UI: grouped functions palette with category headers/icons/colors; seed full function list and categories

src/AdvancedCalculator/Converters/CategoryToBrushConverter.cs

@@ -0,0 +1,31 @@
+using System;
+using System.Globalization;
+using Avalonia.Data.Converters;
+using Avalonia.Media;
+using AdvancedCalculator.Models;
+
+namespace AdvancedCalculator.Converters;
+
+public class CategoryToBrushConverter : IValueConverter
+{
+    public object? Convert(object? value, Type targetType, object? parameter, CultureInfo culture)
+    {
+        if (value is not FunctionCategory cat) return Brushes.Gray;
+
+        // Soft header background colors per category
+        return cat switch
+        {
+            FunctionCategory.Base => new SolidColorBrush(Color.FromRgb(0xE3, 0xF2, 0xFD)), // light blue 50
+            FunctionCategory.Angle => new SolidColorBrush(Color.FromRgb(0xE8, 0xF5, 0xE9)), // green 50
+            FunctionCategory.Rounding => new SolidColorBrush(Color.FromRgb(0xFF, 0xF3, 0xE0)), // orange 50
+            FunctionCategory.Trigonometry => new SolidColorBrush(Color.FromRgb(0xF3, 0xE5, 0xF5)), // purple 50
+            FunctionCategory.HyperbolicTrig => new SolidColorBrush(Color.FromRgb(0xE0, 0xF7, 0xFA)), // cyan 50
+            FunctionCategory.NumberTheory => new SolidColorBrush(Color.FromRgb(0xFF, 0xFD, 0xE7)), // yellow 50
+            FunctionCategory.Random => new SolidColorBrush(Color.FromRgb(0xFC, 0xE4, 0xEC)), // pink 50
+            _ => Brushes.Gray
+        };
+    }
+
+    public object? ConvertBack(object? value, Type targetType, object? parameter, CultureInfo culture) => throw new NotSupportedException();
+}
+

src/AdvancedCalculator/Models/FunctionDefinitionItem.cs

@@ -1,4 +1,5 @@
 using System.Collections.Generic;
+using System.Linq;
 
 namespace AdvancedCalculator.Models;
 
@@ -6,23 +7,115 @@ public class FunctionDefinitionItem
 {
     public string FunctionName { get; private set; } = string.Empty;
     public string FunctionDescription { get; private set; } = string.Empty;
-    public string Icon { get; private set; } = string.Empty;
     public IEnumerable<KeyValuePair<string, string>> FunctionArguments { get; private set; } = new List<KeyValuePair<string, string>>();
+    public FunctionCategory Category { get; private set; }
+
+    public string Signature => $"{FunctionName}({string.Join(", ", FunctionArguments.Select(a => a.Key))})";
 
     public static IEnumerable<FunctionDefinitionItem> DefinedFunctions
     {
         get
         {
-            yield return new FunctionDefinitionItem { FunctionName = "sin", Icon = IconFont.SineWave, FunctionDescription = "Returns the sine value of a given expression.", FunctionArguments = new[] { new KeyValuePair<string, string>("expression", "An expression to compute.") } };
+            // Base
-            yield return new FunctionDefinitionItem { FunctionName = "cos", Icon = IconFont.CosineWave, FunctionDescription = "Returns the cosine value of a given expression.", FunctionArguments = new[] { new KeyValuePair<string, string>("expression", "An expression to compute.") } };
+            yield return new FunctionDefinitionItem { FunctionName = "abs", Category = FunctionCategory.Base, FunctionDescription = "Absolute value of a number.", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
-            yield return new FunctionDefinitionItem { FunctionName = "tan", Icon = IconFont.MathTan, FunctionDescription = "Returns the tangent value of a given expression.", FunctionArguments = new[] { new KeyValuePair<string, string>("expression", "An expression to compute.") } };
+            yield return new FunctionDefinitionItem { FunctionName = "sign", Category = FunctionCategory.Base, FunctionDescription = "Sign of a number: 1 or -1.", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
-            yield return new FunctionDefinitionItem { FunctionName = "round", Icon = IconFont.RoundedCorner, FunctionDescription = "Rounds an expression to the nearest whole number.", FunctionArguments = new[] { new KeyValuePair<string, string>("expression", "An expression to compute.") } };
+            yield return new FunctionDefinitionItem { FunctionName = "min", Category = FunctionCategory.Base, FunctionDescription = "Minimum of two numbers.", FunctionArguments = new[] { new KeyValuePair<string, string>("first", "number"), new KeyValuePair<string, string>("second", "number") } };
-            yield return new FunctionDefinitionItem { FunctionName = "sqrt", Icon = IconFont.SquareRoot, FunctionDescription = "Returns the square root of a given expression.", FunctionArguments = new[] { new KeyValuePair<string, string>("expression", "An expression to compute.") } };
+            yield return new FunctionDefinitionItem { FunctionName = "max", Category = FunctionCategory.Base, FunctionDescription = "Maximum of two numbers.", FunctionArguments = new[] { new KeyValuePair<string, string>("first", "number"), new KeyValuePair<string, string>("second", "number") } };
-            yield return new FunctionDefinitionItem { FunctionName = "abs", Icon = IconFont.PlusCircle, FunctionDescription = "Returns the absolute value of a given expression.", FunctionArguments = new[] { new KeyValuePair<string, string>("expression", "An expression to compute.") } };
+
-            yield return new FunctionDefinitionItem { FunctionName = "exp", Icon = IconFont.AlphaECircle, FunctionDescription = "Returns the constant e to a given power.", FunctionArguments = new[] { new KeyValuePair<string, string>("power", "An expression to compute.") } };
+            // Angle
-            yield return new FunctionDefinitionItem { FunctionName = "log", Icon = IconFont.MathLog, FunctionDescription = "Returns the log of the first expression to the base of the second expression.", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "An expression to compute."), new KeyValuePair<string, string>("base", "An expression to compute.") } };
+            yield return new FunctionDefinitionItem { FunctionName = "degrees", Category = FunctionCategory.Angle, FunctionDescription = "Converts radians to degrees.", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
-            yield return new FunctionDefinitionItem { FunctionName = "precision", Icon = IconFont.DecimalIncrease, FunctionDescription = "Returns the value of expression1 to a given precision.", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "An expression to compute."), new KeyValuePair<string, string>("precision", "An expression to compute.") } };
+            yield return new FunctionDefinitionItem { FunctionName = "radians", Category = FunctionCategory.Angle, FunctionDescription = "Converts degrees to radians.", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "wrapangle", Category = FunctionCategory.Angle, FunctionDescription = "Wraps angle into [start, end).", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number"), new KeyValuePair<string, string>("periodStart", "number"), new KeyValuePair<string, string>("periodEnd", "number") } };
+
+            // Rounding
+            yield return new FunctionDefinitionItem { FunctionName = "floor", Category = FunctionCategory.Rounding, FunctionDescription = "Largest integer ≤ value.", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "ceiling", Category = FunctionCategory.Rounding, FunctionDescription = "Smallest integer ≥ value.", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "truncate", Category = FunctionCategory.Rounding, FunctionDescription = "Integer part toward zero.", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "round", Category = FunctionCategory.Rounding, FunctionDescription = "Round to precision (banker's).", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number"), new KeyValuePair<string, string>("precision", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "frac", Category = FunctionCategory.Rounding, FunctionDescription = "Fractional part of a number.", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "clamp", Category = FunctionCategory.Rounding, FunctionDescription = "Clamp to [low, high].", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number"), new KeyValuePair<string, string>("low", "number"), new KeyValuePair<string, string>("high", "number") } };
+
+            // Trigonometry
+            yield return new FunctionDefinitionItem { FunctionName = "sin", Category = FunctionCategory.Trigonometry, FunctionDescription = "Sine of angle (radians).", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "cos", Category = FunctionCategory.Trigonometry, FunctionDescription = "Cosine of angle (radians).", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "tan", Category = FunctionCategory.Trigonometry, FunctionDescription = "Tangent of angle (radians).", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "asin", Category = FunctionCategory.Trigonometry, FunctionDescription = "Arcsine (radians).", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "acos", Category = FunctionCategory.Trigonometry, FunctionDescription = "Arccosine (radians).", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "atan", Category = FunctionCategory.Trigonometry, FunctionDescription = "Arctangent (radians).", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "atan2", Category = FunctionCategory.Trigonometry, FunctionDescription = "Arctan(y/x) (radians).", FunctionArguments = new[] { new KeyValuePair<string, string>("y", "number"), new KeyValuePair<string, string>("x", "number") } };
+
+            // Hyperbolic Trig
+            yield return new FunctionDefinitionItem { FunctionName = "sinh", Category = FunctionCategory.HyperbolicTrig, FunctionDescription = "Hyperbolic sine.", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "cosh", Category = FunctionCategory.HyperbolicTrig, FunctionDescription = "Hyperbolic cosine.", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "tanh", Category = FunctionCategory.HyperbolicTrig, FunctionDescription = "Hyperbolic tangent.", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "asinh", Category = FunctionCategory.HyperbolicTrig, FunctionDescription = "Inverse hyperbolic sine.", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "acosh", Category = FunctionCategory.HyperbolicTrig, FunctionDescription = "Inverse hyperbolic cosine.", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "atanh", Category = FunctionCategory.HyperbolicTrig, FunctionDescription = "Inverse hyperbolic tangent.", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
+
+            // Number Theory
+            yield return new FunctionDefinitionItem { FunctionName = "fac", Category = FunctionCategory.NumberTheory, FunctionDescription = "Factorial; Γ(n+1) for non-integers; 0 outside 0..20.", FunctionArguments = new[] { new KeyValuePair<string, string>("value", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "ncr", Category = FunctionCategory.NumberTheory, FunctionDescription = "Binomial coefficient 0 ≤ r ≤ n ≤ 20.", FunctionArguments = new[] { new KeyValuePair<string, string>("first", "number"), new KeyValuePair<string, string>("second", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "npr", Category = FunctionCategory.NumberTheory, FunctionDescription = "Permutations 0 ≤ r ≤ n ≤ 20.", FunctionArguments = new[] { new KeyValuePair<string, string>("first", "number"), new KeyValuePair<string, string>("second", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "gcd", Category = FunctionCategory.NumberTheory, FunctionDescription = "GCD of two positive integers.", FunctionArguments = new[] { new KeyValuePair<string, string>("first", "number"), new KeyValuePair<string, string>("second", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "lcm", Category = FunctionCategory.NumberTheory, FunctionDescription = "LCM of two positive integers.", FunctionArguments = new[] { new KeyValuePair<string, string>("first", "number"), new KeyValuePair<string, string>("second", "number") } };
+
+            // Random
+            yield return new FunctionDefinitionItem { FunctionName = "flip", Category = FunctionCategory.Random, FunctionDescription = "Fair coin flip → boolean.", FunctionArguments = Enumerable.Empty<KeyValuePair<string, string>>() };
+            yield return new FunctionDefinitionItem { FunctionName = "bern", Category = FunctionCategory.Random, FunctionDescription = "Bernoulli trial with probability p.", FunctionArguments = new[] { new KeyValuePair<string, string>("p", "number in [0,1]") } };
+            yield return new FunctionDefinitionItem { FunctionName = "rand", Category = FunctionCategory.Random, FunctionDescription = "Uniform random in [0,1).", FunctionArguments = Enumerable.Empty<KeyValuePair<string, string>>() };
+            yield return new FunctionDefinitionItem { FunctionName = "rands", Category = FunctionCategory.Random, FunctionDescription = "Uniform random in [lower, upper).", FunctionArguments = new[] { new KeyValuePair<string, string>("lower", "number"), new KeyValuePair<string, string>("upper", "number") } };
+            yield return new FunctionDefinitionItem { FunctionName = "randn", Category = FunctionCategory.Random, FunctionDescription = "Standard normal N(0,1).", FunctionArguments = Enumerable.Empty<KeyValuePair<string, string>>() };
+            yield return new FunctionDefinitionItem { FunctionName = "randns", Category = FunctionCategory.Random, FunctionDescription = "Normal scaled by (upper − lower).", FunctionArguments = new[] { new KeyValuePair<string, string>("lower", "number"), new KeyValuePair<string, string>("upper", "number") } };
+        }
+    }
+
+    public static IEnumerable<FunctionGroup> DefinedFunctionGroups
+    {
+        get
+        {
+            var groups = new[]
+            {
+                new { Category = FunctionCategory.Base, Name = "Base", Icon = IconFont.FunctionVariant },
+                new { Category = FunctionCategory.Angle, Name = "Angle", Icon = IconFont.Protractor },
+                new { Category = FunctionCategory.Rounding, Name = "Rounding", Icon = IconFont.Ruler },
+                new { Category = FunctionCategory.Trigonometry, Name = "Trigonometry", Icon = IconFont.SineWave },
+                new { Category = FunctionCategory.HyperbolicTrig, Name = "Hyperbolic Trig", Icon = IconFont.Waveform },
+                new { Category = FunctionCategory.NumberTheory, Name = "Number Theory", Icon = IconFont.Abacus },
+                new { Category = FunctionCategory.Random, Name = "Random", Icon = IconFont.DiceMultipleOutline },
+            };
+
+            var all = DefinedFunctions.ToList();
+            foreach (var g in groups)
+            {
+                var items = all.Where(f => f.Category == g.Category).OrderBy(f => f.FunctionName).ToList();
+                if (items.Count == 0) continue;
+                yield return new FunctionGroup
+                {
+                    Category = g.Category,
+                    GroupName = g.Name,
+                    Icon = g.Icon,
+                    Functions = items
+                };
+            }
         }
     }
 }
 
+public enum FunctionCategory
+{
+    Base,
+    Angle,
+    Rounding,
+    Trigonometry,
+    HyperbolicTrig,
+    NumberTheory,
+    Random
+}
+
+public class FunctionGroup
+{
+    public FunctionCategory Category { get; set; }
+    public string GroupName { get; set; } = string.Empty;
+    public string Icon { get; set; } = string.Empty; // MDI glyph
+    public IEnumerable<FunctionDefinitionItem> Functions { get; set; } = new List<FunctionDefinitionItem>();
+}

src/AdvancedCalculator/Models/IconFont.cs

@@ -6,6 +6,7 @@ public static class IconFont
     public const string ArrowRightDropCircle = "\U000f0059";
     public const string DecimalIncrease = "\U000f01b5";
     public const string Function = "\U000f0295";
+    public const string FunctionVariant = "\U000f070f";
     public const string PlusCircle = "\U000f0417";
     public const string RoundedCorner = "\U000f0607";
     public const string SquareRoot = "\U000f0784";
@@ -15,5 +16,10 @@ public static class IconFont
     public const string MathTan = "\U000f0c98";
     public const string MathLog = "\U000f1085";
     public const string CosineWave = "\U000f1479";
+    public const string AngleAcute = "\U000f0937";
+    public const string Protractor = "\U000f0b4f";
+    public const string Ruler = "\U000f0463";
+    public const string Waveform = "\U000f147c";
+    public const string Abacus = "\U000f16e0";
+    public const string DiceMultipleOutline = "\U000f1156";
 }
-

src/AdvancedCalculator/Views/MainView.axaml

@@ -15,6 +15,7 @@
 		<conv:IsZeroConverter x:Key="IsZeroConverter" />
 		<conv:WidthToSplitViewModeConverter x:Key="WidthToSplitViewModeConverter" />
 		<conv:WidthToPaneOpenConverter x:Key="WidthToPaneOpenConverter" />
+        <conv:CategoryToBrushConverter x:Key="CategoryToBrushConverter" />
 	</UserControl.Resources>
 	<!-- Replace columns with a responsive SplitView -->
 	<SplitView x:Name="RootSplit"
@@ -132,50 +133,55 @@
 					<!-- Functions flyout anchored to this button -->
 					<Button Grid.Column="1" Command="{Binding ToggleFunctionsCommand}" Margin="0,0,6,0" MinHeight="40" MinWidth="40"
 							AutomationProperties.Name="Toggle functions panel">
-						<Button.Flyout>
+            <Button.Flyout>
-							<Flyout IsOpen="{Binding IsFunctionsPanelOpen, Mode=TwoWay}" Placement="BottomEdgeAlignedLeft">
+                <Flyout IsOpen="{Binding IsFunctionsPanelOpen, Mode=TwoWay}" Placement="BottomEdgeAlignedLeft">
-								<Border Padding="8" MinWidth="320" MaxHeight="400">
+                    <Border Padding="8" MinWidth="360" MaxHeight="420">
-									<ScrollViewer>
+                        <ScrollViewer>
-										<ListBox ItemsSource="{x:Static m:FunctionDefinitionItem.DefinedFunctions}"
+                            <StackPanel>
-												 BorderThickness="0"
+                                <ItemsControl ItemsSource="{x:Static m:FunctionDefinitionItem.DefinedFunctionGroups}">
-												 AutomationProperties.Name="Functions list">
+                                    <ItemsControl.ItemTemplate>
-											<ListBox.ItemTemplate>
+                                        <DataTemplate x:DataType="m:FunctionGroup">
-												<DataTemplate x:DataType="m:FunctionDefinitionItem">
+                                            <StackPanel Margin="0,0,0,8">
-													<Button x:DataType="vm:MainViewModel"
+                                                <!-- Group Header -->
-															DataContext="{Binding #Root.DataContext}"
+                                                <Border Background="{Binding Category, Converter={StaticResource CategoryToBrushConverter}}"
-															Command="{Binding InsertFunctionCommand}"
+                                                        CornerRadius="6" Padding="8" Margin="0,0,0,6">
-                            CommandParameter="{Binding $parent[ListBoxItem].DataContext}"
+                                                    <StackPanel Orientation="Horizontal" Spacing="8" VerticalAlignment="Center">
-															Background="Transparent" BorderThickness="0" Padding="8" MinHeight="44"
+                                                        <TextBlock FontFamily="{StaticResource MDI}" Text="{Binding Icon}"/>
-															AutomationProperties.Name="Insert function">
+                                                        <TextBlock Text="{Binding GroupName}" FontWeight="Bold"/>
-														<StackPanel Spacing="8"
+                                                    </StackPanel>
-																	DataContext="{Binding $parent[ListBoxItem].DataContext}"
+                                                </Border>
-																	x:DataType="m:FunctionDefinitionItem">
+
-															<StackPanel Orientation="Horizontal" Spacing="8">
+                                                <!-- Group Items: simple rows -->
-																<TextBlock FontFamily="{StaticResource MDI}" Text="{Binding Icon}" />
+                                                <ListBox ItemsSource="{Binding Functions}" BorderThickness="0" SelectedIndex="-1">
-																<TextBlock Text="{Binding FunctionName}" FontWeight="Bold" />
+                                                    <ListBox.ItemTemplate>
-															</StackPanel>
+                                                        <DataTemplate x:DataType="m:FunctionDefinitionItem">
-															<TextBlock Text="{Binding FunctionDescription}" FontStyle="Italic" TextWrapping="Wrap" />
+                                                            <Button x:DataType="vm:MainViewModel"
-															<ItemsControl ItemsSource="{Binding FunctionArguments}">
+                                                                    DataContext="{Binding #Root.DataContext}"
-																<ItemsControl.ItemTemplate>
+                                                                    Command="{Binding InsertFunctionCommand}"
-																	<DataTemplate>
+                                                                    CommandParameter="{Binding $parent[ListBoxItem].DataContext}"
-																		<StackPanel>
+                                                                    Background="Transparent" BorderThickness="0" Padding="8" MinHeight="36"
-																			<TextBlock Text="{Binding Key}" />
+                                                                    AutomationProperties.Name="Insert function">
-																			<TextBlock Text="{Binding Value}" FontStyle="Italic" Margin="8,0,0,0" />
+                                                                <Grid ColumnDefinitions="*,Auto">
-																		</StackPanel>
+                                                                    <StackPanel>
-																	</DataTemplate>
+                                                                        <TextBlock Text="{Binding Signature}" FontWeight="Bold"/>
-																</ItemsControl.ItemTemplate>
+                                                                        <TextBlock Text="{Binding FunctionDescription}" Opacity="0.8"/>
-															</ItemsControl>
+                                                                    </StackPanel>
-														</StackPanel>
+                                                                </Grid>
-													</Button>
+                                                            </Button>
-												</DataTemplate>
+                                                        </DataTemplate>
-											</ListBox.ItemTemplate>
+                                                    </ListBox.ItemTemplate>
-										</ListBox>
+                                                </ListBox>
-									</ScrollViewer>
+                                            </StackPanel>
-								</Border>
+                                        </DataTemplate>
-							</Flyout>
+                                    </ItemsControl.ItemTemplate>
-						</Button.Flyout>
+                                </ItemsControl>
-						<TextBlock FontFamily="{StaticResource MDI}" Text="{x:Static m:IconFont.Function}" />
+                            </StackPanel>
-					</Button>
+                        </ScrollViewer>
+                    </Border>
+                </Flyout>
+            </Button.Flyout>
+            <TextBlock FontFamily="{StaticResource MDI}" Text="{x:Static m:IconFont.Function}" />
+        </Button>
 
                     <TextBox Grid.Column="2" Text="{Binding InputText, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged}" MinHeight="44"
                              AutomationProperties.Name="Expression input"