Just another update

Task/Arithmetic-Complex/Groovy/arithmetic-complex-2.groovy

@@ -1,36 +1,17 @@
-def tol = 0.000000001  // tolerance: acceptable "wrongness" to account for rounding error
+import org.codehaus.groovy.runtime.DefaultGroovyMethods
 
-println 'Demo 1: functionality as requested'
-def a = [5,3] as Complex
-println 'a == ' + a
-def b = [0.5,6] as Complex
-println 'b == ' + b
+class ComplexCategory {
+    static Complex getI (Number a) { [0, a] as Complex }
 
-println "a + b == (${a}) + (${b}) == " + (a + b)
-println "a * b == (${a}) * (${b}) == " + (a * b)
-assert a + (-a) == 0
-println "-a == -(${a}) == " + (-a)
-assert (a * a.recip() - 1).abs() < tol
-println "1/a == (${a}).recip() == " + (a.recip())
-println()
+    static Complex plus (Number a, Complex b) { b + a }
+    static Complex minus (Number a, Complex b) { -b + a }
+    static Complex multiply (Number a, Complex b) { b * a }
+    static Complex div (Number a, Complex b) { ([a] as Complex) / b  }
+    static Complex power (Number a, Complex b) { ([a] as Complex) ** b }
 
-println 'Demo 2: other functionality not requested, but important for completeness'
-println "a - b == (${a}) - (${b}) == " + (a - b)
-println "a / b == (${a}) / (${b}) == " + (a / b)
-println "a ** b == (${a}) ** (${b}) == " + (a ** b)
-println 'a.real == ' + a.real
-println 'a.imag == ' + a.imag
-println 'a.rho == ' + a.rho
-println 'a.theta == ' + a.theta
-println '|a| == ' + a.abs()
-println 'a_bar == ' + ~a
-
-def rho = 10
-def piOverTheta = 3
-def theta = Math.PI / piOverTheta
-def fromPolar1 = Complex.fromPolar(rho, theta)          // direct polar-to-cartesian conversion
-def fromPolar2 = Complex.exp(Complex.I * theta) * rho     // Euler's equation
-println "rho*cos(theta) +  rho*i*sin(theta) == ${rho}*cos(pi/${piOverTheta}) +  ${rho}*i*sin(pi/${piOverTheta}) == " + fromPolar1
-println "rho * exp(i * theta) == ${rho} * exp(i * pi/${piOverTheta}) == " + fromPolar2
-assert (fromPolar1 - fromPolar2).abs() < tol
-println()
+    static <T> T asType (Number a, Class<T> type) {
+        type == Complex \
+            ? [a] as Complex
+            : DefaultGroovyMethods.asType(a, type)
+    }
+}