Complex numbers support

analysis_options.yaml

@@ -0,0 +1,3 @@
+formatter:
+  trailing_commas: preserve
+  page_width: 80

lib/function_tree.dart

@@ -3,3 +3,5 @@
 export "src/extensions.dart" show FunctionTreeStringMethods;
 export "src/trees.dart"
     show FunctionTree, SingleVariableFunction, MultiVariableFunction;
+export "src/complex.dart" show Complex;
+export "src/complex_math.dart" show ComplexMath;

lib/src/base.dart

@@ -1,7 +1,11 @@
+import 'package:function_tree/src/complex.dart';
+
 /// Base class for tree nodes.
 abstract class Node {
   num call(Map<String, num> variableValues);
 
+  Complex complexCall(Map<String, Complex> variableValues);
+
   Node derivative(String variableName);
 
   /// A TeX expression representing the node.

lib/src/branches.dart

@@ -1,3 +1,5 @@
+import "package:function_tree/src/complex.dart";
+
 import "base.dart" show Node;
 import "defs.dart" as defs;
 import "derivatives.dart" show derivativesMap;
@@ -21,6 +23,10 @@ class FunctionBranch extends Branch {
   num call(Map<String, num> variables) =>
       defs.oneParameterFunctionMap[name]!(child(variables));
 
+  @override
+  Complex complexCall(Map<String, Complex> variables) =>
+      defs.complexOneParameterFunctionMap[name]!(child.complexCall(variables));
+
   @override
   String toTeX() => defs.oneParameterFunctionLatexRepresentation[name]!
       .replaceAll("C", child.toTeX());
@@ -52,6 +58,10 @@ class ParenthesisBranch extends Branch {
   @override
   num call(Map<String, num> variables) => child(variables);
 
+  @override
+  Complex complexCall(Map<String, Complex> variables) =>
+      child.complexCall(variables);
+
   @override
   String toTeX() => r"\left(C\right)".replaceAll("C", child.toTeX());
 
@@ -78,6 +88,10 @@ class NegationBranch extends Branch {
   @override
   num call(Map<String, num> variables) => -child(variables);
 
+  @override
+  Complex complexCall(Map<String, Complex> variables) =>
+      -child.complexCall(variables);
+
   @override
   String toTeX() => "-${child.toTeX()}";
 
@@ -104,6 +118,10 @@ class AffirmationBranch extends Branch {
   @override
   num call(Map<String, num> variables) => child(variables);
 
+  @override
+  Complex complexCall(Map<String, Complex> variables) =>
+      child.complexCall(variables);
+
   @override
   String toTeX() => "+${child.toTeX()}";
 

lib/src/complex.dart

@@ -0,0 +1,75 @@
+import 'dart:math' as math;
+import 'complex_math.dart';
+
+class Complex {
+  final double real;
+
+  final double imaginary;
+
+  const Complex(this.real, this.imaginary);
+
+  Complex.polar(double magnitude, double phase)
+      : real = magnitude * math.cos(phase),
+        imaginary = magnitude * math.sin(phase);
+
+  static const zero = Complex(0, 0);
+
+  static const one = Complex(1, 0);
+
+  static const e = Complex(math.e, 0);
+
+  static const i = Complex(0, 1);
+
+  static const pi = Complex(math.pi, 0);
+
+  double get magnitude => math.sqrt(real * real + imaginary * imaginary);
+
+  double get phase => math.atan2(imaginary, real);
+
+  bool get isInfinite => real.isInfinite || imaginary.isInfinite;
+
+  bool get isNaN => real.isNaN || imaginary.isNaN;
+
+  bool get isReal => imaginary == 0;
+
+  Complex operator +(Complex other) => ComplexMath.add(this, other);
+
+  Complex operator -(Complex other) => ComplexMath.subtract(this, other);
+
+  Complex operator -() => ComplexMath.negate(this);
+
+  Complex operator *(Complex other) => ComplexMath.multiply(this, other);
+
+  Complex operator /(Complex other) => ComplexMath.divide(this, other);
+
+  Complex operator %(Complex other) => ComplexMath.modulo(this, other);
+
+  double operator [](int index) {
+    if (index == 0) return real;
+    if (index == 1) return imaginary;
+    throw RangeError.index(index, this, 'Index out of range: $index');
+  }
+
+  Complex ceil() => ComplexMath.ceil(this);
+
+  Complex floor() => ComplexMath.floor(this);
+
+  Complex round() => ComplexMath.round(this);
+
+  @override
+  bool operator ==(Object other) {
+    if (other is Complex) {
+      return real == other.real && imaginary == other.imaginary;
+    }
+    return false;
+  }
+
+  @override
+  int get hashCode => Object.hash(real, imaginary);
+}
+
+extension NumToComplex on num {
+  Complex toComplex() {
+    return Complex(toDouble(), 0);
+  }
+}