2ab cos⁡γ"),
+            new Formula("Trigonometry", "Euler's formula", "e^(iθ)=cos⁡θ+i sin⁡θ"),
+
+            new Formula("Calculus", "Definition of the derivative", "f′(x)=lim┬(h→0) (f(x+h)-f(x))/h"),
+            new Formula("Calculus", "Product rule", "(fg)′=f′g+fg′"),
+            new Formula("Calculus", "Chain rule", "ⅆ/ⅆx f(g(x))=f′(g(x)) g′(x)"),
+            new Formula("Calculus", "Power rule", "ⅆ/ⅆx x^n=nx^(n-1)"),
+            new Formula("Calculus", "Fundamental theorem", "∫_a^b f′(x) ⅆx=f(b)-f(a)"),
+            new Formula("Calculus", "Integration by parts", "∫ u ⅆv=uv-∫ v ⅆu"),
+            new Formula("Calculus", "Taylor series", "f(x)=∑_(n=0)^∞ (f^((n)) (a))/n! (x-a)^n"),
+            new Formula("Calculus", "Gaussian integral", "∫_-∞^∞ e^(-x^2) ⅆx=√π"),
+            new Formula("Calculus", "A limit", "lim┬(x→0) sin⁡x/x=1"),
+
+            new Formula("Statistics", "Mean", "x̄=1/n ∑_(i=1)^n x_i"),
+            new Formula("Statistics", "Standard deviation", "σ=√(1/N ∑_(i=1)^N (x_i-μ)^2)"),
+            new Formula("Statistics", "Binomial coefficient", "(n¦k)=n!/(k!(n-k)!)"),
+            new Formula("Statistics", "Normal distribution", "f(x)=1/(σ√2π) e^(-1/2 ((x-μ)/σ)^2)"),
+            new Formula("Statistics", "Bayes' theorem", "P(A|B)=(P(B|A) P(A))/P(B)"),
+
+            new Formula("Physics", "Newton's second law", "𝐅=m𝐚"),
+            new Formula("Physics", "Mass–energy equivalence", "E=mc^2"),
+            new Formula("Physics", "Kinetic energy", "E_k=1/2 mv^2"),
+            new Formula("Physics", "Uniform acceleration", "s=v_0 t+1/2 at^2"),
+            new Formula("Physics", "Universal gravitation", "F=G (m_1 m_2)/r^2"),
+            new Formula("Physics", "Coulomb's law", "F=1/(4πε_0) (q_1 q_2)/r^2"),
+            new Formula("Physics", "Ideal gas law", "pV=nRT"),
+            new Formula("Physics", "Schrödinger equation", "iℏ ∂/∂t Ψ=ĤΨ"),
+        };
+
+        /// <summary>The subjects, in the order of the library.</summary>
+        public static IReadOnlyList<string> Subjects { get; } = All.Select(f => f.Subject).Distinct().ToList();
+
+        /// <summary>The formulas of a subject (all of them for null) whose name or subject contains the text, ignoring case.</summary>
+        public static IEnumerable<Formula> Find(string? subject, string? text) => All.Where(f =>
+            (subject == null || f.Subject == subject)
+            && (string.IsNullOrWhiteSpace(text)
+                || f.Name.Contains(text!.Trim(), StringComparison.OrdinalIgnoreCase)
+                || f.Subject.Contains(text!.Trim(), StringComparison.OrdinalIgnoreCase)));
+    }
+}

samples/SharpEquations.Avalonia.MathTools.Demo/FormulasPage.cs

@@ -0,0 +1,117 @@
+namespace SharpEquations.Avalonia.MathTools
+{
+    using System;
+    using System.Collections.Generic;
+    using System.Linq;
+    using global::Avalonia;
+    using global::Avalonia.Controls;
+    using global::Avalonia.Controls.Primitives;
+    using global::Avalonia.Layout;
+    using global::Avalonia.Media;
+    using SharpEquations;
+
+    /// <summary>
+    /// The library of formulas: each one drawn by a <see cref="MathView"/>, filtered by subject and by name, and opened in
+    /// the calculator with a click.
+    /// </summary>
+    public sealed class FormulasPage : UserControl
+    {
+        private static readonly EquationOptions Display = new EquationOptions { Display = true };
+
+        private readonly Action<Equation> open;
+        private readonly List<(Formula Formula, Button Card)> cards = new List<(Formula, Button)>();
+        private readonly List<ToggleButton> subjects = new List<ToggleButton>();
+        private string? subject;
+
+        public FormulasPage(Action<Equation> open)
+        {
+            this.open = open;
+
+            Search = new TextBox { PlaceholderText = "Search a formula", Width = 260 };
+            // the property, not TextChanged, which Avalonia raises later, on the dispatcher
+            Search.PropertyChanged += (_, e) =>
+            {
+                if (e.Property == TextBox.TextProperty)
+                    Filter();
+            };
+
+            var chips = Ui.Row(Search);
+            foreach (var name in new string?[] { null }.Concat(Formulas.Subjects))
+            {
+                var chip = new ToggleButton
+                {
+                    Content = name ?? "All",
+                    IsChecked = name == null,
+                    CornerRadius = new CornerRadius(16),
+                    Padding = new Thickness(14, 5),
+                };
+                chip.Click += (_, _) => ShowSubject(name);
+                subjects.Add(chip);
+                chips.Children.Add(chip);
+            }
+
+            var list = new WrapPanel { Orientation = Orientation.Horizontal, ItemSpacing = 12, LineSpacing = 12 };
+            foreach (var formula in Formulas.All)
+            {
+                var card = Card(formula);
+                cards.Add((formula, card));
+                list.Children.Add(card);
+            }
+
+            Content = Ui.Card("Formulas", "A library of formulas of algebra, geometry, trigonometry, calculus, statistics and physics: click one to open it in the calculator", new StackPanel
+            {
+                Spacing = 16,
+                Children = { chips, list },
+            });
+        }
+
+        /// <summary>The search box: the formulas whose name or subject contain its text.</summary>
+        public TextBox Search { get; }
+
+        /// <summary>The formulas shown, after the subject and the search.</summary>
+        public IEnumerable<Formula> Shown => cards.Where(c => c.Card.IsVisible).Select(c => c.Formula);
+
+        /// <summary>Shows the formulas of a subject, or all of them for null.</summary>
+        public void ShowSubject(string? name)
+        {
+            subject = name;
+            for (var i = 0; i < subjects.Count; i++)
+                subjects[i].IsChecked = (i == 0 ? null : Formulas.Subjects[i - 1]) == name;
+            Filter();
+        }
+
+        /// <summary>Opens a formula in the calculator, as a click on it does.</summary>
+        public void Open(Formula formula) => open(Equation.Parse(formula.UnicodeMath, EquationFormat.UnicodeMath, Display));
+
+        private void Filter()
+        {
+            var shown = new HashSet<Formula>(Formulas.Find(subject, Search.Text));
+            foreach (var (formula, card) in cards)
+                card.IsVisible = shown.Contains(formula);
+        }
+
+        private Button Card(Formula formula)
+        {
+            var caption = Ui.Muted(formula.Subject.ToUpperInvariant() + "  ·  " + formula.Name, 11.5);
+            var view = Ui.Math(formula.UnicodeMath, 19, display: true);
+            view.HorizontalAlignment = HorizontalAlignment.Left;
+            var button = new Button
+            {
+                Width = 352,
+                MinHeight = 108,
+                CornerRadius = new CornerRadius(12),
+                Padding = new Thickness(14, 10),
+                BorderThickness = new Thickness(1),
+                Focusable = false,
+                HorizontalContentAlignment = HorizontalAlignment.Stretch,
+                VerticalContentAlignment = VerticalAlignment.Top,
+                Content = new StackPanel { Spacing = 8, Children = { caption, view } },
+            };
+            button.Bind(Button.BackgroundProperty, button.GetResourceObservable("CodeBrush"));
+            button.Bind(Button.BorderBrushProperty, button.GetResourceObservable("CardBorderBrush"));
+            ToolTip.SetTip(button, "Open in the calculator");
+            button.Click += (_, _) => Open(formula);
+            return button;
+        }
+    }
+}

samples/SharpEquations.Avalonia.MathTools.Demo/MathToolsView.cs

@@ -9,8 +9,8 @@ namespace SharpEquations.Avalonia.MathTools
     using SharpEquations;
 
     /// <summary>
-    /// The math tools, a page each: the scientific keypad around the equation editor. The desktop window and the
-    /// WebAssembly page show the same view.
+    /// The math tools, a page each: the scientific keypad around the equation editor, and the library of formulas. The
+    /// desktop window and the WebAssembly page show the same view.
     /// </summary>
     public sealed class MathToolsView : UserControl
     {
@@ -20,24 +20,33 @@ public MathToolsView()
         {
             Ui.AddBrushes(Resources);
             Calculator = new CalculatorPage();
-
-            var tabs = new TabControl
+            Tabs = new TabControl { Margin = new Thickness(20, 12, 20, 0) };
+            FormulaLibrary = new FormulasPage(equation =>
             {
-                Margin = new Thickness(20, 12, 20, 0),
-                ItemsSource = new[]
-                {
-                    Tab("Calculator", Calculator),
-                },
+                Calculator.Editor.Equation = equation;
+                Tabs.SelectedIndex = 0;
+                Calculator.Editor.Focus();
+            });
+            Tabs.ItemsSource = new[]
+            {
+                Tab("Calculator", Calculator),
+                Tab("Formulas", FormulaLibrary),
             };
 
-            var root = new DockPanel { Children = { Ui.Docked(Header(), Dock.Top), tabs } };
+            var root = new DockPanel { Children = { Ui.Docked(Header(), Dock.Top), Tabs } };
             root.Bind(Panel.BackgroundProperty, root.GetResourceObservable("PageBrush"));
             Content = root;
         }
 
         /// <summary>The page of the scientific keypad.</summary>
         public CalculatorPage Calculator { get; }
 
+        /// <summary>The page of the library of formulas.</summary>
+        public FormulasPage FormulaLibrary { get; }
+
+        /// <summary>The tabs of the pages.</summary>
+        public TabControl Tabs { get; }
+
         private static TabItem Tab(string header, Control page) => new TabItem
         {
             Header = new TextBlock { Text = header, FontSize = 15, FontWeight = FontWeight.SemiBold },

tests/SharpEquations.Avalonia.Tests/MathTools/FormulasTests.cs

@@ -0,0 +1,41 @@
+#if NET10_0_OR_GREATER
+namespace SharpEquations.Avalonia.Tests.MathTools
+{
+    using System.Linq;
+    using System.Threading.Tasks;
+    using SharpEquations;
+    using SharpEquations.Avalonia.MathTools;
+
+    /// <summary>The formulas of the library parse without errors, and their UnicodeMath and LaTeX read back.</summary>
+    public class FormulasTests
+    {
+        private static readonly EquationOptions Display = new EquationOptions { Display = true };
+
+        public static System.Collections.Generic.IEnumerable<string> Names() => Formulas.All.Select(f => f.Name);
+
+        [Test]
+        [MethodDataSource(nameof(Names))]
+        public async Task FormulaParses(string name)
+        {
+            var formula = Formulas.All.Single(f => f.Name == name);
+            var equation = Equation.Parse(formula.UnicodeMath, EquationFormat.UnicodeMath, Display);
+            await Assert.That(equation.ToMathML().Descendants().Any(e => e.Name.LocalName == "merror")).IsFalse();
+            await Assert.That(Equation.Parse(equation.ToString(EquationFormat.UnicodeMath), EquationFormat.UnicodeMath, Display)).IsEqualTo(equation);
+            await Assert.That(Equation.TryParse(equation.ToString(EquationFormat.LaTeX), EquationFormat.LaTeX, out _)).IsTrue();
+        }
+
+        [Test]
+        public async Task NamesAreUnique() => await Assert.That(Formulas.All.Select(f => f.Name).Distinct().Count()).IsEqualTo(Formulas.All.Count);
+
+        [Test]
+        public async Task FindBySubjectAndName()
+        {
+            await Assert.That(Formulas.Find(null, null).Count()).IsEqualTo(Formulas.All.Count);
+            await Assert.That(Formulas.Find("Geometry", null).All(f => f.Subject == "Geometry")).IsTrue();
+            await Assert.That(Formulas.Find(null, "  PYTHAGOREAN ").Select(f => f.Name)).IsEquivalentTo(new[] { "Pythagorean theorem", "Pythagorean identity" });
+            await Assert.That(Formulas.Find("Trigonometry", "pythagorean").Single().Name).IsEqualTo("Pythagorean identity");
+            await Assert.That(Formulas.Find(null, "calculus").Count()).IsEqualTo(Formulas.Find("Calculus", null).Count());
+        }
+    }
+}
+#endif

tests/SharpEquations.Avalonia.Tests/MathTools/MathToolsWindowTests.cs

@@ -45,6 +45,29 @@ public async Task KeypadTypesIntoTheEditor()
             await Assert.That(equation).IsEqualTo(Equation.Parse("sin(x)^2+cos(x)^2=1", EquationFormat.UnicodeMath, new EquationOptions { Display = true }));
             await Assert.That(unicodeMath).IsNotNull();
         }
+
+        [Test]
+        public async Task FormulaOpensInTheCalculator()
+        {
+            var (shown, equation, tab) = await Headless.Run(() =>
+            {
+                var window = new MainWindow();
+                window.Show();
+                var view = window.GetVisualDescendants().OfType<MathToolsView>().Single();
+                view.Tabs.SelectedIndex = 1;
+                view.FormulaLibrary.Search.Text = "law";
+                Save(window, "math-tools-formulas");
+                var names = view.FormulaLibrary.Shown.Select(f => f.Name).ToList();
+                view.FormulaLibrary.Open(Formulas.All.Single(f => f.Name == "Law of cosines"));
+                var result = (names, view.Calculator.Editor.Equation, view.Tabs.SelectedIndex);
+                window.Close();
+                return result;
+            });
+            await Assert.That(shown).Contains("Law of sines");
+            await Assert.That(shown).DoesNotContain("Pythagorean theorem");
+            await Assert.That(equation).IsEqualTo(Equation.Parse("c^2=a^2+b^2-2ab cos⁡γ", EquationFormat.UnicodeMath, new EquationOptions { Display = true }));
+            await Assert.That(tab).IsEqualTo(0);
+        }
     }
 }
 #endif