A-M baby

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

@@ -0,0 +1,36 @@
+def tol = 0.000000001  // tolerance: acceptable "wrongness" to account for rounding error
+
+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
+
+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()
+
+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()