úÎ!HTE/      !"#$%&'()*+,-.(c) Scott N. Walck 2012-2017GPL-3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimental Trustworthy6p& cyclotomicA cyclotomic number. cyclotomicThe primitive n"th root of unity. For example, (4) = , is the primitive 4th root of unity, and G(5) = exp(2*pi*i/5) is the primitive 5th root of unity. In general,  n = exp(2*pi*i/n). cyclotomicThe square root of an /. cyclotomicThe square root of a 0 number. cyclotomicThe square root of -1. cyclotomicMake a Gaussian rational; gaussianRat p q is the same as  p + q * i. cyclotomic8A complex number in polar form, with rational magnitude r and rational angle s of the form r * exp(2*pi*i*s);  polarRat r s is the same as  r * e q ^ p , where s = p/q . This function is the same as . cyclotomicYA complex number in polar form, with rational magnitude and rational angle in degrees. cyclotomic]A complex number in polar form, with rational magnitude and rational angle in revolutions.  cyclotomicComplex conjugate.  cyclotomic#Real part of the cyclotomic number.  cyclotomic(Imaginary part of the cyclotomic number.1 cyclotomic&Step 1 of cyclotomic is gcd reduction.2 cyclotomic<Step 2 of cyclotomic is reduction to a rational if possible.3 cyclotomic–Compute phi(n), the number of prime factors, and test if n is square-free. We do these all together for efficiency, so we only call factorise once.4 cyclotomic&Step 3 of cyclotomic is base reduction5 cyclotomicSum of two cyclotomic numbers.6 cyclotomic"Product of two cyclotomic numbers.7 cyclotomic5Product of a rational number and a cyclotomic number.8 cyclotomicAdditive identity.9 cyclotomicAdditive inverse.: cyclotomicMultiplicative inverse.  cyclotomic Is the cyclotomic a real number?  cyclotomicIs the cyclotomic a rational? cyclotomic&Is the cyclotomic a Gaussian rational? cyclotomic$Export as an inexact complex number. cyclotomic-Export as an inexact real number if possible. cyclotomic,Return an exact rational number if possible. cyclotomic'Sine function with argument in degrees. cyclotomic)Cosine function with argument in degrees. cyclotomic+Sine function with argument in revolutions. cyclotomic-Cosine function with argument in revolutions. cyclotomicThe golden ratio,  (1 + "5)/2. cyclotomicDiscrete Fourier transform, 7X_k = sum_{n=0}^{N-1} x_n cdot e^{-i 2 pi frac{k}{N} n}. cyclotomic'Inverse discrete Fourier transform, Ax_n = frac{1}{N} sum_{k=0}^{N-1} X_k cdot e^{i 2 pi frac{k}{N} n}. cyclotomicGSolutions to the quadratic equation a x^2 + b x + c = 0. Returns ; if a == 0. cyclotomicHHeron's formula for the area of a triangle with side lengths a, b, c. cyclotomicabs and signumw are partial functions. A cyclotomic number is not guaranteed to have a cyclotomic absolute value. When defined, signum cL is the complex number with magnitude 1 that has the same argument as c; signum c = c / abs c. cyclotomic magnitude cyclotomicangle, in revolutions cyclotomiccyclotomic number cyclotomic magnitude cyclotomicangle, in degrees cyclotomiccyclotomic number cyclotomic magnitude cyclotomicangle, in revolutions cyclotomiccyclotomic number cyclotomica cyclotomicb cyclotomicc cyclotomicroots cyclotomica cyclotomicb cyclotomicc cyclotomicarea of triangle  (c) Scott N. Walck 2012-2017GPL-3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimentalSafeD   cyclotomicA real cyclotomic number.  cyclotomicThe square root of a 0 number.! cyclotomic'Sine function with argument in degrees." cyclotomic)Cosine function with argument in degrees.# cyclotomic+Sine function with argument in revolutions.$ cyclotomic-Cosine function with argument in revolutions.% cyclotomicIs the cyclotomic a rational?& cyclotomic,Return an exact rational number if possible.' cyclotomic!Export as an inexact real number.( cyclotomicThe golden ratio,  (1 + "5)/2.) cyclotomicHHeron's formula for the area of a triangle with side lengths a, b, c.* cyclotomic1The square of the magnitude of a real cyclotomic.- cyclotomicabs and signum are undefined.) cyclotomica cyclotomicb cyclotomicc cyclotomicarea of triangle  !"#$%&'()*  !"#$%&'*()<      !"#$%&'()*+,-./01234567+89:%cyclotomic-1.0-9bv6t1bjWikGxcrtTzc4mgData.Complex.CyclotomicData.Number.RealCyclotomic Cyclotomice sqrtIntegersqrtRati gaussianRatpolarRat polarRatDeg polarRatRevconjrealimagisRealisRat isGaussianRat toComplextoRealtoRatsinDegcosDegsinRevcosRev goldenRatiodftdftInv rootsQuadEqheron$fShowCyclotomic$fFractionalCyclotomic$fNumCyclotomic$fEqCyclotomicRealCyclotomicmagSq$fShowRealCyclotomic$fFractionalRealCyclotomic$fNumRealCyclotomic$fEqRealCyclotomic integer-gmpGHC.Integer.TypeIntegerbaseGHC.RealRational gcdReduce tryRational phiNrpSqfree tryReducesumCycprodCyc prodRatCyczeroCycaInvCycinvCyc GHC.MaybeNothing