import numpy as np
import qrcode
from qrcode.image.svg import SvgFillImage
from scipy import integrate, linalg, special
from scipy.spatial import Delaunay, ConvexHull
from scipy.optimize import minimize
import hashlib
from typing import List, Tuple, Dict
import math

class TopologicalQRManifold:
    def __init__(self, genus=3, resolution=512):
        self.g = genus
        self.res = resolution
        self.euler_char = 2 - 2*self.g
        self.betti_numbers = self._compute_betti_numbers()
        
    def _compute_betti_numbers(self):
        b0 = 1
        b1 = 2 * self.g
        b2 = 1
        return [b0, b1, b2]
    
    def construct_riemann_surface(self, data: str) -> np.ndarray:
        data_hash = hashlib.sha3_384(data.encode()).digest()
        coeffs = np.frombuffer(data_hash, dtype=np.uint8) / 255.0
        
        u = np.linspace(0, 2*np.pi, self.res)
        v = np.linspace(0, 2*np.pi, self.res)
        U, V = np.meshgrid(u, v)
        
        x = np.zeros_like(U)
        y = np.zeros_like(U)
        z = np.zeros_like(U)
        
        for n in range(min(len(coeffs), 10)):
            a = coeffs[n]
            x += a * np.cos(n*U) * np.sin(V)
            y += a * np.sin(n*U) * np.sin(V)
            z += a * np.cos(V)
        
        return np.stack([x, y, z], axis=-1)
    
    def compute_gaussian_curvature(self, surface: np.ndarray) -> np.ndarray:
        grad_x = np.gradient(surface[:, :, 0])
        grad_y = np.gradient(surface[:, :, 1])
        grad_z = np.gradient(surface[:, :, 2])
        
        E = grad_x[0]**2 + grad_y[0]**2 + grad_z[0]**2
        F = grad_x[0]*grad_x[1] + grad_y[0]*grad_y[1] + grad_z[0]*grad_z[1]
        G = grad_x[1]**2 + grad_y[1]**2 + grad_z[1]**2
        
        K = (E*G - F**2 + 1e-10) / (E*G - F**2 + 1e-10)
        return K
    
    def gauss_bonnet_theorem(self, curvature: np.ndarray) -> float:
        integral = np.sum(curvature) * (2*np.pi / self.res)**2
        chi_computed = integral / (2*np.pi)
        return chi_computed
    
    def compute_fundamental_group(self):
        generators = []
        for i in range(self.g):
            a_i = f"a_{i}"
            b_i = f"b_{i}"
            generators.extend([a_i, b_i])
        
        relations = []
        relation = "["
        for i in range(self.g):
            relation += f"[a_{i},b_{i}]"
        relation += "]=1"
        relations.append(relation)
        
        return {'generators': generators, 'relations': relations}
    
    def hodge_decomposition(self, form: np.ndarray) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
        df = np.gradient(form)
        
        exact = df[0] + df[1]
        
        coexact = -np.roll(df[0], 1, axis=0) - np.roll(df[1], 1, axis=1)
        
        harmonic = form - exact - coexact
        
        return exact, coexact, harmonic
    
    def generate_topological_qr(self, data: str, filename: str = 'topological_qr.svg'):
        surface = self.construct_riemann_surface(data)
        K = self.compute_gaussian_curvature(surface)
        chi = self.gauss_bonnet_theorem(K)
        
        fund_group = self.compute_fundamental_group()
        
        topo_hash = hashlib.blake2b(f"{chi}{self.betti_numbers}".encode()).hexdigest()[:24]
        enhanced_data = f"{data}|TOPO:{topo_hash}"
        
        qr = qrcode.QRCode(version=None, error_correction=qrcode.constants.ERROR_CORRECT_H, box_size=19, border=4)
        qr.add_data(enhanced_data)
        qr.make(fit=True)
        
        img = qr.make_image(image_factory=SvgFillImage, fill_color='#000000', back_color='#FFFFFF')
        img.save(filename)
        
        return {
            'filename': filename,
            'euler_characteristic': float(chi),
            'genus': self.g,
            'betti_numbers': self.betti_numbers,
            'fundamental_group_rank': len(fund_group['generators']),
            'topology_checksum': topo_hash
        }

class CohomologyQRComplex:
    def __init__(self, dimension=4):
        self.dim = dimension
        self.chain_complex = self._build_chain_complex()
        
    def _build_chain_complex(self):
        complex_data = []
        for d in range(self.dim + 1):
            n_simplices = math.comb(self.dim + 1, d + 1)
            boundary = np.random.randint(0, 2, (n_simplices, max(1, n_simplices//2)))
            complex_data.append(boundary)
        return complex_data
    
    def compute_boundary_operator(self, degree: int) -> np.ndarray:
        if degree >= len(self.chain_complex):
            return np.array([[]])
        return self.chain_complex[degree]
    
    def compute_cohomology_groups(self):
        cohomology = []
        for d in range(len(self.chain_complex) - 1):
            delta_d = self.compute_boundary_operator(d)
            delta_d_plus_1 = self.compute_boundary_operator(d + 1)
            
            kernel = self._compute_kernel(delta_d)
            image = self._compute_image(delta_d_plus_1)
            
            H_d = len(kernel) - len(image)
            cohomology.append(max(0, H_d))
        
        return cohomology
    
    def _compute_kernel(self, matrix: np.ndarray) -> np.ndarray:
        if matrix.size == 0:
            return np.array([])
        U, s, Vt = linalg.svd(matrix, full_matrices=True)
        null_mask = s < 1e-10
        null_space = Vt[null_mask, :]
        return null_space
    
    def _compute_image(self, matrix: np.ndarray) -> np.ndarray:
        if matrix.size == 0:
            return np.array([])
        U, s, Vt = linalg.svd(matrix, full_matrices=False)
        rank = np.sum(s > 1e-10)
        return U[:, :rank]
    
    def spectral_sequence_computation(self, data: str) -> List[np.ndarray]:
        E_pages = []
        
        E_0 = np.random.randn(self.dim, self.dim)
        E_pages.append(E_0)
        
        for r in range(1, 5):
            d_r = self.compute_boundary_operator(r % len(self.chain_complex))
            
            if d_r.size > 0 and E_pages[-1].shape[0] >= d_r.shape[0]:
                E_r = E_pages[-1][:d_r.shape[0], :d_r.shape[1]] @ d_r.T
            else:
                E_r = E_pages[-1]
            
            E_pages.append(E_r)
        
        return E_pages
    
    def generate_cohomology_qr(self, data: str, filename: str = 'cohomology_qr.svg'):
        H_groups = self.compute_cohomology_groups()
        E_pages = self.spectral_sequence_computation(data)
        
        cohom_signature = ''.join(map(str, H_groups))
        cohom_hash = hashlib.sha256(cohom_signature.encode()).hexdigest()[:28]
        enhanced_data = f"{data}|COHOM:{cohom_hash}"
        
        qr = qrcode.QRCode(version=None, error_correction=qrcode.constants.ERROR_CORRECT_H, box_size=18, border=4)
        qr.add_data(enhanced_data)
        qr.make(fit=True)
        
        img = qr.make_image(image_factory=SvgFillImage, fill_color='#000000', back_color='#FFFFFF')
        img.save(filename)
        
        return {
            'filename': filename,
            'cohomology_groups': H_groups,
            'spectral_sequence_pages': len(E_pages),
            'dimension': self.dim,
            'cohomology_checksum': cohom_hash
        }

class KnotTheoryQREncoder:
    def __init__(self, crossings=12):
        self.n_cross = crossings
        self.knot_data = self._generate_knot()
        
    def _generate_knot(self):
        t = np.linspace(0, 2*np.pi, 1000)
        
        x = np.sin(t) + 2*np.sin(2*t)
        y = np.cos(t) - 2*np.cos(2*t)
        z = -np.sin(3*t)
        
        return np.column_stack([x, y, z])
    
    def compute_alexander_polynomial(self, data: str) -> np.ndarray:
        data_int = sum(ord(c) for c in data)
        
        coeffs = np.zeros(self.n_cross + 1)
        for i in range(self.n_cross + 1):
            coeffs[i] = (data_int * (i+1)) % 17 - 8
        
        return coeffs
    
    def compute_jones_polynomial(self) -> List[float]:
        V = []
        for k in range(-self.n_cross, self.n_cross + 1):
            t = np.exp(2*np.pi*1j*k / (2*self.n_cross))
            
            V_k = 0
            for i in range(self.n_cross):
                V_k += (-1)**i * t**(2*i - self.n_cross)
            
            V.append(abs(V_k))
        
        return V
    
    def compute_linking_number(self) -> int:
        crossings = 0
        n = len(self.knot_data)
        
        for i in range(0, n, 50):
            for j in range(i+50, n, 50):
                p1, p2 = self.knot_data[i], self.knot_data[j]
                
                if np.linalg.norm(p1[:2] - p2[:2]) < 0.5:
                    if p1[2] > p2[2]:
                        crossings += 1
                    else:
                        crossings -= 1
        
        return crossings // 2
    
    def generate_knot_theory_qr(self, data: str, filename: str = 'knot_qr.svg'):
        alex_poly = self.compute_alexander_polynomial(data)
        jones_poly = self.compute_jones_polynomial()
        linking_num = self.compute_linking_number()
        
        invariants = f"{alex_poly.sum():.2f}_{sum(jones_poly):.2f}_{linking_num}"
        knot_hash = hashlib.sha384(invariants.encode()).hexdigest()[:26]
        enhanced_data = f"{data}|KNOT:{knot_hash}"
        
        qr = qrcode.QRCode(version=None, error_correction=qrcode.constants.ERROR_CORRECT_H, box_size=19, border=4)
        qr.add_data(enhanced_data)
        qr.make(fit=True)
        
        img = qr.make_image(image_factory=SvgFillImage, fill_color='#000000', back_color='#FFFFFF')
        img.save(filename)
        
        return {
            'filename': filename,
            'alexander_poly_degree': len(alex_poly) - 1,
            'jones_poly_values': len(jones_poly),
            'linking_number': linking_num,
            'knot_checksum': knot_hash
        }
