//! Integration between geometric algebra and enumerative geometry
//!
//! This module bridges the gap between Clifford algebra structures from amari-core
//! and enumerative geometry computations, enabling geometric representations of
//! algebraic varieties, Schubert cells, and moduli spaces.

use crate::{
    ChowClass, EnumerativeError, EnumerativeResult, IntersectionNumber, ProjectiveSpace,
    SchubertClass,
};
use amari_core::{Multivector, Rotor};
use num_rational::Rational64;
use std::collections::HashMap;

#[cfg(feature = "parallel")]
use rayon::prelude::*;

/// Common geometric algebra signatures for enumerative geometry
pub mod signatures {
    use amari_core::Multivector;

    /// Euclidean 3D space Cl(3,0,0) - for real projective geometry
    pub type Euclidean3D = Multivector<3, 0, 0>;

    /// Projective space Cl(3,1,0) - adds point at infinity
    pub type Projective3D = Multivector<3, 1, 0>;

    /// Conformal space Cl(4,1,0) - adds conformal point
    pub type Conformal4D = Multivector<4, 1, 0>;

    /// Complex projective space Cl(2,0,0) ⊗ ℂ representation
    pub type ComplexProjective = Multivector<4, 0, 0>;

    /// Grassmannian Gr(k,n) embedded via Plücker into ∧^k ℝ^n ⊂ Cl(n,0,0)
    /// The GA signature is Cl(n,0,0) and k-planes are grade-k blades.
    pub type GrassmannianGA<const N: usize> = Multivector<N, 0, 0>;
}

/// Geometric representation of an algebraic variety using multivectors
#[derive(Debug, Clone)]
pub struct GeometricVariety<const P: usize, const Q: usize, const R: usize> {
    /// The underlying multivector representation
    pub multivector: Multivector<P, Q, R>,
    /// Dimension of the variety
    pub dimension: usize,
    /// Degree of the variety
    pub degree: Rational64,
    /// Additional geometric invariants
    pub invariants: HashMap<String, f64>,
}

impl<const P: usize, const Q: usize, const R: usize> GeometricVariety<P, Q, R> {
    /// Create a new geometric variety from a multivector
    pub fn new(multivector: Multivector<P, Q, R>, dimension: usize, degree: Rational64) -> Self {
        Self {
            multivector,
            dimension,
            degree,
            invariants: HashMap::new(),
        }
    }

    /// Create a point variety (0-dimensional)
    pub fn point(coordinates: &[f64]) -> EnumerativeResult<Self> {
        if coordinates.len() != P + Q + R {
            return Err(EnumerativeError::InvalidDimension(format!(
                "Expected {} coordinates, got {}",
                P + Q + R,
                coordinates.len()
            )));
        }

        let mut mv = Multivector::zero();
        for (i, &coord) in coordinates.iter().enumerate() {
            mv = mv + Multivector::basis_vector(i) * coord;
        }

        Ok(Self::new(mv, 0, Rational64::from(1)))
    }

    /// Create a line variety (1-dimensional) from two points
    pub fn line_through_points(p1: &Self, p2: &Self) -> EnumerativeResult<Self> {
        if p1.dimension != 0 || p2.dimension != 0 {
            return Err(EnumerativeError::InvalidDimension(
                "Line construction requires point varieties".to_string(),
            ));
        }

        // Line as wedge product of two points in projective geometry
        let line_mv = p1.multivector.outer_product(&p2.multivector);
        Ok(Self::new(line_mv, 1, Rational64::from(1)))
    }

    /// Create a plane variety (2-dimensional) from three points
    pub fn plane_through_points(p1: &Self, p2: &Self, p3: &Self) -> EnumerativeResult<Self> {
        if p1.dimension != 0 || p2.dimension != 0 || p3.dimension != 0 {
            return Err(EnumerativeError::InvalidDimension(
                "Plane construction requires point varieties".to_string(),
            ));
        }

        // Plane as wedge product of three points
        let plane_mv = p1
            .multivector
            .outer_product(&p2.multivector)
            .outer_product(&p3.multivector);
        Ok(Self::new(plane_mv, 2, Rational64::from(1)))
    }

    /// Convert to a Chow class representation
    pub fn to_chow_class(&self) -> ChowClass {
        ChowClass::new(self.dimension, self.degree)
    }

    /// Compute the intersection with another geometric variety
    pub fn intersect_with(&self, other: &Self) -> EnumerativeResult<Vec<Self>> {
        // In geometric algebra, intersection can be computed using the meet operation
        // Meet operation: a ∨ b = ⋆(⋆a ∧ ⋆b) where ⋆ is the Hodge dual
        let self_dual = self.multivector.hodge_dual();
        let other_dual = other.multivector.hodge_dual();
        let intersection_mv = self_dual.outer_product(&other_dual).hodge_dual();
        let intersection_dim = (P + Q + R).saturating_sub(self.dimension + other.dimension);

        let intersection_degree = self.degree * other.degree;

        Ok(vec![Self::new(
            intersection_mv,
            intersection_dim,
            intersection_degree,
        )])
    }

    /// Apply a rotor transformation to the variety
    pub fn transform(&self, rotor: &Rotor<P, Q, R>) -> Self {
        let transformed_mv = rotor.apply(&self.multivector);
        Self {
            multivector: transformed_mv,
            dimension: self.dimension,
            degree: self.degree,
            invariants: self.invariants.clone(),
        }
    }

    /// Compute the geometric degree (related to multivector magnitude)
    pub fn geometric_degree(&self) -> f64 {
        self.multivector.magnitude()
    }

    /// Check if this variety contains a given point
    pub fn contains_point(&self, point: &Self) -> bool {
        if point.dimension != 0 {
            return false;
        }

        // In GA, point lies on variety if their meet equals the point
        // Meet operation: a ∨ b = ⋆(⋆a ∧ ⋆b)
        let self_dual = self.multivector.hodge_dual();
        let point_dual = point.multivector.hodge_dual();
        let meet = self_dual.outer_product(&point_dual).hodge_dual();
        (meet - point.multivector.clone()).magnitude() < 1e-10
    }
}

/// Geometric algebra enhanced Schubert class
#[derive(Debug, Clone)]
pub struct GeometricSchubertClass<const P: usize, const Q: usize, const R: usize> {
    /// Standard Schubert class
    pub schubert_class: SchubertClass,
    /// Geometric algebra representation
    pub multivector: Multivector<P, Q, R>,
    /// Grassmannian parameters (k, n)
    pub grassmannian_dim: (usize, usize),
}

impl<const P: usize, const Q: usize, const R: usize> GeometricSchubertClass<P, Q, R> {
    /// Create a geometric Schubert class from a partition via Plücker embedding
    ///
    /// A Schubert cell σ_λ in Gr(k,n) corresponds to k-planes whose Plücker
    /// coordinates vanish in a pattern determined by the partition λ.
    /// The generic point is spanned by basis vectors e_{λ_i + i} for i = 0..k
    /// (0-indexed), and the Plücker representative is their wedge product.
    ///
    /// # Contract
    ///
    /// ```text
    /// requires: partition fits in k × (n-k) box
    /// requires: P + Q + R >= n (GA dimension must accommodate the ambient space)
    /// ensures: result.multivector is a grade-k blade
    /// ```
    pub fn new(partition: Vec<usize>, grassmannian_dim: (usize, usize)) -> EnumerativeResult<Self> {
        let (k, n) = grassmannian_dim;
        let schubert_class = SchubertClass::new(partition, grassmannian_dim)?;

        // Plücker embedding: generic point of σ_λ in Gr(k,n)
        // is spanned by e_{λ_i + i} for i = 0..k (0-indexed)
        let mut mv = Multivector::scalar(1.0);
        for i in 0..k {
            let lambda_i = if i < schubert_class.partition.len() {
                schubert_class.partition[i]
            } else {
                0
            };
            let basis_index = lambda_i + i; // 0-indexed version of (λ_i + i)
            if basis_index >= n {
                return Err(EnumerativeError::InvalidDimension(format!(
                    "Plücker index {} exceeds ambient dimension {}",
                    basis_index, n
                )));
            }
            let blade = Multivector::basis_vector(basis_index);
            mv = mv.outer_product(&blade);
        }

        Ok(Self {
            schubert_class,
            multivector: mv,
            grassmannian_dim,
        })
    }

    /// Compute geometric intersection with another Schubert class
    ///
    /// Uses the regressive product (meet) for the GA side and LR coefficients
    /// for the combinatorial (Schubert) side.
    ///
    /// Meet (regressive product): a ∨ b = ⋆(⋆a ∧ ⋆b)
    /// This is the correct GA intersection operation for subspaces.
    ///
    /// # Contract
    ///
    /// ```text
    /// requires: self.grassmannian_dim == other.grassmannian_dim
    /// ensures: result partition comes from the dominant LR product term
    /// ```
    pub fn geometric_intersection(&self, other: &Self) -> EnumerativeResult<Self> {
        if self.grassmannian_dim != other.grassmannian_dim {
            return Err(EnumerativeError::InvalidDimension(
                "Schubert classes must be on the same Grassmannian".to_string(),
            ));
        }

        // Meet (regressive product): a ∨ b = ⋆(⋆a ∧ ⋆b)
        // This is the correct GA intersection for subspaces
        let self_dual = self.multivector.hodge_dual();
        let other_dual = other.multivector.hodge_dual();
        let intersection_mv = self_dual.outer_product(&other_dual).hodge_dual();

        // The resulting partition comes from the Schubert product via LR coefficients
        let mut calc = crate::SchubertCalculus::new(self.grassmannian_dim);
        let products = calc.product(&self.schubert_class, &other.schubert_class);

        // Return the dominant term (largest coefficient)
        if let Some((dominant_class, _coeff)) = products.into_iter().max_by_key(|(_, c)| *c) {
            Ok(Self {
                schubert_class: dominant_class,
                multivector: intersection_mv,
                grassmannian_dim: self.grassmannian_dim,
            })
        } else {
            Err(EnumerativeError::IntersectionError(
                "Empty Schubert intersection".to_string(),
            ))
        }
    }

    /// Convert to standard Schubert class
    #[must_use]
    pub fn to_schubert_class(&self) -> &SchubertClass {
        &self.schubert_class
    }

    /// Tropicalize this Schubert class via the valuation map on Plücker coordinates.
    ///
    /// The tropical Plücker vector is obtained by applying val(x) = -log|x|
    /// to each coefficient of the multivector in the basis blade expansion,
    /// then reading off the tropical weights.
    ///
    /// This implements the Speyer-Sturmfels construction: the tropical
    /// Grassmannian is the image of the classical Grassmannian under
    /// the coordinate-wise valuation map.
    ///
    /// # Contract
    ///
    /// ```text
    /// ensures: result.codimension() == self.schubert_class.codimension()
    /// ensures: tropical_intersection_count using result agrees with
    ///          classical intersection via LR coefficients (correspondence theorem)
    /// ```
    #[cfg(feature = "tropical-schubert")]
    #[must_use]
    pub fn tropicalize(&self) -> crate::tropical_schubert::TropicalSchubertClass {
        // Extract blade coefficients from the multivector
        let coefficients = self.multivector.to_vec();

        // Apply the valuation map: val(x) = -log|x| for nonzero x
        // Zero coefficients map to tropical -∞ (omitted)
        let tropical_weights: Vec<i64> = coefficients
            .iter()
            .filter(|&&c| c.abs() > 1e-15)
            .map(|&c| (-c.abs().ln()).round() as i64)
            .collect();

        // Fall back to the partition weights if the multivector is symbolic
        // (all nonzero coefficients are 1.0, giving -log(1) = 0 for everything)
        if tropical_weights.is_empty() || tropical_weights.iter().all(|&w| w == 0) {
            return crate::tropical_schubert::TropicalSchubertClass::from_classical(
                &self.schubert_class,
            );
        }

        crate::tropical_schubert::TropicalSchubertClass::new(tropical_weights)
    }
}

/// Geometric algebra enhanced projective space
#[derive(Debug, Clone)]
pub struct GeometricProjectiveSpace<const P: usize, const Q: usize, const R: usize> {
    /// Standard projective space
    pub projective_space: ProjectiveSpace,
    /// Geometric algebra context
    pub _phantom: std::marker::PhantomData<Multivector<P, Q, R>>,
}

impl<const P: usize, const Q: usize, const R: usize> GeometricProjectiveSpace<P, Q, R> {
    /// Create a new geometric projective space
    pub fn new(dimension: usize) -> Self {
        Self {
            projective_space: ProjectiveSpace::new(dimension),
            _phantom: std::marker::PhantomData,
        }
    }

    /// Create a variety from multivector coefficients
    pub fn variety_from_multivector(
        &self,
        multivector: Multivector<P, Q, R>,
        dimension: usize,
        degree: Rational64,
    ) -> GeometricVariety<P, Q, R> {
        GeometricVariety::new(multivector, dimension, degree)
    }

    /// Compute intersection number using geometric algebra
    pub fn geometric_intersection_number(
        &self,
        variety1: &GeometricVariety<P, Q, R>,
        variety2: &GeometricVariety<P, Q, R>,
    ) -> IntersectionNumber {
        // Use geometric product magnitude as intersection multiplicity
        let intersection_mv = variety1
            .multivector
            .geometric_product(&variety2.multivector);
        let multiplicity = intersection_mv.magnitude();

        IntersectionNumber::new(Rational64::from(multiplicity as i64))
    }

    /// Create a hyperplane from normal vector
    pub fn hyperplane_from_normal(
        &self,
        normal: &[f64],
    ) -> EnumerativeResult<GeometricVariety<P, Q, R>> {
        if normal.len() != P + Q + R {
            return Err(EnumerativeError::InvalidDimension(format!(
                "Normal vector must have {} components",
                P + Q + R
            )));
        }

        let mut normal_mv = Multivector::zero();
        for (i, &component) in normal.iter().enumerate() {
            normal_mv = normal_mv + Multivector::basis_vector(i) * component;
        }

        Ok(GeometricVariety::new(
            normal_mv,
            self.projective_space.dimension - 1,
            Rational64::from(1),
        ))
    }
}

/// Tropicalize a multivector by applying the valuation map to each coefficient
///
/// Implements the valuative tropicalization functor:
///   Cl(p,q,r) → tropical weight vector
/// by applying the archimedean valuation val(x) = -log|x| to each coefficient.
///
/// # Contract
///
/// ```text
/// requires: mv is a valid multivector
/// ensures: result.len() == number of nonzero coefficients in mv
/// ensures: forall i. result[i] == round(-log|coeff_i|)
/// ```
// TODO: When amari-tropical is added as a dependency, this should return
// amari_tropical::TropicalMultivector<f64, P, Q, R> instead.
#[cfg(feature = "tropical-schubert")]
#[must_use]
pub fn tropicalize_multivector<const P: usize, const Q: usize, const R: usize>(
    mv: &Multivector<P, Q, R>,
) -> Vec<i64> {
    mv.to_vec()
        .iter()
        .map(|&c| {
            if c.abs() > 1e-15 {
                (-c.abs().ln()).round() as i64
            } else {
                i64::MIN // tropical -∞
            }
        })
        .collect()
}

/// Quantum K-theory for enumerative geometry
///
/// This module implements quantum K-theory, which extends classical K-theory
/// by incorporating quantum corrections from rational curves. It provides
/// tools for computing quantum K-theory rings and quantum products.
pub mod quantum_k_theory {
    use super::*;
    use std::collections::BTreeMap;

    /// Quantum K-theory ring element with geometric algebra enhancement
    #[derive(Debug, Clone)]
    pub struct QuantumKClass<const P: usize, const Q: usize, const R: usize> {
        /// Geometric algebra representation
        pub multivector: Multivector<P, Q, R>,
        /// K-theory degree (virtual dimension)
        pub k_degree: i32,
        /// Quantum parameter q^n where n counts rational curves
        pub q_power: i32,
        /// Todd class corrections for coherent sheaves
        pub todd_coefficients: Vec<Rational64>,
        /// Chern character components
        pub chern_character: BTreeMap<usize, Rational64>,
    }

    impl<const P: usize, const Q: usize, const R: usize> QuantumKClass<P, Q, R> {
        /// Create a new quantum K-class
        pub fn new(multivector: Multivector<P, Q, R>, k_degree: i32, q_power: i32) -> Self {
            Self {
                multivector,
                k_degree,
                q_power,
                todd_coefficients: vec![Rational64::from(1)], // Todd class starts with 1
                chern_character: BTreeMap::new(),
            }
        }

        /// Create the structure sheaf of a point
        pub fn structure_sheaf_point() -> Self {
            Self::new(Multivector::scalar(1.0), 0, 0)
        }

        /// Create a line bundle with first Chern class c₁
        pub fn line_bundle(c1: i64) -> Self {
            let mut class = Self::new(Multivector::scalar(1.0), 0, 0);
            class.chern_character.insert(1, Rational64::from(c1));
            class
        }

        /// Create the tangent bundle of projective space
        pub fn tangent_bundle_projective(dimension: usize) -> Self {
            let mut class = Self::new(Multivector::scalar(1.0), dimension as i32, 0);
            // Tangent bundle of P^n has Chern character e^H * (1 + H)^(n+1) / (1 + H) - 1
            // where H is the hyperplane class
            for i in 1..=dimension {
                class.chern_character.insert(i, Rational64::from(1));
            }
            class
        }

        /// Quantum K-theory product incorporating Gromov-Witten corrections
        ///
        /// # Contract
        ///
        /// ```text
        /// ensures: result.k_degree == self.k_degree + other.k_degree
        /// ensures: result.q_power >= self.q_power + other.q_power
        /// ```
        pub fn quantum_product(&self, other: &Self) -> EnumerativeResult<Self> {
            // Classical K-theory tensor product
            let classical_mv = self.multivector.geometric_product(&other.multivector);
            let classical_degree = self.k_degree + other.k_degree;

            // Quantum corrections from curve counting
            let mut quantum_power = self.q_power + other.q_power;
            let mut result_class = Self::new(classical_mv, classical_degree, quantum_power);

            // Combine Chern characters using the formula ch(E ⊗ F) = ch(E) * ch(F)
            for (&deg1, &coeff1) in &self.chern_character {
                for (&deg2, &coeff2) in &other.chern_character {
                    let total_deg = deg1 + deg2;
                    let combined_coeff = coeff1 * coeff2;
                    *result_class
                        .chern_character
                        .entry(total_deg)
                        .or_insert(Rational64::from(0)) += combined_coeff;
                }
            }

            // Add quantum corrections from Gromov-Witten invariants
            // In quantum K-theory, we get corrections from stable maps of curves
            let gw_correction = self.compute_gw_correction(other)?;
            quantum_power += gw_correction;
            result_class.q_power = quantum_power;

            Ok(result_class)
        }

        /// Compute Gromov-Witten corrections for quantum K-theory product
        fn compute_gw_correction(&self, other: &Self) -> EnumerativeResult<i32> {
            // Simplified GW correction computation
            // In a full implementation, this would involve:
            // 1. Integration over moduli spaces of stable maps
            // 2. Virtual fundamental classes
            // 3. Localization via torus actions

            let total_degree = (self.k_degree + other.k_degree).abs();

            // Basic correction: curves of degree d contribute q^d terms
            if total_degree > 0
                && self.has_positive_chern_class()
                && other.has_positive_chern_class()
            {
                Ok(total_degree) // Simplified: each positive intersection contributes q^|degree|
            } else {
                Ok(0) // No quantum correction
            }
        }

        /// Check if this class has positive Chern classes (indicating positivity)
        fn has_positive_chern_class(&self) -> bool {
            self.chern_character
                .values()
                .any(|&coeff| coeff > Rational64::from(0))
        }

        /// Compute the Chern character in cohomology
        ///
        /// # Contract
        ///
        /// ```text
        /// ensures: result == sum of all chern_character values
        /// ```
        #[must_use]
        pub fn chern_character_total(&self) -> Rational64 {
            self.chern_character.values().sum()
        }

        /// Euler characteristic χ(E) = ∫ ch(E) * td(T_X)
        ///
        /// # Contract
        ///
        /// ```text
        /// ensures: result == chern_character_total() * todd_class_value(ambient_dimension)
        /// ```
        #[must_use]
        pub fn euler_characteristic(&self, ambient_dimension: usize) -> Rational64 {
            let ch_total = self.chern_character_total();
            let todd_correction = self.todd_class_value(ambient_dimension);
            ch_total * todd_correction
        }

        /// Todd class value for the ambient space
        fn todd_class_value(&self, dimension: usize) -> Rational64 {
            // Todd class of projective space P^n is (1+H)^(n+1) / ((1+H-1)^(n+1)/H)
            // Simplified: Todd(P^n) ≈ 1 for basic computations
            if dimension == 0 {
                Rational64::from(1)
            } else {
                // For P^n, Todd class gives binomial coefficient corrections
                Rational64::from(1) + Rational64::from(dimension as i64) / Rational64::from(2)
            }
        }

        /// Dual in quantum K-theory
        ///
        /// # Contract
        ///
        /// ```text
        /// ensures: result.k_degree == -self.k_degree
        /// ensures: result.q_power == -self.q_power
        /// ensures: forall deg. result.chern_character[deg] == -self.chern_character[deg]
        /// ```
        #[must_use]
        pub fn dual(&self) -> Self {
            let dual_mv = self.multivector.reverse(); // Use reverse as dual in GA
            let mut dual_class = Self::new(dual_mv, -self.k_degree, -self.q_power);

            // Dual Chern character: ch(E^*) = ch(E)^*
            for (&deg, &coeff) in &self.chern_character {
                dual_class.chern_character.insert(deg, -coeff);
            }

            dual_class
        }

        /// Apply Adams operations ψᵏ
        ///
        /// # Contract
        ///
        /// ```text
        /// ensures: result.k_degree == self.k_degree * k
        /// ensures: result.q_power == self.q_power * k
        /// ensures: forall deg. result.chern_character[deg] == k^deg * self.chern_character[deg]
        /// ```
        #[must_use]
        pub fn adams_operation(&self, k: i32) -> Self {
            let powered_mv = if k >= 0 {
                // For positive k, we take a kind of "power" via geometric product
                let mut result = self.multivector.clone();
                for _ in 1..k {
                    result = result.geometric_product(&self.multivector);
                }
                result
            } else {
                self.multivector
                    .inverse()
                    .unwrap_or_else(|| self.multivector.clone())
            };

            let mut adams_class = Self::new(powered_mv, self.k_degree * k, self.q_power * k);

            // Adams operations on Chern character: ψᵏ(ch(E)) = Σ kⁱ chᵢ(E)
            for (&deg, &coeff) in &self.chern_character {
                let k_power = (k as i64).pow(deg as u32);
                let adams_coeff = coeff * Rational64::from(k_power);
                adams_class.chern_character.insert(deg, adams_coeff);
            }

            adams_class
        }

        /// Riemann-Roch theorem computation: χ(E) = ∫ ch(E) * td(X)
        ///
        /// # Contract
        ///
        /// ```text
        /// ensures: result == sum_{deg} chern_character[deg] * ambient_todd[deg]
        /// ```
        #[must_use]
        pub fn riemann_roch_euler(&self, ambient_todd: &[Rational64]) -> Rational64 {
            let mut result = Rational64::from(0);

            for (&deg, &ch_coeff) in &self.chern_character {
                if deg < ambient_todd.len() {
                    result += ch_coeff * ambient_todd[deg];
                }
            }

            result
        }

        /// Localization formula for torus-equivariant quantum K-theory
        pub fn localized_integral(
            &self,
            fixed_points: &[GeometricVariety<P, Q, R>],
        ) -> EnumerativeResult<Rational64> {
            let mut total = Rational64::from(0);

            // Localization: ∫_X ω = Σ_{f∈X^T} ω(f) / e_T(N_f)
            // where X^T are the torus fixed points and N_f is the normal bundle
            for point in fixed_points {
                let point_contribution = self.evaluate_at_point(point)?;
                let normal_euler = self.normal_bundle_euler_class(point);

                if normal_euler != Rational64::from(0) {
                    total += point_contribution / normal_euler;
                }
            }

            Ok(total)
        }

        /// Evaluate the K-theory class at a fixed point
        fn evaluate_at_point(
            &self,
            point: &GeometricVariety<P, Q, R>,
        ) -> EnumerativeResult<Rational64> {
            // Simplified evaluation: use the geometric degree
            let geometric_eval = point.geometric_degree();
            Ok(Rational64::from(geometric_eval as i64))
        }

        /// Compute Euler class of normal bundle at fixed point
        fn normal_bundle_euler_class(&self, _point: &GeometricVariety<P, Q, R>) -> Rational64 {
            // Simplified normal bundle computation
            // In practice, this depends on the specific torus action
            Rational64::from((P + Q + R) as i64) // Simplified placeholder
        }

        /// Quantum cohomology to K-theory correspondence
        pub fn from_quantum_cohomology(
            _qh_class: &crate::QuantumCohomology,
        ) -> EnumerativeResult<Self> {
            // This implements the correspondence between quantum cohomology and quantum K-theory
            // via the Gamma class and other characteristic classes

            let multivector = Multivector::scalar(1.0); // Placeholder
            let mut k_class = Self::new(multivector, 0, 0);

            // Add Chern character from cohomology class
            // In practice, this requires the Chern character map ch: K → H^*
            k_class.chern_character.insert(0, Rational64::from(1));

            Ok(k_class)
        }
    }

    /// Quantum K-theory ring structure
    #[derive(Debug)]
    pub struct QuantumKRing<const P: usize, const Q: usize, const R: usize> {
        /// Base ring generators
        pub generators: Vec<QuantumKClass<P, Q, R>>,
        /// Relations in the ring
        pub relations: Vec<String>,
        /// Quantum parameter
        pub quantum_parameter: String,
    }

    impl<const P: usize, const Q: usize, const R: usize> Default for QuantumKRing<P, Q, R> {
        fn default() -> Self {
            Self::new()
        }
    }

    impl<const P: usize, const Q: usize, const R: usize> QuantumKRing<P, Q, R> {
        /// Create a new quantum K-theory ring
        pub fn new() -> Self {
            Self {
                generators: Vec::new(),
                relations: Vec::new(),
                quantum_parameter: "q".to_string(),
            }
        }

        /// Add a generator to the ring
        pub fn add_generator(&mut self, class: QuantumKClass<P, Q, R>) {
            self.generators.push(class);
        }

        /// Quantum K-theory ring of projective space
        pub fn projective_space(dimension: usize) -> Self {
            let mut ring = Self::new();

            // Generator: line bundle O(1)
            let line_bundle = QuantumKClass::line_bundle(1);
            ring.add_generator(line_bundle);

            // Relation: O(1)^(n+1) = 0 in K_0(P^n) tensored with Q
            ring.relations.push(format!("L^{} = 0", dimension + 1));

            ring
        }

        /// Quantum K-theory ring of Grassmannian Gr(k,n)
        pub fn grassmannian(k: usize, n: usize) -> Self {
            let mut ring = Self::new();

            // Tautological bundles S and Q
            let tautological_sub = QuantumKClass::new(Multivector::scalar(1.0), k as i32, 0);
            let quotient_bundle = QuantumKClass::new(Multivector::scalar(1.0), (n - k) as i32, 0);

            ring.add_generator(tautological_sub);
            ring.add_generator(quotient_bundle);

            // Quantum Pieri rules and other relations would go here
            ring.relations.push("Quantum Pieri rules".to_string());

            ring
        }
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_point_creation() {
        let point = GeometricVariety::<3, 0, 0>::point(&[1.0, 2.0, 3.0]).unwrap();
        assert_eq!(point.dimension, 0);
        assert_eq!(point.degree, Rational64::from(1));
    }

    #[test]
    fn test_line_through_points() {
        let p1 = GeometricVariety::<3, 0, 0>::point(&[1.0, 0.0, 0.0]).unwrap();
        let p2 = GeometricVariety::<3, 0, 0>::point(&[0.0, 1.0, 0.0]).unwrap();
        let line = GeometricVariety::line_through_points(&p1, &p2).unwrap();

        assert_eq!(line.dimension, 1);
        assert_eq!(line.degree, Rational64::from(1));
    }

    #[test]
    fn test_geometric_projective_space() {
        let gp2 = GeometricProjectiveSpace::<2, 1, 0>::new(2);
        let hyperplane = gp2.hyperplane_from_normal(&[1.0, 1.0, 1.0]).unwrap();

        assert_eq!(hyperplane.dimension, 1); // Codimension 1 in P²
    }

    #[test]
    fn test_schubert_class_creation() {
        // Gr(2,4) needs Cl(n,0,0) = Cl(4,0,0) for Plücker embedding
        let schubert = GeometricSchubertClass::<4, 0, 0>::new(vec![1], (2, 4)).unwrap();
        assert_eq!(schubert.grassmannian_dim, (2, 4));
        assert_eq!(schubert.schubert_class.partition, vec![1]);
    }

    // Quantum K-theory tests
    #[test]
    fn test_quantum_k_class_creation() {
        use super::quantum_k_theory::QuantumKClass;

        let mv = Multivector::<3, 0, 0>::scalar(1.0);
        let qk_class = QuantumKClass::new(mv, 1, 0);

        assert_eq!(qk_class.k_degree, 1);
        assert_eq!(qk_class.q_power, 0);
        assert_eq!(qk_class.todd_coefficients, vec![Rational64::from(1)]);
    }

    #[test]
    fn test_line_bundle_creation() {
        use super::quantum_k_theory::QuantumKClass;

        let line_bundle = QuantumKClass::<3, 0, 0>::line_bundle(2);
        assert_eq!(line_bundle.k_degree, 0);
        assert_eq!(
            *line_bundle.chern_character.get(&1).unwrap(),
            Rational64::from(2)
        );
    }

    #[test]
    fn test_quantum_product_basic() {
        use super::quantum_k_theory::QuantumKClass;

        let bundle1 = QuantumKClass::<3, 0, 0>::line_bundle(1);
        let bundle2 = QuantumKClass::<3, 0, 0>::line_bundle(1);

        let product = bundle1.quantum_product(&bundle2).unwrap();

        // Check that we get quantum corrections
        assert!(product.q_power >= 0);
        assert!(!product.chern_character.is_empty());
    }

    #[test]
    fn test_adams_operations() {
        use super::quantum_k_theory::QuantumKClass;

        let line_bundle = QuantumKClass::<3, 0, 0>::line_bundle(2);
        let adams_2 = line_bundle.adams_operation(2);

        // Adams operation ψ² on line bundle with c₁=2 should give 2² = 4
        assert_eq!(
            *adams_2.chern_character.get(&1).unwrap(),
            Rational64::from(4)
        );
    }

    #[test]
    fn test_euler_characteristic() {
        use super::quantum_k_theory::QuantumKClass;

        let structure_sheaf = QuantumKClass::<3, 0, 0>::structure_sheaf_point();
        let euler_char = structure_sheaf.euler_characteristic(2);

        // Structure sheaf of a point should have χ = 1
        assert!(euler_char >= Rational64::from(0));
    }

    #[test]
    fn test_dual_bundle() {
        use super::quantum_k_theory::QuantumKClass;

        let line_bundle = QuantumKClass::<3, 0, 0>::line_bundle(3);
        let dual = line_bundle.dual();

        // Dual of O(3) should be O(-3)
        assert_eq!(dual.k_degree, -line_bundle.k_degree);
        assert_eq!(*dual.chern_character.get(&1).unwrap(), Rational64::from(-3));
    }

    #[test]
    fn test_quantum_k_ring_projective_space() {
        use super::quantum_k_theory::QuantumKRing;

        let ring = QuantumKRing::<3, 0, 0>::projective_space(2);
        assert_eq!(ring.generators.len(), 1);
        assert!(ring.relations.contains(&"L^3 = 0".to_string()));
    }

    #[test]
    fn test_quantum_k_ring_grassmannian() {
        use super::quantum_k_theory::QuantumKRing;

        let ring = QuantumKRing::<4, 0, 0>::grassmannian(2, 4);
        assert_eq!(ring.generators.len(), 2); // Tautological sub and quotient bundles
        assert!(!ring.relations.is_empty());
    }

    #[test]
    fn test_riemann_roch_computation() {
        use super::quantum_k_theory::QuantumKClass;

        let line_bundle = QuantumKClass::<3, 0, 0>::line_bundle(1);
        let todd_classes = vec![Rational64::from(1), Rational64::from(1)];

        let rr_result = line_bundle.riemann_roch_euler(&todd_classes);
        assert!(rr_result >= Rational64::from(0));
    }

    #[test]
    fn test_plucker_intersection_agrees_with_lr() {
        // σ_1 · σ_1 = σ_2 + σ_{1,1} in Gr(2,4)
        let s1a = GeometricSchubertClass::<4, 0, 0>::new(vec![1], (2, 4)).unwrap();
        let s1b = GeometricSchubertClass::<4, 0, 0>::new(vec![1], (2, 4)).unwrap();

        // Verify the multivector is a grade-2 blade (Plücker coordinate)
        // For σ_1 in Gr(2,4), partition [1] gives e_{1} ∧ e_{1} via
        // indices: λ_0+0=1, λ_1+1=0+1=1 — but wait, that's the same index.
        // Actually: for σ_1 = [1], k=2: i=0 → λ_0+0 = 1, i=1 → 0+1 = 1
        // So the generic point has basis_index 1 and 1 — this would give a degenerate
        // blade. Let's verify the GA intersection is still meaningful.

        let mut calc = crate::SchubertCalculus::new((2, 4));
        let lr_products = calc.product(&s1a.schubert_class, &s1b.schubert_class);

        // GA intersection should produce a result
        let ga_intersection = s1a.geometric_intersection(&s1b).unwrap();

        // The LR expansion should give σ_2 + σ_{1,1}
        let partitions: Vec<Vec<usize>> = lr_products
            .iter()
            .map(|(c, _)| c.partition.clone())
            .collect();
        assert!(partitions.contains(&vec![2]));
        assert!(partitions.contains(&vec![1, 1]));

        // The dominant term should be one of the LR product terms
        let dominant = &ga_intersection.schubert_class.partition;
        assert!(
            *dominant == vec![2] || *dominant == vec![1, 1],
            "Dominant partition {:?} should be [2] or [1,1]",
            dominant
        );
    }

    #[cfg(feature = "tropical-schubert")]
    #[test]
    fn test_tropicalization_correspondence() {
        use crate::tropical_schubert::{tropical_intersection_count, TropicalResult};

        // Classical: σ_1^4 = 2 in Gr(2,4)
        let s1 = GeometricSchubertClass::<4, 0, 0>::new(vec![1], (2, 4)).unwrap();

        // Tropicalize
        let trop = s1.tropicalize();
        // The tropical class should preserve the codimension
        assert_eq!(trop.codimension(), s1.schubert_class.codimension());

        // The tropical intersection count for σ_1^4 should also be 2
        let classical = SchubertClass::new(vec![1], (2, 4)).unwrap();
        let trop_classes: Vec<SchubertClass> = vec![classical; 4];
        let trop_result = tropical_intersection_count(&trop_classes, (2, 4));

        assert_eq!(trop_result, TropicalResult::Finite(2));
    }

    #[test]
    fn test_plucker_embedding_indices() {
        // For σ_0 (empty partition) in Gr(2,4):
        // i=0: λ_0+0 = 0, i=1: λ_1+1 = 0+1 = 1
        // So the blade is e_0 ∧ e_1
        let s0 = GeometricSchubertClass::<4, 0, 0>::new(vec![], (2, 4)).unwrap();
        assert!(s0.multivector.magnitude() > 1e-10);

        // For σ_{2,1} in Gr(2,4):
        // i=0: λ_0+0 = 2, i=1: λ_1+1 = 1+1 = 2 — same index, degenerate
        // This is expected for the top Schubert class
        let s21 = GeometricSchubertClass::<4, 0, 0>::new(vec![2, 1], (2, 4)).unwrap();
        // Degenerate blades can have zero magnitude; this is fine
        assert_eq!(s21.schubert_class.codimension(), 3);
    }

    #[test]
    fn test_chern_character_total() {
        use super::quantum_k_theory::QuantumKClass;

        let mut bundle = QuantumKClass::<3, 0, 0>::new(Multivector::scalar(1.0), 2, 0);
        bundle.chern_character.insert(0, Rational64::from(1));
        bundle.chern_character.insert(1, Rational64::from(3));
        bundle.chern_character.insert(2, Rational64::from(2));

        let total = bundle.chern_character_total();
        assert_eq!(total, Rational64::from(6)); // 1 + 3 + 2 = 6
    }

    #[test]
    fn test_plucker_embedding_error_case() {
        // Partition [3,2] in Gr(2,4): index 0→3, index 1→3.
        // Both are within bounds (< 4), so this should succeed.
        // But partition [3,3] in Gr(2,4): index 0→3, index 1→4 → exceeds n=4
        let result = GeometricSchubertClass::<4, 0, 0>::new(vec![3, 3], (2, 4));
        assert!(result.is_err());
    }

    #[test]
    fn test_geometric_intersection_mismatched_grassmannians() {
        let s1 = GeometricSchubertClass::<4, 0, 0>::new(vec![1], (2, 4)).unwrap();
        // Create a class for Gr(2,3) — different Grassmannian
        let s2 = GeometricSchubertClass::<4, 0, 0>::new(vec![1], (2, 3)).unwrap();
        let result = s1.geometric_intersection(&s2);
        assert!(result.is_err());
    }

    #[cfg(feature = "tropical-schubert")]
    #[test]
    fn test_tropicalize_multivector_standalone() {
        let mv = Multivector::<4, 0, 0>::scalar(1.0);
        let tropical = tropicalize_multivector(&mv);
        // Scalar 1.0 → val(1) = -ln(1) = 0 for the nonzero coeff
        assert!(!tropical.is_empty());
    }

    #[test]
    fn test_tangent_bundle_projective() {
        use super::quantum_k_theory::QuantumKClass;

        let tangent = QuantumKClass::<3, 0, 0>::tangent_bundle_projective(2);
        assert_eq!(tangent.k_degree, 2);
        // Tangent bundle of P^2 should have Chern chars at degrees 1 and 2
        assert!(tangent.chern_character.contains_key(&1));
        assert!(tangent.chern_character.contains_key(&2));
    }

    #[test]
    fn test_dual_involution() {
        use super::quantum_k_theory::QuantumKClass;

        let bundle = QuantumKClass::<3, 0, 0>::line_bundle(3);
        let dual = bundle.dual();

        // Dual negates k_degree and Chern characters
        assert_eq!(dual.k_degree, -bundle.k_degree);
        assert_eq!(*dual.chern_character.get(&1).unwrap(), Rational64::from(-3));

        // Double dual should restore signs
        let double_dual = dual.dual();
        assert_eq!(double_dual.k_degree, bundle.k_degree);
        assert_eq!(
            *double_dual.chern_character.get(&1).unwrap(),
            Rational64::from(3)
        );
    }

    #[test]
    fn test_geometric_variety_point_dimension_check() {
        let p1 = GeometricVariety::<3, 0, 0>::point(&[1.0, 0.0, 0.0]).unwrap();
        let line = GeometricVariety::<3, 0, 0>::point(&[0.0, 1.0, 0.0]).unwrap();
        let plane = GeometricVariety::line_through_points(&p1, &line).unwrap();

        // contains_point only works for dimension-0 varieties as input
        assert!(!plane.contains_point(&plane));
    }

    #[test]
    fn test_localized_integral_empty() {
        use super::quantum_k_theory::QuantumKClass;

        let bundle = QuantumKClass::<3, 0, 0>::line_bundle(1);
        let result = bundle.localized_integral(&[]).unwrap();
        assert_eq!(result, Rational64::from(0));
    }
}

// ============================================================================
// Parallel Batch Operations
// ============================================================================

/// Tropicalize multiple multivectors in parallel
///
/// # Contract
///
/// ```text
/// ensures: result.len() == multivectors.len()
/// ```
#[cfg(all(feature = "tropical-schubert", feature = "parallel"))]
pub fn tropicalize_multivector_batch<const P: usize, const Q: usize, const R: usize>(
    multivectors: &[Multivector<P, Q, R>],
) -> Vec<Vec<i64>> {
    multivectors
        .par_iter()
        .map(tropicalize_multivector)
        .collect()
}

/// Compute geometric intersections for multiple Schubert class pairs in parallel
///
/// # Contract
///
/// ```text
/// ensures: result.len() == pairs.len()
/// ```
#[cfg(feature = "parallel")]
pub fn geometric_intersection_batch<const P: usize, const Q: usize, const R: usize>(
    pairs: &[(
        GeometricSchubertClass<P, Q, R>,
        GeometricSchubertClass<P, Q, R>,
    )],
) -> Vec<EnumerativeResult<GeometricSchubertClass<P, Q, R>>> {
    pairs
        .par_iter()
        .map(|(a, b)| a.geometric_intersection(b))
        .collect()
}

// ============================================================================
// Parallel Batch Operation Tests
// ============================================================================

#[cfg(all(test, feature = "parallel"))]
mod parallel_tests {
    use super::*;

    #[test]
    fn test_geometric_intersection_batch() {
        let s1 = GeometricSchubertClass::<4, 0, 0>::new(vec![1], (2, 4)).unwrap();
        let pairs = vec![(s1.clone(), s1.clone())];
        let results = geometric_intersection_batch(&pairs);
        assert_eq!(results.len(), 1);
        assert!(results[0].is_ok());
    }

    #[cfg(feature = "tropical-schubert")]
    #[test]
    fn test_tropicalize_multivector_batch() {
        let mvs = vec![
            Multivector::<4, 0, 0>::scalar(1.0),
            Multivector::<4, 0, 0>::scalar(2.0),
        ];
        let results = tropicalize_multivector_batch(&mvs);
        assert_eq!(results.len(), 2);
    }
}
