feat: add description field to Formula and example formulas

lib/formula_models.dart

@@ -123,12 +123,14 @@ class VariableSpec {
 
 class Formula {
   final String name;
+  final String? description;
   final List<VariableSpec> input;
   final VariableSpec output;
   final String d4rtCode;
 
   Formula({
     required this.name,
+    this.description,
     required this.input,
     required this.output,
     required this.d4rtCode,
@@ -144,7 +146,7 @@ class Formula {
 
   @override
   String toString() =>
-      'Formula(name: $name, input: $input, output: $output, d4rtCode: $d4rtCode)';
+      'Formula(name: $name, description: $description, input: $input, output: $output, d4rtCode: $d4rtCode)';
 
   @override
   bool operator ==(Object other) =>
@@ -152,13 +154,14 @@ class Formula {
       other is Formula &&
           runtimeType == other.runtimeType &&
           name == other.name &&
+          description == other.description &&
           output == other.output &&
           ListEquality().equals(input, other.input) &&
           d4rtCode == other.d4rtCode;
 
   @override
   int get hashCode =>
-      Object.hash(name, ListEquality().hash(input), output, d4rtCode);
+      Object.hash(name, description, ListEquality().hash(input), output, d4rtCode);
 
   List<String> inputVarNames() =>
       input.map((v) => v.name).toList(growable: false);
@@ -195,6 +198,7 @@ class Formula {
     }
 
     String name = SetUtils.stringValue(theSet, "name");
+    String? description = theSet ["description"] as String?;
     final List<Object?> inputSet = SetUtils.listValue(theSet, "input");
     List<VariableSpec> input = inputSet
         .map((v) => parseVar(v as Map))
@@ -205,6 +209,7 @@ class Formula {
 
     return Formula(
       name: name,
+      description: description,
       input: input,
       output: output,
       d4rtCode: d4rtCode,

lib/formulas.d4rt

@@ -0,0 +1,46 @@
+[
+  // Free fall distance (vertical)
+  {
+    name: "Free Fall Distance",
+    input: [
+      {name: "t", magnitude: "s"},  // Time in seconds
+      {name: "g", magnitude: "m/s²"}  // Gravitational acceleration
+    ],
+    output: {name: "h", magnitude: "m"},  // Height in meters
+    d4rtCode: "0.5 * g * pow(t, 2)"
+  },
+  
+  // Newton's Law of Universal Gravitation
+  {
+    name: "Gravitational Force",
+    input: [
+      {name: "m1", magnitude: "kg"},  // Mass 1
+      {name: "m2", magnitude: "kg"},  // Mass 2
+      {name: "r", magnitude: "m"}     // Distance between masses
+    ],
+    output: {name: "F", magnitude: "N"},  // Force in newtons
+    d4rtCode: "(6.67430e-11 * m1 * m2) / pow(r, 2)"
+  },
+  
+  // Kinetic Energy
+  {
+    name: "Kinetic Energy",
+    input: [
+      {name: "m", magnitude: "kg"},  // Mass
+      {name: "v", magnitude: "m/s"}  // Velocity
+    ],
+    output: {name: "KE", magnitude: "J"},  // Energy in joules
+    d4rtCode: "0.5 * m * pow(v, 2)"
+  },
+  
+  // Projectile Motion Range
+  {
+    name: "Projectile Range",
+    input: [
+      {name: "v", magnitude: "m/s"},  // Initial velocity
+      {name: "θ", magnitude: "deg"}   // Launch angle
+    ],
+    output: {name: "R", magnitude: "m"},  // Horizontal distance
+    d4rtCode: "(pow(v, 2) * sin(2 * radians(θ))) / 9.80665"
+  }
+]