64 lines
2.1 KiB
Groovy
64 lines
2.1 KiB
Groovy
import static Complex.*
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Number.metaClass.mixin ComplexCategory
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def ε = 0.000000001 // tolerance (epsilon): acceptable "wrongness" to account for rounding error
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println 'Demo 1: functionality as requested'
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def a = [5,3] as Complex
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def a1 = [real:5, imag:3] as Complex
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def a2 = 5 + 3.i
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def a3 = 5 + 3*i
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assert a == a1 && a == a2 && a == a3
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println 'a == ' + a
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def b = [0.5,6] as Complex
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println 'b == ' + b
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println "a + b == (${a}) + (${b}) == " + (a + b)
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println "a * b == (${a}) * (${b}) == " + (a * b)
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assert a + (-a) == 0
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println "-a == -(${a}) == " + (-a)
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assert (a * a.recip - 1).abs < ε
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println "1/a == (${a}).recip == " + (a.recip)
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println "a * 1/a == " + (a * a.recip)
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println()
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println 'Demo 2: other functionality not requested, but important for completeness'
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def c = 10
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def d = 10 as Complex
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assert d instanceof Complex && c instanceof Number && d == c
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assert a + c == c + a
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println "a + 10 == 10 + a == " + (c + a)
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assert c - a == -(a - c)
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println "10 - a == -(a - 10) == " + (c - a)
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println "a - b == (${a}) - (${b}) == " + (a - b)
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assert c * a == a * c
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println "10 * a == a * 10 == " + (c * a)
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assert (c / a - (a / c).recip).abs < ε
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println "10 / a == 1 / (a / 10) == " + (c / a)
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println "a / b == (${a}) / (${b}) == " + (a / b)
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assert (a ** 2 - a * a).abs < ε
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println "a ** 2 == a * a == " + (a ** 2)
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println "0.9 ** b == " + (0.9 ** b)
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println "a ** b == (${a}) ** (${b}) == " + (a ** b)
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println 'a.real == ' + a.real
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println 'a.imag == ' + a.imag
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println '|a| == ' + a.abs
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println 'a.rho == ' + a.rho
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println 'a.ρ == ' + a.ρ
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println 'a.theta == ' + a.theta
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println 'a.θ == ' + a.θ
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println '~a (conjugate) == ' + ~a
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def ρ = 10
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def π = Math.PI
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def n = 3
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def θ = π / n
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def fromPolar1 = fromPolar(ρ, θ) // direct polar-to-cartesian conversion
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def fromPolar2 = exp(θ.i) * ρ // Euler's equation
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println "ρ*cos(θ) + i*ρ*sin(θ) == ${ρ}*cos(π/${n}) + i*${ρ}*sin(π/${n})"
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println " == 10*0.5 + i*10*√(3/4) == " + fromPolar1
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println "ρ*exp(i*θ) == ${ρ}*exp(i*π/${n}) == " + fromPolar2
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assert (fromPolar1 - fromPolar2).abs < ε
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