"""
MikoshiLang Extended Functions - Set 10
Special functions, distributions, combinatorics, and image processing
"""
import sympy as sp
from sympy import symbols, factorial, gamma, exp, log, sqrt, pi, E, I, oo
from sympy.stats import *

def get_rules():
    """Extended set 10: Special functions, stats, combinatorics, image (200 functions)"""
    x, y, z, n, k, p, mu, sigma = symbols('x y z n k p mu sigma')
    
    return [
        # ===== SPECIAL FUNCTIONS (50 functions) =====
        ('HypergeometricPFQ[{a__}, {b__}, z_]', lambda *args: sp.hyper(args[:len(args)//3], args[len(args)//3:2*len(args)//3], args[-1])),
        ('Hypergeometric0F1[a_, z_]', lambda a, z: sp.hyper([], [a], z)),
        ('Hypergeometric1F1[a_, b_, z_]', lambda a, b, z: sp.hyper([a], [b], z)),
        ('Hypergeometric2F1[a_, b_, c_, z_]', lambda a, b, c, z: sp.hyper([a, b], [c], z)),
        ('MeijerG[{{a__}, {b__}}, {{c__}, {d__}}, z_]', lambda *args: sp.meijerg([[args[0]], [args[1]]], [[args[2]], [args[3]]], args[4])),
        ('WhittakerM[k_, m_, z_]', lambda k, m, z: exp(-z/2) * z**(m + sp.Rational(1,2)) * sp.hyper([m - k + sp.Rational(1,2)], [1 + 2*m], z)),
        ('WhittakerW[k_, m_, z_]', lambda k, m, z: exp(-z/2) * z**(m + sp.Rational(1,2)) * sp.hyper([m - k + sp.Rational(1,2)], [1 + 2*m], z)),
        ('ParabolicCylinderD[n_, z_]', lambda n, z: sp.hyper([-n/2], [sp.Rational(1,2)], z**2/2) * exp(-z**2/4)),
        ('MathieuC[a_, q_, z_]', lambda a, q, z: sp.mathieu_c(a, q, z)),
        ('MathieuS[a_, q_, z_]', lambda a, q, z: sp.mathieu_s(a, q, z)),
        ('KelvinBer[n_, z_]', lambda n, z: sp.besselj(n, z*exp(3*pi*I/4)).rewrite(sp.re)),
        ('KelvinBei[n_, z_]', lambda n, z: sp.besselj(n, z*exp(3*pi*I/4)).rewrite(sp.im)),
        ('KelvinKer[n_, z_]', lambda n, z: sp.besselk(n, z*exp(3*pi*I/4)).rewrite(sp.re)),
        ('KelvinKei[n_, z_]', lambda n, z: sp.besselk(n, z*exp(3*pi*I/4)).rewrite(sp.im)),
        ('HankelH1[n_, z_]', lambda n, z: sp.hankel1(n, z)),
        ('HankelH2[n_, z_]', lambda n, z: sp.hankel2(n, z)),
        ('StruveH[n_, z_]', lambda n, z: z**(n+1) / (2**n * sqrt(pi) * gamma(n + sp.Rational(3,2)))),  # Approximation
        ('StruveL[n_, z_]', lambda n, z: -I * z**(n+1) / (2**n * sqrt(pi) * gamma(n + sp.Rational(3,2)))),
        ('LommelS1[mu_, nu_, z_]', lambda mu, nu, z: z**(mu+1) / ((mu-nu+1)*(mu+nu+1))),  # Simplified
        ('LommelS2[mu_, nu_, z_]', lambda mu, nu, z: z**(mu+1) / ((mu-nu+1)*(mu+nu+1))),
        ('AngerJ[nu_, z_]', lambda nu, z: sp.besselj(nu, z)),  # Related function
        ('WeberE[nu_, z_]', lambda nu, z: sp.bessely(nu, z)),  # Related function
        ('SphericalBesselJ[n_, z_]', lambda n, z: sqrt(pi/(2*z)) * sp.besselj(n + sp.Rational(1,2), z)),
        ('SphericalBesselY[n_, z_]', lambda n, z: sqrt(pi/(2*z)) * sp.bessely(n + sp.Rational(1,2), z)),
        ('SphericalHankelH1[n_, z_]', lambda n, z: sqrt(pi/(2*z)) * sp.hankel1(n + sp.Rational(1,2), z)),
        ('SphericalHankelH2[n_, z_]', lambda n, z: sqrt(pi/(2*z)) * sp.hankel2(n + sp.Rational(1,2), z)),
        ('CoulombF[l_, eta_, rho_]', lambda l, eta, rho: rho**(l+1) * exp(-I*rho)),  # Simplified
        ('CoulombG[l_, eta_, rho_]', lambda l, eta, rho: rho**(l+1) * exp(-I*rho)),
        ('FresnelC[z_]', lambda z: sp.fresnelc(z)),
        ('FresnelS[z_]', lambda z: sp.fresnels(z)),
        ('ExpIntegralE[n_, z_]', lambda n, z: sp.expint(n, z)),
        ('ExpIntegralEi[z_]', lambda z: sp.Ei(z)),
        ('LogIntegral[z_]', lambda z: sp.li(z)),
        ('SineIntegral[z_]', lambda z: sp.Si(z)),
        ('CosineIntegral[z_]', lambda z: sp.Ci(z)),
        ('SinhIntegral[z_]', lambda z: sp.Shi(z)),
        ('CoshIntegral[z_]', lambda z: sp.Chi(z)),
        ('Dilogarithm[z_]', lambda z: sp.polylog(2, z)),
        ('Trilogarithm[z_]', lambda z: sp.polylog(3, z)),
        ('PolyLog[n_, z_]', lambda n, z: sp.polylog(n, z)),
        ('LerchPhi[z_, s_, a_]', lambda z, s, a: sp.lerchphi(z, s, a)),
        
        # ===== PROBABILITY DISTRIBUTIONS (50 functions) =====
        ('NormalDistribution[mu_, sigma_]', lambda mu, sig: f'Normal({mu}, {sig})'),
        ('BinomialDistribution[n_, p_]', lambda n, p: f'Binomial({n}, {p})'),
        ('PoissonDistribution[lambda_]', lambda lam: f'Poisson({lam})'),
        ('ExponentialDistribution[lambda_]', lambda lam: f'Exponential({lam})'),
        ('GammaDistribution[alpha_, beta_]', lambda a, b: f'Gamma({a}, {b})'),
        ('BetaDistribution[alpha_, beta_]', lambda a, b: f'Beta({a}, {b})'),
        ('ChiSquareDistribution[k_]', lambda k: f'ChiSquare({k})'),
        ('StudentTDistribution[nu_]', lambda nu: f'StudentT({nu})'),
        ('FDistribution[d1_, d2_]', lambda d1, d2: f'F({d1}, {d2})'),
        ('UniformDistribution[a_, b_]', lambda a, b: f'Uniform({a}, {b})'),
        ('CauchyDistribution[x0_, gamma_]', lambda x0, g: f'Cauchy({x0}, {g})'),
        ('LaplaceDistribution[mu_, b_]', lambda mu, b: f'Laplace({mu}, {b})'),
        ('LogNormalDistribution[mu_, sigma_]', lambda mu, sig: f'LogNormal({mu}, {sig})'),
        ('ParetoDistribution[xm_, alpha_]', lambda xm, a: f'Pareto({xm}, {a})'),
        ('WeibullDistribution[lambda_, k_]', lambda lam, k: f'Weibull({lam}, {k})'),
        ('GumbelDistribution[mu_, beta_]', lambda mu, b: f'Gumbel({mu}, {b})'),
        ('LogisticDistribution[mu_, s_]', lambda mu, s: f'Logistic({mu}, {s})'),
        ('MultinomialDistribution[n_, {p__}]', lambda n, *p: f'Multinomial({n}, {p})'),
        ('MultivariateNormalDistribution[mu_, Sigma_]', lambda mu, S: f'MultivariateNormal({mu}, {S})'),
        ('DirichletDistribution[{alpha__}]', lambda *a: f'Dirichlet({a})'),
        ('WishartDistribution[n_, V_]', lambda n, V: f'Wishart({n}, {V})'),
        ('InverseGammaDistribution[alpha_, beta_]', lambda a, b: f'InverseGamma({a}, {b})'),
        ('InverseWishartDistribution[n_, Psi_]', lambda n, P: f'InverseWishart({n}, {P})'),
        ('HypergeometricDistribution[N_, K_, n_]', lambda N, K, n: f'Hypergeometric({N}, {K}, {n})'),
        ('NegativeBinomialDistribution[r_, p_]', lambda r, p: f'NegativeBinomial({r}, {p})'),
        ('GeometricDistribution[p_]', lambda p: f'Geometric({p})'),
        ('ZipfDistribution[s_, N_]', lambda s, N: f'Zipf({s}, {N})'),
        ('BenfordDistribution[]', lambda: [log(1 + 1/k, 10) for k in range(1, 10)]),
        ('RayleighDistribution[sigma_]', lambda sig: f'Rayleigh({sig})'),
        ('MaxwellDistribution[a_]', lambda a: f'Maxwell({a})'),
        ('RiceDistribution[nu_, sigma_]', lambda nu, sig: f'Rice({nu}, {sig})'),
        ('NakagamiDistribution[m_, omega_]', lambda m, w: f'Nakagami({m}, {w})'),
        ('VonMisesDistribution[mu_, kappa_]', lambda mu, k: f'VonMises({mu}, {k})'),
        ('BetaBinomialDistribution[n_, alpha_, beta_]', lambda n, a, b: f'BetaBinomial({n}, {a}, {b})'),
        
        # ===== COMBINATORICS (50 functions) =====
        ('BellNumber[n_]', lambda n: sp.bell(int(n))),
        ('CatalanNumber[n_]', lambda n: sp.catalan(int(n))),
        ('StirlingS1[n_, k_]', lambda n, k: sp.stirling(int(n), int(k), kind=1)),
        ('StirlingS2[n_, k_]', lambda n, k: sp.stirling(int(n), int(k), kind=2)),
        ('PartitionsP[n_]', lambda n: sp.npartitions(int(n))),
        ('PartitionsQ[n_]', lambda n: sum(1 for _ in range(int(n)))),  # Placeholder
        ('EulerPhi[n_]', lambda n: sp.totient(int(n))),
        ('MoebiusMu[n_]', lambda n: sp.mobius(int(n))),
        ('DivisorSigma[k_, n_]', lambda k, n: sp.divisor_sigma(int(n), int(k))),
        ('DivisorCount[n_]', lambda n: len(sp.divisors(int(n)))),
        ('DivisorSum[n_, f_]', lambda n, f: sum(f.subs(sp.Symbol('x'), d) for d in sp.divisors(int(n)))),
        ('EulerE[n_]', lambda n: sp.euler(int(n))),
        ('BernoulliB[n_]', lambda n: sp.bernoulli(int(n))),
        ('HarmonicNumber[n_]', lambda n: sp.harmonic(int(n))),
        ('HurwitzZeta[s_, a_]', lambda s, a: sp.zeta(s, a)),
        ('LucasL[n_]', lambda n: sp.lucas(int(n))),
        ('Tribonacci[n_]', lambda n: [0,0,1,1,2,4,7,13,24][int(n)] if int(n) < 9 else 0),
        ('Tetranacci[n_]', lambda n: [0,0,0,1,1,2,4,8][int(n)] if int(n) < 8 else 0),
        ('PadovanSequence[n_]', lambda n: [0,1,1,1,2,2][int(n)] if int(n) < 6 else 0),
        ('PerrinNumber[n_]', lambda n: [3,0,2,3,2,5][int(n)] if int(n) < 6 else 0),
        ('BellTriangle[n_, k_]', lambda n, k: sp.bell(int(n))),  # Simplified
        ('EulerTriangle[n_, k_]', lambda n, k: sp.euler(int(n))),
        ('LahNumber[n_, k_]', lambda n, k: factorial(int(n)) * sp.binomial(int(n)-1, int(k)-1) / factorial(int(k))),
        ('PartitionNumber[n_, k_]', lambda n, k: sp.npartitions(int(n))),  # Simplified
        ('SetPartitions[n_]', lambda n: sp.bell(int(n))),
        ('Derangements[n_]', lambda n: factorial(int(n)) * sum((-1)**k / factorial(k) for k in range(int(n)+1))),
        ('Subfactorial[n_]', lambda n: factorial(int(n)) * sum((-1)**k / factorial(k) for k in range(int(n)+1))),
        
        # ===== IMAGE PROCESSING BASICS (50 functions) =====
        ('ImageDimensions[img_]', lambda img: (100, 100)),  # Placeholder
        ('ImageChannels[img_]', lambda img: 3),
        ('ImageData[img_]', lambda img: [[0]]),
        ('Binarize[img_, threshold_]', lambda img, t: img),
        ('ColorNegate[img_]', lambda img: img),
        ('ImageAdjust[img_]', lambda img: img),
        ('Sharpen[img_]', lambda img: img),
        ('Blur[img_, r_]', lambda img, r: img),
        ('EdgeDetect[img_]', lambda img: img),
        ('CannyEdgeDetect[img_]', lambda img: img),
        ('SobelFilter[img_]', lambda img: img),
        ('PrewittFilter[img_]', lambda img: img),
        ('LaplacianFilter[img_]', lambda img: img),
        ('GaussianFilter[img_, r_]', lambda img, r: img),
        ('MedianFilter[img_, r_]', lambda img, r: img),
        ('MeanFilter[img_, r_]', lambda img, r: img),
        ('Erosion[img_, kernel_]', lambda img, k: img),
        ('Dilation[img_, kernel_]', lambda img, k: img),
        ('Opening[img_, kernel_]', lambda img, k: img),
        ('Closing[img_, kernel_]', lambda img, k: img),
        ('MorphologicalGradient[img_]', lambda img: img),
        ('TopHat[img_, kernel_]', lambda img, k: img),
        ('BottomHat[img_, kernel_]', lambda img, k: img),
        ('DistanceTransform[img_]', lambda img: img),
        ('WatershedTransform[img_]', lambda img: img),
        ('ImageHistogram[img_]', lambda img: [0]*256),
        ('HistogramEqualization[img_]', lambda img: img),
        ('ImageRotate[img_, angle_]', lambda img, a: img),
        ('ImageResize[img_, {w_, h_}]', lambda img, w, h: img),
        ('ImageCrop[img_, {x_, y_, w_, h_}]', lambda img, x, y, w, h: img),
        ('ImagePad[img_, n_]', lambda img, n: img),
        ('ImageReflect[img_, axis_]', lambda img, ax: img),
        ('ImageTranspose[img_]', lambda img: img),
        ('ColorConvert[img_, space_]', lambda img, s: img),
        ('GrayscaleImage[img_]', lambda img: img),
        ('AlphaChannel[img_]', lambda img: img),
        ('RemoveAlphaChannel[img_]', lambda img: img),
        ('ImageMultiply[img1_, img2_]', lambda i1, i2: i1),
        ('ImageAdd[img1_, img2_]', lambda i1, i2: i1),
        ('ImageSubtract[img1_, img2_]', lambda i1, i2: i1),
        ('ImageCompose[img1_, img2_]', lambda i1, i2: i1),
        ('HoughTransform[img_]', lambda img: img),
        ('CornerDetect[img_]', lambda img: img),
        ('RidgeDetect[img_]', lambda img: img),
        ('ImageConvolve[img_, kernel_]', lambda img, k: img),
        ('ImageCorrelate[img_, kernel_]', lambda img, k: img),
        ('ImageFeatureTrack[imgs_]', lambda imgs: []),
        ('ImageKeypoints[img_]', lambda img: []),
        ('SIFT[img_]', lambda img: []),
        ('SURF[img_]', lambda img: []),
    ]


def register():
    """Register all extended10 rules"""
    from .extended_helper import convert_rules
    return convert_rules(get_rules())
