symplex/output/

latex.rs

//! LaTeX rendering for symbolic expressions.
//!
//! Provides `to_latex()` methods on `Expr`, `Matrix`, and `Quaternion`.
//! Uses direct `ExprNode` matching (no Display string parsing) for
//! robustness against formatting changes.
//!
//! # Architecture
//!
//! Like `display.rs`, this module uses an **explicit work-stack** rather
//! than recursive function calls, guaranteeing stack safety for
//! arbitrarily deep expression trees (Principle 5).
//!
//! For nodes that require global knowledge of all children before
//! rendering (Add sorting, Mul fraction detection), the children are
//! inspected eagerly and the result pushed as an `Owned` string.

use std::fmt;

use num_bigint::BigInt;
use num_rational::Ratio;
use num_traits::Signed;
use smallvec::SmallVec;

use crate::base::arena::Arena;
use crate::base::node::{ExprId, ExprNode};
use crate::prelude::*;

use super::common::{display_sort_key, extract_negative_power, is_neg_coeff_mul, is_neg_one_mul};

// ═══════════════════════════════════════════════════════════════════════════
// Greek letter table
// ═══════════════════════════════════════════════════════════════════════════

const GREEK_LETTERS: &[&str] = &[
    "alpha",
    "beta",
    "gamma",
    "delta",
    "epsilon",
    "zeta",
    "eta",
    "theta",
    "iota",
    "kappa",
    "lambda",
    "mu",
    "nu",
    "xi",
    "omicron",
    "pi",
    "rho",
    "sigma",
    "tau",
    "upsilon",
    "phi",
    "chi",
    "psi",
    "omega",
    // Uppercase variants
    "Alpha",
    "Beta",
    "Gamma",
    "Delta",
    "Epsilon",
    "Zeta",
    "Eta",
    "Theta",
    "Iota",
    "Kappa",
    "Lambda",
    "Mu",
    "Nu",
    "Xi",
    "Omicron",
    "Pi",
    "Rho",
    "Sigma",
    "Tau",
    "Upsilon",
    "Phi",
    "Chi",
    "Psi",
    "Omega",
    // Common variants
    "varepsilon",
    "varphi",
    "vartheta",
    "varrho",
    "varsigma",
];

/// Convert a symbol name to LaTeX, handling Greek letters and subscripts.
fn symbol_to_latex(name: &str) -> String {
    // Check for subscript patterns like "alpha_1" — handle the base name
    if let Some(idx) = name.find('_') {
        let base = &name[..idx];
        let sub = &name[idx + 1..];
        let latex_base = greek_base(base).unwrap_or_else(|| base.to_string());
        return format!("{}_{{{}}}", latex_base, sub);
    }

    if let Some(g) = greek_base(name) {
        return g;
    }

    name.to_string()
}

/// If `name` is a Greek letter, return `\name`; otherwise None.
fn greek_base(name: &str) -> Option<String> {
    for &g in GREEK_LETTERS {
        if name == g {
            return Some(format!("\\{}", g));
        }
    }
    None
}

// ═══════════════════════════════════════════════════════════════════════════
// Work-stack items
// ═══════════════════════════════════════════════════════════════════════════

/// An item on the LaTeX work-stack.
enum LatexItem {
    /// A literal string to write verbatim.
    Lit(&'static str),
    /// A dynamically-built string to write.
    Owned(String),
    /// An expression that needs to be expanded.
    Expr(ExprId),
}

// ═══════════════════════════════════════════════════════════════════════════
// Core formatting function (iterative)
// ═══════════════════════════════════════════════════════════════════════════

/// Format an expression rooted at `id` as LaTeX into `f`.
///
/// **This function uses an explicit stack — it never recurses.**
pub(crate) fn fmt_latex(arena: &Arena, f: &mut fmt::Formatter<'_>, id: ExprId) -> fmt::Result {
    let mut stack: Vec<LatexItem> = Vec::with_capacity(32);
    stack.push(LatexItem::Expr(id));

    while let Some(item) = stack.pop() {
        match item {
            LatexItem::Lit(s) => write!(f, "{s}")?,
            LatexItem::Owned(s) => write!(f, "{s}")?,
            LatexItem::Expr(eid) => expand_latex(arena, eid, &mut stack),
        }
    }

    Ok(())
}

/// Helper: render an ExprId to a String using `fmt_latex`.
fn latex_to_string(arena: &Arena, id: ExprId) -> String {
    let w = LatexWriter { arena, id };
    format!("{}", w)
}

/// Display wrapper for converting an ExprId to a LaTeX string.
struct LatexWriter<'a> {
    arena: &'a Arena,
    id: ExprId,
}

impl fmt::Display for LatexWriter<'_> {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        fmt_latex(self.arena, f, self.id)
    }
}

// ═══════════════════════════════════════════════════════════════════════════
// Mul rendering helpers
// ═══════════════════════════════════════════════════════════════════════════

/// Heuristic: does this rendered string look like a plain number?
fn looks_like_number(s: &str) -> bool {
    if s.is_empty() {
        return false;
    }
    let s = s.strip_prefix('-').unwrap_or(s);
    s.chars().all(|c| c.is_ascii_digit())
}

/// Join multiplication factors with implicit multiplication (space) or \cdot.
fn join_mul_factors(factors: &[String]) -> String {
    if factors.len() == 1 {
        return factors[0].clone();
    }

    let mut result = String::new();
    for (i, f) in factors.iter().enumerate() {
        if i > 0 {
            let prev = &factors[i - 1];
            if looks_like_number(prev) && looks_like_number(f) {
                // Two adjacent numbers need an explicit multiplication sign.
                result.push_str(r" \cdot ");
            } else if looks_like_number(prev) {
                // Numeric coefficient followed by a non-numeric factor:
                // use implicit multiplication (no separator), e.g. "3x^{2}".
            } else {
                result.push(' ');
            }
        }
        result.push_str(f);
    }
    result
}

/// Render a single Mul factor, wrapping Add children in \left(...\right).
fn render_mul_factor(arena: &Arena, id: ExprId) -> String {
    let s = latex_to_string(arena, id);
    if matches!(arena.node(id), ExprNode::Add(_)) {
        format!("\\left({}\\right)", s)
    } else {
        s
    }
}

/// Render a Pow base, wrapping compound expressions in \left(...\right).
///
/// Besides sums/products/negations this also wraps nested powers (a bare
/// `x^{a}^{b}` is a LaTeX "double superscript" error) and negative or
/// non-integer numeric bases (`\left(-2\right)^{x}`,
/// `\left(\frac{2}{3}\right)^{x}`).
fn render_pow_base(arena: &Arena, base: ExprId) -> String {
    let s = latex_to_string(arena, base);
    let wrap = match arena.node(base) {
        ExprNode::Add(_) | ExprNode::Mul(_) | ExprNode::Neg(_) | ExprNode::Pow(_, _) => true,
        ExprNode::Num(nid) => {
            let r = arena.num(*nid);
            r.is_negative() || !r.is_integer()
        }
        _ => false,
    };
    if wrap {
        format!("\\left({}\\right)", s)
    } else {
        s
    }
}

/// Render a Mul node to a complete LaTeX string.
///
/// Handles: leading -1/1, fraction rendering (negative powers → denominator),
/// implicit multiplication.
fn render_mul(arena: &Arena, children: &[ExprId]) -> String {
    if children.is_empty() {
        return "1".to_string();
    }

    // Check for leading -1 or 1
    let first_node = arena.node(children[0]);
    let is_neg_one = if let ExprNode::Num(nid) = first_node {
        *arena.num(*nid) == Ratio::from(BigInt::from(-1))
    } else {
        false
    };
    let is_pos_one = if let ExprNode::Num(nid) = first_node {
        *arena.num(*nid) == Ratio::from(BigInt::from(1))
    } else {
        false
    };

    let (skip_first, prefix) = if children.len() > 1 && is_neg_one {
        (true, "-")
    } else if children.len() > 1 && is_pos_one {
        (true, "")
    } else {
        (false, "")
    };

    let start_idx = if skip_first { 1 } else { 0 };
    let factors = &children[start_idx..];

    // Separate numerator and denominator factors
    let mut numer_factors: Vec<String> = Vec::new();
    let mut denom_factors: Vec<String> = Vec::new();

    for &factor in factors {
        if let Some((base_id, pos_exp_str)) = extract_negative_power(arena, factor) {
            let base_latex = render_pow_base(arena, base_id);
            if pos_exp_str == "1" {
                denom_factors.push(base_latex);
            } else {
                denom_factors.push(format!("{}^{{{}}}", base_latex, pos_exp_str));
            }
        } else {
            numer_factors.push(render_mul_factor(arena, factor));
        }
    }

    if denom_factors.is_empty() {
        // Pure product
        let body = if numer_factors.is_empty() {
            "1".to_string()
        } else {
            join_mul_factors(&numer_factors)
        };
        format!("{}{}", prefix, body)
    } else {
        // Fraction
        let numer_str = if numer_factors.is_empty() {
            "1".to_string()
        } else {
            join_mul_factors(&numer_factors)
        };
        let denom_str = join_mul_factors(&denom_factors);
        if prefix == "-" {
            format!("-\\frac{{{}}}{{{}}}", numer_str, denom_str)
        } else {
            format!("\\frac{{{}}}{{{}}}", numer_str, denom_str)
        }
    }
}

// ═══════════════════════════════════════════════════════════════════════════
// Add rendering helpers
// ═══════════════════════════════════════════════════════════════════════════

/// Render a Mul with leading -1 without the leading factor.
/// Returns the LaTeX for the remaining factors.
fn render_mul_without_neg_one(arena: &Arena, id: ExprId) -> String {
    if let ExprNode::Mul(children) = arena.node(id) {
        let rest = &children[1..];
        if rest.len() == 1 {
            return latex_to_string(arena, rest[0]);
        }
        // Render as a Mul of the remaining factors
        render_mul(arena, rest)
    } else {
        latex_to_string(arena, id)
    }
}

/// Render a Mul with negative leading coefficient as subtraction content.
/// Returns the LaTeX string with the coefficient negated.
fn render_neg_coeff_mul_as_subtraction(arena: &Arena, id: ExprId) -> String {
    if let ExprNode::Mul(children) = arena.node(id)
        && let Some(&first) = children.first()
        && let ExprNode::Num(nid) = arena.node(first)
    {
        let r = arena.num(*nid);
        let pos_r = -r.clone();

        // Build a new children list with the positive coefficient
        // Replace the first child in the rendering
        let coeff_str = render_num_value(&pos_r);

        let rest_factors: Vec<String> = children[1..]
            .iter()
            .map(|&c| render_mul_factor(arena, c))
            .collect();

        if pos_r == Ratio::from(BigInt::from(1)) {
            // Coefficient is 1 after negation → just render rest
            if rest_factors.is_empty() {
                return "1".to_string();
            }
            return join_mul_factors(&rest_factors);
        }

        let mut all_factors = vec![coeff_str];
        all_factors.extend(rest_factors);

        // Check for fraction rendering (negative powers in rest)
        // For simplicity, delegate to render_mul with modified children
        // Actually, let's just join them
        return join_mul_factors(&all_factors);
    }
    latex_to_string(arena, id)
}

// ═══════════════════════════════════════════════════════════════════════════
// Number rendering helper
// ═══════════════════════════════════════════════════════════════════════════

/// Render a rational number to LaTeX.
fn render_num_value(r: &Ratio<BigInt>) -> String {
    if r.is_integer() {
        format!("{}", r.numer())
    } else if r.numer().is_negative() {
        format!("-\\frac{{{}}}{{{}}}", -r.numer(), r.denom())
    } else {
        format!("\\frac{{{}}}{{{}}}", r.numer(), r.denom())
    }
}

// ═══════════════════════════════════════════════════════════════════════════
// Node expansion
// ═══════════════════════════════════════════════════════════════════════════

/// Push a LaTeX function call `\name\left(arg\right)` onto the stack.
/// If `id` is a trig/hyperbolic function node, return (`\funcname`, arg).
fn trig_func_parts(arena: &Arena, id: ExprId) -> Option<(&'static str, ExprId)> {
    match arena.node(id) {
        ExprNode::Sin(x) => Some((r"\sin", *x)),
        ExprNode::Cos(x) => Some((r"\cos", *x)),
        ExprNode::Tan(x) => Some((r"\tan", *x)),
        ExprNode::Sinh(x) => Some((r"\sinh", *x)),
        ExprNode::Cosh(x) => Some((r"\cosh", *x)),
        ExprNode::Tanh(x) => Some((r"\tanh", *x)),
        ExprNode::Asin(x) => Some((r"\arcsin", *x)),
        ExprNode::Acos(x) => Some((r"\arccos", *x)),
        ExprNode::Atan(x) => Some((r"\arctan", *x)),
        ExprNode::Asinh(x) => Some((r"\operatorname{asinh}", *x)),
        ExprNode::Acosh(x) => Some((r"\operatorname{acosh}", *x)),
        ExprNode::Atanh(x) => Some((r"\operatorname{atanh}", *x)),
        _ => None,
    }
}

fn push_latex_func(name: &'static str, arg: ExprId, stack: &mut Vec<LatexItem>) {
    stack.push(LatexItem::Lit(r"\right)"));
    stack.push(LatexItem::Expr(arg));
    stack.push(LatexItem::Owned(format!("{}\\left(", name)));
}

/// Push `head\left(args[0], args[1], …\right)` (reverse order).
fn push_latex_call(head: &str, args: &[ExprId], stack: &mut Vec<LatexItem>) {
    stack.push(LatexItem::Lit(r"\right)"));
    for (i, &arg) in args.iter().enumerate().rev() {
        stack.push(LatexItem::Expr(arg));
        if i > 0 {
            stack.push(LatexItem::Lit(", "));
        }
    }
    stack.push(LatexItem::Owned(format!("{head}\\left(")));
}

/// LaTeX for the 0.9 `Apply`-based special functions, following SymPy's
/// printer: `\operatorname{erfi}`, `\operatorname{E}_{n}`, `S`/`C`,
/// `\gamma`/`\Gamma`, `\operatorname{Li}_{s}`, `\eta`, `\operatorname{Ai}`,
/// `K`/`E`/`F\left(\phi\middle| m\right)`/`\Pi`, `C_{n}^{\left(a\right)}`,
/// `\operatorname{B}_{(x_1, x_2)}`/`\operatorname{I}_{(x_1, x_2)}`, …
///
/// Returns `false` (pushing nothing) for any other name.
fn push_special_09_latex(name: &str, args: &[ExprId], stack: &mut Vec<LatexItem>) -> bool {
    use crate::base::arena::{
        FN_AIRYAI, FN_AIRYAIPRIME, FN_AIRYBI, FN_AIRYBIPRIME, FN_ASSOC_LAGUERRE, FN_ASSOC_LEGENDRE,
        FN_BETAINC, FN_BETAINC_REGULARIZED, FN_CHI, FN_DIRICHLET_ETA, FN_ELLIPTIC_E, FN_ELLIPTIC_F,
        FN_ELLIPTIC_K, FN_ELLIPTIC_PI, FN_ERFCINV, FN_ERFI, FN_ERFINV, FN_EXPINT, FN_FRESNELC,
        FN_FRESNELS, FN_GEGENBAUER, FN_JACOBI, FN_LOWERGAMMA, FN_POLYLOG, FN_SHI, FN_UPPERGAMMA,
    };
    // Plain `head(args)` renderings.
    let head: Option<&str> = match (name, args.len()) {
        (FN_ERFI, 1) => Some(r"\operatorname{erfi}"),
        (FN_ERFINV, 1) => Some(r"\operatorname{erf}^{-1}"),
        (FN_ERFCINV, 1) => Some(r"\operatorname{erfc}^{-1}"),
        (FN_SHI, 1) => Some(r"\operatorname{Shi}"),
        (FN_CHI, 1) => Some(r"\operatorname{Chi}"),
        (FN_FRESNELS, 1) => Some("S"),
        (FN_FRESNELC, 1) => Some("C"),
        (FN_LOWERGAMMA, 2) => Some(r"\gamma"),
        (FN_UPPERGAMMA, 2) => Some(r"\Gamma"),
        (FN_DIRICHLET_ETA, 1) => Some(r"\eta"),
        (FN_AIRYAI, 1) => Some(r"\operatorname{Ai}"),
        (FN_AIRYBI, 1) => Some(r"\operatorname{Bi}"),
        (FN_AIRYAIPRIME, 1) => Some(r"\operatorname{Ai}^\prime"),
        (FN_AIRYBIPRIME, 1) => Some(r"\operatorname{Bi}^\prime"),
        (FN_ELLIPTIC_K, 1) => Some("K"),
        (FN_ELLIPTIC_E, 1) => Some("E"),
        _ => None,
    };
    if let Some(head) = head {
        push_latex_call(head, args, stack);
        return true;
    }
    match (name, args.len()) {
        // head_{param}\left(x\right)
        (FN_EXPINT, 2) | (FN_POLYLOG, 2) => {
            let head = if name == FN_EXPINT {
                r"\operatorname{E}_{"
            } else {
                r"\operatorname{Li}_{"
            };
            stack.push(LatexItem::Lit(r"\right)"));
            stack.push(LatexItem::Expr(args[1]));
            stack.push(LatexItem::Lit(r"}\left("));
            stack.push(LatexItem::Expr(args[0]));
            stack.push(LatexItem::Lit(head));
            true
        }
        // F\left(\phi\middle| m\right), \Pi\left(n\middle| m\right)
        (FN_ELLIPTIC_F, 2) | (FN_ELLIPTIC_PI, 2) => {
            stack.push(LatexItem::Lit(r"\right)"));
            stack.push(LatexItem::Expr(args[1]));
            stack.push(LatexItem::Lit(r"\middle| "));
            stack.push(LatexItem::Expr(args[0]));
            stack.push(LatexItem::Lit(if name == FN_ELLIPTIC_F {
                r"F\left("
            } else {
                r"\Pi\left("
            }));
            true
        }
        // C_{n}^{\left(a\right)}\left(x\right), P_{n}^{\left(m\right)}, L_{n}^{\left(a\right)}
        (FN_GEGENBAUER, 3) | (FN_ASSOC_LEGENDRE, 3) | (FN_ASSOC_LAGUERRE, 3) => {
            let letter = match name {
                FN_GEGENBAUER => r"C_{",
                FN_ASSOC_LEGENDRE => r"P_{",
                _ => r"L_{",
            };
            stack.push(LatexItem::Lit(r"\right)"));
            stack.push(LatexItem::Expr(args[2]));
            stack.push(LatexItem::Lit(r"\right)}\left("));
            stack.push(LatexItem::Expr(args[1]));
            stack.push(LatexItem::Lit(r"}^{\left("));
            stack.push(LatexItem::Expr(args[0]));
            stack.push(LatexItem::Lit(letter));
            true
        }
        // P_{n}^{\left(a,b\right)}\left(x\right)
        (FN_JACOBI, 4) => {
            stack.push(LatexItem::Lit(r"\right)"));
            stack.push(LatexItem::Expr(args[3]));
            stack.push(LatexItem::Lit(r"\right)}\left("));
            stack.push(LatexItem::Expr(args[2]));
            stack.push(LatexItem::Lit(","));
            stack.push(LatexItem::Expr(args[1]));
            stack.push(LatexItem::Lit(r"}^{\left("));
            stack.push(LatexItem::Expr(args[0]));
            stack.push(LatexItem::Lit(r"P_{"));
            true
        }
        // \operatorname{B}_{(x_1, x_2)}\left(a, b\right), \operatorname{I}_{(x_1, x_2)}\left(a, b\right)
        (FN_BETAINC, 4) | (FN_BETAINC_REGULARIZED, 4) => {
            stack.push(LatexItem::Lit(r"\right)"));
            stack.push(LatexItem::Expr(args[1]));
            stack.push(LatexItem::Lit(", "));
            stack.push(LatexItem::Expr(args[0]));
            stack.push(LatexItem::Lit(r")}\left("));
            stack.push(LatexItem::Expr(args[3]));
            stack.push(LatexItem::Lit(", "));
            stack.push(LatexItem::Expr(args[2]));
            stack.push(LatexItem::Lit(if name == FN_BETAINC {
                r"\operatorname{B}_{("
            } else {
                r"\operatorname{I}_{("
            }));
            true
        }
        _ => false,
    }
}

/// Expand a single expression node into LaTeX work items on the stack.
///
/// Items are pushed in **reverse** display order so that popping
/// yields left-to-right output.
fn expand_latex(arena: &Arena, id: ExprId, stack: &mut Vec<LatexItem>) {
    let node = arena.node(id).clone();

    match node {
        // ── Atoms ──────────────────────────────────────────────────
        ExprNode::Num(nid) => {
            let r = arena.num(nid);
            stack.push(LatexItem::Owned(render_num_value(r)));
        }

        ExprNode::Symbol(sid) => {
            let name = arena.symbol_name(sid);
            stack.push(LatexItem::Owned(symbol_to_latex(name)));
        }

        ExprNode::Pi => stack.push(LatexItem::Lit(r"\pi")),
        ExprNode::E => stack.push(LatexItem::Lit("e")),
        ExprNode::ImaginaryUnit => stack.push(LatexItem::Lit("i")),
        ExprNode::EulerGamma => stack.push(LatexItem::Lit(r"\gamma")),
        ExprNode::Catalan => stack.push(LatexItem::Lit("G")),
        ExprNode::GoldenRatio => stack.push(LatexItem::Lit(r"\phi")),
        ExprNode::PhysicalConstant(name_id, _) => {
            stack.push(LatexItem::Owned(symbol_to_latex(
                arena.symbol_name(name_id),
            )));
        }
        ExprNode::Infinity => stack.push(LatexItem::Lit(r"\infty")),
        ExprNode::NegInfinity => stack.push(LatexItem::Lit(r"-\infty")),
        ExprNode::ComplexInfinity => stack.push(LatexItem::Lit(r"\tilde{\infty}")),
        ExprNode::NaN => stack.push(LatexItem::Lit(r"\text{NaN}")),

        // ── Add ────────────────────────────────────────────────────
        //
        // Rendered eagerly because we need to sort children and detect
        // subtraction patterns across the entire child list.
        ExprNode::Add(ref children) => {
            let children = children.clone();
            if children.is_empty() {
                stack.push(LatexItem::Lit("0"));
                return;
            }

            // Sort children by display key
            let mut display_order: SmallVec<[ExprId; 6]> = children;
            display_order.sort_by_key(|a| display_sort_key(arena, *a));

            let mut result = String::new();

            for (i, &child) in display_order.iter().enumerate() {
                let child_node = arena.node(child);

                if let ExprNode::Neg(inner) = child_node {
                    // Neg(x) → " - x"
                    let inner = *inner;
                    let inner_latex = latex_to_string(arena, inner);
                    if i == 0 {
                        // Wrap Add children of inner in parens
                        if matches!(arena.node(inner), ExprNode::Add(_)) {
                            result.push_str(&format!("-\\left({}\\right)", inner_latex));
                        } else {
                            result.push_str(&format!("-{}", inner_latex));
                        }
                    } else if matches!(arena.node(inner), ExprNode::Add(_)) {
                        result.push_str(&format!(" - \\left({}\\right)", inner_latex));
                    } else {
                        result.push_str(&format!(" - {}", inner_latex));
                    }
                } else if is_neg_one_mul(arena, child) {
                    // Mul([-1, rest...]) → " - rest"
                    let rest_latex = render_mul_without_neg_one(arena, child);
                    if i == 0 {
                        result.push_str(&format!("-{}", rest_latex));
                    } else {
                        result.push_str(&format!(" - {}", rest_latex));
                    }
                } else if is_neg_coeff_mul(arena, child) {
                    // Mul([-n, rest...]) → " - n*rest"
                    let sub_latex = render_neg_coeff_mul_as_subtraction(arena, child);
                    if i == 0 {
                        result.push_str(&format!("-{}", sub_latex));
                    } else {
                        result.push_str(&format!(" - {}", sub_latex));
                    }
                } else if i == 0 {
                    // Check if the child is a negative number
                    if let ExprNode::Num(nid) = arena.node(child) {
                        let r = arena.num(*nid);
                        if r.is_negative() && !r.is_integer() {
                            // Negative fraction at leading position
                            result.push_str(&render_num_value(r));
                        } else {
                            result.push_str(&latex_to_string(arena, child));
                        }
                    } else {
                        result.push_str(&latex_to_string(arena, child));
                    }
                } else {
                    // Check if child is a negative number
                    if let ExprNode::Num(nid) = arena.node(child) {
                        let r = arena.num(*nid);
                        if r.is_negative() {
                            let pos_r = -r.clone();
                            let pos_str = render_num_value(&pos_r);
                            result.push_str(&format!(" - {}", pos_str));
                        } else {
                            result.push_str(&format!(" + {}", latex_to_string(arena, child)));
                        }
                    } else {
                        result.push_str(&format!(" + {}", latex_to_string(arena, child)));
                    }
                }
            }

            stack.push(LatexItem::Owned(result));
        }

        // ── Mul ────────────────────────────────────────────────────
        //
        // Rendered eagerly because fraction detection requires scanning
        // all children.
        ExprNode::Mul(ref children) => {
            let children_vec: Vec<ExprId> = children.iter().copied().collect();
            stack.push(LatexItem::Owned(render_mul(arena, &children_vec)));
        }

        // ── Pow ────────────────────────────────────────────────────
        ExprNode::Pow(base, exp) => {
            // Special case: exp = 1/2 → \sqrt{base}
            if let ExprNode::Num(nid) = arena.node(exp) {
                let r = arena.num(*nid);
                if *r == Ratio::new(BigInt::from(1), BigInt::from(2)) {
                    stack.push(LatexItem::Lit("}"));
                    stack.push(LatexItem::Expr(base));
                    stack.push(LatexItem::Lit(r"\sqrt{"));
                    return;
                }
                // exp = 1/3 → \sqrt[3]{base}
                if *r == Ratio::new(BigInt::from(1), BigInt::from(3)) {
                    stack.push(LatexItem::Lit("}"));
                    stack.push(LatexItem::Expr(base));
                    stack.push(LatexItem::Lit(r"\sqrt[3]{"));
                    return;
                }
                // exp = 1/n → \sqrt[n]{base}
                if !r.is_integer() && !r.is_negative() && *r.numer() == BigInt::from(1) {
                    let n = r.denom();
                    stack.push(LatexItem::Lit("}"));
                    stack.push(LatexItem::Expr(base));
                    stack.push(LatexItem::Owned(format!("\\sqrt[{}]{{", n)));
                    return;
                }
                // exp = -1 → \frac{1}{base}
                if *r == Ratio::from(BigInt::from(-1)) {
                    let base_latex = render_pow_base(arena, base);
                    stack.push(LatexItem::Owned(format!("\\frac{{1}}{{{}}}", base_latex)));
                    return;
                }
                // exp = -n (negative integer, not -1) → \frac{1}{base^{n}}
                if r.is_integer() && r.is_negative() {
                    let pos_n = -r.numer();
                    let base_latex = render_pow_base(arena, base);
                    stack.push(LatexItem::Owned(format!(
                        "\\frac{{1}}{{{}^{{{}}}}}",
                        base_latex, pos_n
                    )));
                    return;
                }
            }

            // Trig function power: sin(x)^n → \sin^{n}\left(x\right)
            if let Some((func_name, arg)) = trig_func_parts(arena, base) {
                stack.push(LatexItem::Lit(r"\right)"));
                stack.push(LatexItem::Expr(arg));
                stack.push(LatexItem::Lit(r"}\left("));
                stack.push(LatexItem::Expr(exp));
                stack.push(LatexItem::Owned(format!("{}^{{", func_name)));
                return;
            }

            // General case: base^{exp}
            let base_latex = render_pow_base(arena, base);
            stack.push(LatexItem::Lit("}"));
            stack.push(LatexItem::Expr(exp));
            stack.push(LatexItem::Owned(format!("{}^{{", base_latex)));
        }

        // ── Neg ────────────────────────────────────────────────────
        ExprNode::Neg(inner) => {
            if matches!(arena.node(inner), ExprNode::Add(_)) {
                stack.push(LatexItem::Lit(r"\right)"));
                stack.push(LatexItem::Expr(inner));
                stack.push(LatexItem::Lit(r"-\left("));
            } else {
                stack.push(LatexItem::Expr(inner));
                stack.push(LatexItem::Lit("-"));
            }
        }

        // ── Trig functions ─────────────────────────────────────────
        ExprNode::Sin(x) => push_latex_func(r"\sin", x, stack),
        ExprNode::Cos(x) => push_latex_func(r"\cos", x, stack),
        ExprNode::Tan(x) => push_latex_func(r"\tan", x, stack),
        ExprNode::Asin(x) => push_latex_func(r"\arcsin", x, stack),
        ExprNode::Acos(x) => push_latex_func(r"\arccos", x, stack),
        ExprNode::Atan(x) => push_latex_func(r"\arctan", x, stack),
        ExprNode::Sinh(x) => push_latex_func(r"\sinh", x, stack),
        ExprNode::Cosh(x) => push_latex_func(r"\cosh", x, stack),
        ExprNode::Tanh(x) => push_latex_func(r"\tanh", x, stack),
        ExprNode::Asinh(x) => push_latex_func(r"\operatorname{asinh}", x, stack),
        ExprNode::Acosh(x) => push_latex_func(r"\operatorname{acosh}", x, stack),
        ExprNode::Atanh(x) => push_latex_func(r"\operatorname{atanh}", x, stack),

        // ── Transcendental ─────────────────────────────────────────
        ExprNode::Exp(x) => push_latex_func(r"\exp", x, stack),
        ExprNode::Ln(x) => push_latex_func(r"\ln", x, stack),

        // ── Special functions ──────────────────────────────────────
        ExprNode::Sign(x) => push_latex_func(r"\operatorname{sgn}", x, stack),
        ExprNode::Heaviside(x) => push_latex_func(r"\operatorname{H}", x, stack),
        ExprNode::DiracDelta(x) => push_latex_func(r"\delta", x, stack),
        ExprNode::Gamma(x) => push_latex_func(r"\Gamma", x, stack),
        ExprNode::LogGamma(x) => push_latex_func(r"\ln \Gamma", x, stack),
        ExprNode::Digamma(x) => push_latex_func(r"\psi", x, stack),
        ExprNode::Erf(x) => push_latex_func(r"\operatorname{erf}", x, stack),
        ExprNode::Erfc(x) => push_latex_func(r"\operatorname{erfc}", x, stack),
        ExprNode::LambertW(x) => push_latex_func(r"\operatorname{W}", x, stack),

        // ── Complex analysis ────────────────────────────────────────────
        ExprNode::Re(x) => push_latex_func(r"\Re", x, stack),
        ExprNode::Im(x) => push_latex_func(r"\Im", x, stack),
        ExprNode::Conjugate(x) => {
            stack.push(LatexItem::Lit("}"));
            stack.push(LatexItem::Expr(x));
            stack.push(LatexItem::Lit(r"\overline{"));
        }
        ExprNode::Arg(x) => push_latex_func(r"\arg", x, stack),

        // ── Special functions (0.2) ──────────────────────────────────────
        ExprNode::Si(x) => push_latex_func(r"\operatorname{Si}", x, stack),
        ExprNode::Ci(x) => push_latex_func(r"\operatorname{Ci}", x, stack),
        ExprNode::Ei(x) => push_latex_func(r"\operatorname{Ei}", x, stack),
        ExprNode::Li(x) => push_latex_func(r"\operatorname{li}", x, stack),
        ExprNode::Zeta(x) => push_latex_func(r"\zeta", x, stack),
        ExprNode::Polygamma(n, x) => {
            // \psi^{(n)}\left(x\right)
            stack.push(LatexItem::Lit(r"\right)"));
            stack.push(LatexItem::Expr(x));
            stack.push(LatexItem::Lit(r")}\left("));
            stack.push(LatexItem::Expr(n));
            stack.push(LatexItem::Lit(r"\psi^{("));
        }
        ExprNode::KroneckerDelta(i, j) => {
            // \delta_{i j}
            stack.push(LatexItem::Lit("}"));
            stack.push(LatexItem::Expr(j));
            stack.push(LatexItem::Lit(" "));
            stack.push(LatexItem::Expr(i));
            stack.push(LatexItem::Lit(r"\delta_{"));
        }

        // ── Abs: \left|x\right| ───────────────────────────────────
        ExprNode::Abs(x) => {
            stack.push(LatexItem::Lit(r"\right|"));
            stack.push(LatexItem::Expr(x));
            stack.push(LatexItem::Lit(r"\left|"));
        }

        // ── Floor / Ceiling ────────────────────────────────────────
        ExprNode::Floor(x) => {
            stack.push(LatexItem::Lit(r"\rfloor"));
            stack.push(LatexItem::Expr(x));
            stack.push(LatexItem::Lit(r"\lfloor "));
        }
        ExprNode::Ceiling(x) => {
            stack.push(LatexItem::Lit(r"\rceil"));
            stack.push(LatexItem::Expr(x));
            stack.push(LatexItem::Lit(r"\lceil "));
        }

        // ── Factorial: n! ──────────────────────────────────────────
        ExprNode::Factorial(x) => {
            if arena.node(x).is_atom() {
                stack.push(LatexItem::Lit("!"));
                stack.push(LatexItem::Expr(x));
            } else {
                stack.push(LatexItem::Lit(r"\right)!"));
                stack.push(LatexItem::Expr(x));
                stack.push(LatexItem::Lit(r"\left("));
            }
        }

        // ── Binomial: \binom{n}{k} ────────────────────────────────
        ExprNode::Binomial(n, k) => {
            stack.push(LatexItem::Lit("}"));
            stack.push(LatexItem::Expr(k));
            stack.push(LatexItem::Lit("}{"));
            stack.push(LatexItem::Expr(n));
            stack.push(LatexItem::Lit(r"\binom{"));
        }

        // ── Beta: \mathrm{B}(a, b) ────────────────────────────────
        ExprNode::Beta(a, b) => {
            stack.push(LatexItem::Lit(r"\right)"));
            stack.push(LatexItem::Expr(b));
            stack.push(LatexItem::Lit(", "));
            stack.push(LatexItem::Expr(a));
            stack.push(LatexItem::Lit(r"\mathrm{B}\left("));
        }

        // ── Atan2 ──────────────────────────────────────────────────
        ExprNode::Atan2(y, x) => {
            stack.push(LatexItem::Lit(r"\right)"));
            stack.push(LatexItem::Expr(x));
            stack.push(LatexItem::Lit(", "));
            stack.push(LatexItem::Expr(y));
            stack.push(LatexItem::Lit(r"\operatorname{atan2}\left("));
        }

        // ── Min / Max ──────────────────────────────────────────────
        ExprNode::Min(ref args) => {
            let args = args.clone();
            stack.push(LatexItem::Lit(r"\right)"));
            for (i, &arg) in args.iter().enumerate().rev() {
                stack.push(LatexItem::Expr(arg));
                if i > 0 {
                    stack.push(LatexItem::Lit(", "));
                }
            }
            stack.push(LatexItem::Lit(r"\min\left("));
        }
        ExprNode::Max(ref args) => {
            let args = args.clone();
            stack.push(LatexItem::Lit(r"\right)"));
            for (i, &arg) in args.iter().enumerate().rev() {
                stack.push(LatexItem::Expr(arg));
                if i > 0 {
                    stack.push(LatexItem::Lit(", "));
                }
            }
            stack.push(LatexItem::Lit(r"\max\left("));
        }

        // ── Sum / Product ──────────────────────────────────────────
        ExprNode::Sum(body, var, lo, hi) => {
            stack.push(LatexItem::Expr(body));
            stack.push(LatexItem::Lit("} "));
            stack.push(LatexItem::Expr(hi));
            stack.push(LatexItem::Lit("^{"));
            stack.push(LatexItem::Expr(lo));
            stack.push(LatexItem::Lit("="));
            stack.push(LatexItem::Expr(var));
            stack.push(LatexItem::Lit(r"\sum_{"));
        }
        ExprNode::Product_(body, var, lo, hi) => {
            stack.push(LatexItem::Expr(body));
            stack.push(LatexItem::Lit("} "));
            stack.push(LatexItem::Expr(hi));
            stack.push(LatexItem::Lit("^{"));
            stack.push(LatexItem::Expr(lo));
            stack.push(LatexItem::Lit("="));
            stack.push(LatexItem::Expr(var));
            stack.push(LatexItem::Lit(r"\prod_{"));
        }

        // ── Derivative: \frac{d}{dvar} body ───────────────────────
        ExprNode::Derivative(body, var) => {
            stack.push(LatexItem::Expr(body));
            stack.push(LatexItem::Lit("} "));
            stack.push(LatexItem::Expr(var));
            stack.push(LatexItem::Lit(r"\frac{d}{d"));
        }

        // ── Integral: \int body \, dvar ───────────────────────────
        ExprNode::Integral(body, var) => {
            stack.push(LatexItem::Expr(var));
            stack.push(LatexItem::Lit(r"\, d"));
            stack.push(LatexItem::Expr(body));
            stack.push(LatexItem::Lit(r"\int "));
        }

        // ── DefiniteIntegral: \int_{lo}^{hi} body \, dvar ────────────
        ExprNode::DefiniteIntegral(body, var, lo, hi) => {
            stack.push(LatexItem::Expr(var));
            stack.push(LatexItem::Lit(r"\, d"));
            stack.push(LatexItem::Expr(body));
            stack.push(LatexItem::Lit("} "));
            stack.push(LatexItem::Expr(hi));
            stack.push(LatexItem::Lit("}^{"));
            stack.push(LatexItem::Expr(lo));
            stack.push(LatexItem::Lit(r"\int_{"));
        }

        // ── Limit: \lim_{var \to point} body ──────────────────────
        ExprNode::Limit(body, var, point) => {
            stack.push(LatexItem::Expr(body));
            stack.push(LatexItem::Lit("} "));
            stack.push(LatexItem::Expr(point));
            stack.push(LatexItem::Lit(r" \to "));
            stack.push(LatexItem::Expr(var));
            stack.push(LatexItem::Lit(r"\lim_{"));
        }

        // ── Series ─────────────────────────────────────────────────
        ExprNode::Series(body, var, point, order) => {
            stack.push(LatexItem::Lit(r"\right)"));
            stack.push(LatexItem::Expr(order));
            stack.push(LatexItem::Lit(", "));
            stack.push(LatexItem::Expr(point));
            stack.push(LatexItem::Lit(", "));
            stack.push(LatexItem::Expr(var));
            stack.push(LatexItem::Lit(", "));
            stack.push(LatexItem::Expr(body));
            stack.push(LatexItem::Lit(r"\operatorname{Series}\left("));
        }

        // ── Laplace Transform: \mathcal{L}\left\{body\right\} ────
        ExprNode::LaplaceTransform(body, _t, _s) => {
            stack.push(LatexItem::Lit(r"\right\}"));
            stack.push(LatexItem::Expr(body));
            stack.push(LatexItem::Lit(r"\mathcal{L}\left\{"));
        }

        // ── Inverse Laplace Transform ──────────────────────────────
        ExprNode::InverseLaplaceTransform(body, _s, _t) => {
            stack.push(LatexItem::Lit(r"\right\}"));
            stack.push(LatexItem::Expr(body));
            stack.push(LatexItem::Lit(r"\mathcal{L}^{-1}\left\{"));
        }

        // ── Residue: \operatorname{Res}_{var=point} body ──────────
        ExprNode::Residue(body, var, point) => {
            stack.push(LatexItem::Expr(body));
            stack.push(LatexItem::Lit("} "));
            stack.push(LatexItem::Expr(point));
            stack.push(LatexItem::Lit("="));
            stack.push(LatexItem::Expr(var));
            stack.push(LatexItem::Lit(r"\operatorname{Res}_{"));
        }

        // ── RootOf ─────────────────────────────────────────────────
        ExprNode::RootOf(poly, index) => {
            stack.push(LatexItem::Lit(r"\right)"));
            stack.push(LatexItem::Expr(index));
            stack.push(LatexItem::Lit(", "));
            stack.push(LatexItem::Expr(poly));
            stack.push(LatexItem::Lit(r"\operatorname{RootOf}\left("));
        }

        // ── DSolve ─────────────────────────────────────────────────
        ExprNode::DSolve(expr, func, var) => {
            stack.push(LatexItem::Lit(r"\right)"));
            stack.push(LatexItem::Expr(var));
            stack.push(LatexItem::Lit(", "));
            stack.push(LatexItem::Expr(func));
            stack.push(LatexItem::Lit(", "));
            stack.push(LatexItem::Expr(expr));
            stack.push(LatexItem::Lit(r"\operatorname{DSolve}\left("));
        }

        // ── RootSum ────────────────────────────────────────────────
        // Display as: \operatorname{RootSum}\left(poly,\, sumvar \mapsto body\right)
        ExprNode::RootSum(poly, body, sumvar) => {
            stack.push(LatexItem::Lit(r"\right)"));
            stack.push(LatexItem::Expr(body));
            stack.push(LatexItem::Lit(r" \mapsto "));
            stack.push(LatexItem::Expr(sumvar));
            stack.push(LatexItem::Lit(r",\, "));
            stack.push(LatexItem::Expr(poly));
            stack.push(LatexItem::Lit(r"\operatorname{RootSum}\left("));
        }

        // ── ConditionSet: \left\{var \mid condition\right\} ───────
        ExprNode::ConditionSet(var, condition) => {
            stack.push(LatexItem::Lit(r"\right\}"));
            stack.push(LatexItem::Expr(condition));
            stack.push(LatexItem::Lit(r" \mid "));
            stack.push(LatexItem::Expr(var));
            stack.push(LatexItem::Lit(r"\left\{"));
        }

        // ── Apply (user-defined function) ──────────────────────────
        ExprNode::Apply(sym_id, ref args) => {
            let name = arena.symbol_name(sym_id).to_owned();
            let args = args.clone();
            if push_special_09_latex(&name, &args, stack) {
                return;
            }
            stack.push(LatexItem::Lit(r"\right)"));
            for (i, &arg) in args.iter().enumerate().rev() {
                stack.push(LatexItem::Expr(arg));
                if i > 0 {
                    stack.push(LatexItem::Lit(", "));
                }
            }
            stack.push(LatexItem::Owned(format!("{}\\left(", name)));
        }

        // ── Piecewise ──────────────────────────────────────────────
        ExprNode::Piecewise(ref pieces) => {
            let pieces = pieces.clone();
            let mut result = String::from("\\begin{cases}\n");
            for (i, &(val, cond)) in pieces.iter().enumerate() {
                let val_latex = latex_to_string(arena, val);
                let cond_latex = latex_to_string(arena, cond);
                result.push_str(&format!("  {} & \\text{{if }} {}", val_latex, cond_latex));
                if i + 1 < pieces.len() {
                    result.push_str(" \\\\\n");
                } else {
                    result.push('\n');
                }
            }
            result.push_str("\\end{cases}");
            stack.push(LatexItem::Owned(result));
        }

        // ── Boolean atoms ──────────────────────────────────────────
        ExprNode::BoolTrue => stack.push(LatexItem::Lit(r"\text{True}")),
        ExprNode::BoolFalse => stack.push(LatexItem::Lit(r"\text{False}")),

        // ── Relational operators ───────────────────────────────────
        ExprNode::Gt(a, b) => {
            stack.push(LatexItem::Expr(b));
            stack.push(LatexItem::Lit(" > "));
            stack.push(LatexItem::Expr(a));
        }
        ExprNode::Ge(a, b) => {
            stack.push(LatexItem::Expr(b));
            stack.push(LatexItem::Lit(r" \geq "));
            stack.push(LatexItem::Expr(a));
        }
        ExprNode::Eq_(a, b) => {
            stack.push(LatexItem::Expr(b));
            stack.push(LatexItem::Lit(" = "));
            stack.push(LatexItem::Expr(a));
        }
        ExprNode::Ne(a, b) => {
            stack.push(LatexItem::Expr(b));
            stack.push(LatexItem::Lit(r" \neq "));
            stack.push(LatexItem::Expr(a));
        }

        // ── Logical connectives ────────────────────────────────────
        ExprNode::And(ref children) => {
            let children = children.clone();
            for (i, &child) in children.iter().enumerate().rev() {
                stack.push(LatexItem::Expr(child));
                if i > 0 {
                    stack.push(LatexItem::Lit(r" \land "));
                }
            }
        }
        ExprNode::Or(ref children) => {
            let children = children.clone();
            for (i, &child) in children.iter().enumerate().rev() {
                stack.push(LatexItem::Expr(child));
                if i > 0 {
                    stack.push(LatexItem::Lit(r" \lor "));
                }
            }
        }
        ExprNode::Not(x) => {
            stack.push(LatexItem::Expr(x));
            stack.push(LatexItem::Lit(r"\lnot "));
        }

        // ── Set atoms ──────────────────────────────────────────────
        ExprNode::EmptySet => stack.push(LatexItem::Lit(r"\emptyset")),
        ExprNode::UniversalSet => stack.push(LatexItem::Lit(r"\mathbb{R}")),

        // ── Set constructors — fallback to Display ─────────────────
        ExprNode::Interval(a, b, flags) => {
            let left = if flags & crate::base::node::INTERVAL_LEFT_OPEN != 0 {
                "("
            } else {
                "["
            };
            let right = if flags & crate::base::node::INTERVAL_RIGHT_OPEN != 0 {
                ")"
            } else {
                "]"
            };
            let a_latex = latex_to_string(arena, a);
            let b_latex = latex_to_string(arena, b);
            stack.push(LatexItem::Owned(format!(
                "{}{}, {}{}",
                left, a_latex, b_latex, right
            )));
        }

        ExprNode::FiniteSet(ref elems) => {
            let elems = elems.clone();
            stack.push(LatexItem::Lit("\\}"));
            for (i, &elem) in elems.iter().enumerate().rev() {
                stack.push(LatexItem::Expr(elem));
                if i > 0 {
                    stack.push(LatexItem::Lit(", "));
                }
            }
            stack.push(LatexItem::Lit("\\{"));
        }

        ExprNode::SetUnion(ref sets) => {
            let sets = sets.clone();
            for (i, &set) in sets.iter().enumerate().rev() {
                stack.push(LatexItem::Expr(set));
                if i > 0 {
                    stack.push(LatexItem::Lit(r" \cup "));
                }
            }
        }

        ExprNode::SetIntersection(ref sets) => {
            let sets = sets.clone();
            for (i, &set) in sets.iter().enumerate().rev() {
                stack.push(LatexItem::Expr(set));
                if i > 0 {
                    stack.push(LatexItem::Lit(r" \cap "));
                }
            }
        }

        ExprNode::SetComplement(a, b) => {
            stack.push(LatexItem::Expr(b));
            stack.push(LatexItem::Lit(r" \setminus "));
            stack.push(LatexItem::Expr(a));
        }
    }
}

// ═══════════════════════════════════════════════════════════════════════════
// Public API on Expr<S>
// ═══════════════════════════════════════════════════════════════════════════

impl<S: Sort> Expr<S> {
    /// Render this expression as a LaTeX math string (no delimiters).
    ///
    /// Uses direct `ExprNode` matching for robustness.
    ///
    /// # Examples
    ///
    /// ```
    /// use symplex::prelude::*;
    ///
    /// let ctx = Context::new();
    /// let x = ctx.symbol("x");
    /// assert_eq!(x.powi(2).to_latex(), r"x^{2}");
    /// assert_eq!(x.sin().to_latex(), r"\sin\left(x\right)");
    /// ```
    pub fn to_latex(&self) -> String {
        let inner = self.inner.read();
        let w = LatexWriter {
            arena: &inner.arena,
            id: self.raw_id(),
        };
        format!("{}", w)
    }

    /// Render as an inline LaTeX expression with `$` delimiters.
    ///
    /// # Examples
    ///
    /// ```
    /// use symplex::prelude::*;
    ///
    /// let ctx = Context::new();
    /// let x = ctx.symbol("x");
    /// assert_eq!(x.to_latex_inline(), "$x$");
    /// ```
    pub fn to_latex_inline(&self) -> String {
        format!("${}$", self.to_latex())
    }

    /// Render as a display LaTeX expression with `$$` delimiters.
    ///
    /// # Examples
    ///
    /// ```
    /// use symplex::prelude::*;
    ///
    /// let ctx = Context::new();
    /// let x = ctx.symbol("x");
    /// assert_eq!(x.to_latex_display(), "$$x$$");
    /// ```
    pub fn to_latex_display(&self) -> String {
        format!("$${}$$", self.to_latex())
    }
}

// ═══════════════════════════════════════════════════════════════════════════
// Tests
// ═══════════════════════════════════════════════════════════════════════════

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

    // ── Number tests ───────────────────────────────────────────────

    #[test]
    fn latex_integer() {
        assert_eq!(crate::api::context::Context::new().int(42).to_latex(), "42");
    }

    #[test]
    fn latex_zero() {
        assert_eq!(crate::api::context::Context::new().int(0).to_latex(), "0");
    }

    #[test]
    fn latex_negative_integer() {
        let neg = crate::api::context::Context::new().int(-3);
        let latex = neg.to_latex();
        assert!(latex == "-3", "got: {latex}");
    }

    #[test]
    fn latex_fraction() {
        let half = crate::api::context::Context::new().rational(1, 2);
        assert_eq!(half.to_latex(), r"\frac{1}{2}");
    }

    #[test]
    fn latex_negative_fraction() {
        let neg_frac = crate::api::context::Context::new().rational(-5, 7);
        let latex = neg_frac.to_latex();
        assert!(
            latex == r"-\frac{5}{7}" || latex == r"\frac{-5}{7}",
            "got: {latex}"
        );
    }

    // ── Symbol tests ───────────────────────────────────────────────

    #[test]
    fn latex_symbol() {
        assert_eq!(
            crate::api::context::Context::new().symbol("x").to_latex(),
            "x"
        );
    }

    #[test]
    fn latex_symbol_multichar() {
        assert_eq!(
            crate::api::context::Context::new().symbol("foo").to_latex(),
            "foo"
        );
    }

    #[test]
    fn latex_greek_theta() {
        assert_eq!(
            crate::api::context::Context::new()
                .symbol("theta")
                .to_latex(),
            r"\theta"
        );
    }

    #[test]
    fn latex_greek_alpha() {
        assert_eq!(
            crate::api::context::Context::new()
                .symbol("alpha")
                .to_latex(),
            r"\alpha"
        );
    }

    #[test]
    fn latex_greek_omega() {
        assert_eq!(
            crate::api::context::Context::new()
                .symbol("omega")
                .to_latex(),
            r"\omega"
        );
    }

    #[test]
    fn latex_greek_lambda() {
        assert_eq!(
            crate::api::context::Context::new()
                .symbol("lambda")
                .to_latex(),
            r"\lambda"
        );
    }

    #[test]
    fn latex_symbol_subscript() {
        let x1 = crate::api::context::Context::new().symbol("x_1");
        assert_eq!(x1.to_latex(), "x_{1}");
    }

    // ── Constant tests ─────────────────────────────────────────────

    #[test]
    fn latex_pi() {
        assert_eq!(crate::api::context::Context::new().pi().to_latex(), r"\pi");
    }

    #[test]
    fn latex_e() {
        assert_eq!(crate::api::context::Context::new().e().to_latex(), "e");
    }

    #[test]
    fn latex_imaginary() {
        assert_eq!(crate::api::context::Context::new().i_unit().to_latex(), "i");
    }

    #[test]
    fn latex_infinity() {
        assert_eq!(
            crate::api::context::Context::new().infinity().to_latex(),
            r"\infty"
        );
    }

    #[test]
    fn latex_neg_infinity() {
        assert_eq!(
            crate::api::context::Context::new()
                .neg_infinity()
                .to_latex(),
            r"-\infty"
        );
    }

    // ── Pow tests ──────────────────────────────────────────────────

    #[test]
    fn latex_power() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.powi(2);
        assert_eq!(expr.to_latex(), r"x^{2}");
    }

    #[test]
    fn latex_power_cube() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.powi(3);
        assert_eq!(expr.to_latex(), r"x^{3}");
    }

    #[test]
    fn latex_sqrt() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.sqrt();
        assert_eq!(expr.to_latex(), r"\sqrt{x}");
    }

    #[test]
    fn latex_cbrt() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.cbrt();
        assert_eq!(expr.to_latex(), r"\sqrt[3]{x}");
    }

    #[test]
    fn latex_inverse() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.powi(-1);
        let latex = expr.to_latex();
        assert_eq!(latex, r"\frac{1}{x}");
    }

    // ── Neg tests ──────────────────────────────────────────────────

    #[test]
    fn latex_neg_symbol() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = -&x;
        assert_eq!(expr.to_latex(), "-x");
    }

    // ── Add tests ──────────────────────────────────────────────────

    #[test]
    fn latex_add_simple() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = &x + 1;
        let latex = expr.to_latex();
        assert!(latex == "x + 1" || latex == "1 + x", "got: {latex}");
    }

    #[test]
    fn latex_add_power_and_const() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.powi(2) + 1;
        let latex = expr.to_latex();
        assert!(
            latex == r"x^{2} + 1" || latex == r"1 + x^{2}",
            "got: {latex}"
        );
    }

    // ── Mul tests ──────────────────────────────────────────────────

    #[test]
    fn latex_mul_coefficient() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = &x * 2;
        let latex = expr.to_latex();
        assert!(
            latex == "2 x" || latex == "x \\cdot 2" || latex == "2x",
            "got: {latex}"
        );
    }

    // ── Trig function tests ────────────────────────────────────────

    #[test]
    fn latex_sin() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.sin();
        assert_eq!(expr.to_latex(), r"\sin\left(x\right)");
    }

    #[test]
    fn latex_cos() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.cos();
        assert_eq!(expr.to_latex(), r"\cos\left(x\right)");
    }

    #[test]
    fn latex_tan() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.tan();
        assert_eq!(expr.to_latex(), r"\tan\left(x\right)");
    }

    #[test]
    fn latex_sinh() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.sinh();
        assert_eq!(expr.to_latex(), r"\sinh\left(x\right)");
    }

    #[test]
    fn latex_cosh() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.cosh();
        assert_eq!(expr.to_latex(), r"\cosh\left(x\right)");
    }

    // ── Exp/Ln tests ───────────────────────────────────────────────

    #[test]
    fn latex_exp() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.exp();
        assert_eq!(expr.to_latex(), r"\exp\left(x\right)");
    }

    #[test]
    fn latex_ln() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.ln();
        assert_eq!(expr.to_latex(), r"\ln\left(x\right)");
    }

    // ── Abs test ───────────────────────────────────────────────────

    #[test]
    fn latex_abs() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.abs();
        assert_eq!(expr.to_latex(), r"\left|x\right|");
    }

    // ── Inverse trig ───────────────────────────────────────────────

    #[test]
    fn latex_asin() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.asin();
        assert_eq!(expr.to_latex(), r"\arcsin\left(x\right)");
    }

    #[test]
    fn latex_acos() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.acos();
        assert_eq!(expr.to_latex(), r"\arccos\left(x\right)");
    }

    #[test]
    fn latex_atan() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.atan();
        assert_eq!(expr.to_latex(), r"\arctan\left(x\right)");
    }

    // ── Derivative test ────────────────────────────────────────────

    #[test]
    fn latex_derivative() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.powi(2).formal_diff(&x);
        let latex = expr.to_latex();
        assert_eq!(latex, r"\frac{d}{dx} x^{2}");
    }

    // ── Integral test ──────────────────────────────────────────────

    #[test]
    fn latex_integral() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.sin().sin();
        let integral = expr.integrate(&x);
        let latex = integral.to_latex();
        if integral.expr_type() == crate::api::expr::ExprType::Integral {
            assert!(latex.starts_with(r"\int"), "got: {latex}");
            assert!(latex.ends_with(r"\, dx"), "got: {latex}");
        }
        assert!(!latex.is_empty());
    }

    #[test]
    fn latex_definite_integral() {
        let ctx = crate::api::context::Context::new();
        let x = ctx.symbol("x");
        let node = x.sin().definite_integral_node(&x, &ctx.int(0), &ctx.pi());
        assert_eq!(node.to_latex(), r"\int_{0}^{\pi} \sin\left(x\right)\, dx");
    }

    // ── Compound expressions ───────────────────────────────────────

    #[test]
    fn latex_sin_squared() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.sin().powi(2);
        let latex = expr.to_latex();
        assert_eq!(latex, r"\sin^{2}\left(x\right)");
    }

    #[test]
    fn latex_nested_function() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = x.sin().exp();
        let latex = expr.to_latex();
        assert_eq!(latex, r"\exp\left(\sin\left(x\right)\right)");
    }

    // ── Delimiter tests ────────────────────────────────────────────

    #[test]
    fn latex_inline_delimiters() {
        let x = crate::api::context::Context::new().symbol("x");
        assert_eq!(x.to_latex_inline(), "$x$");
    }

    #[test]
    fn latex_display_delimiters() {
        let x = crate::api::context::Context::new().symbol("x");
        assert_eq!(x.to_latex_display(), "$$x$$");
    }

    // ── Boolean / Relational ───────────────────────────────────────

    #[test]
    fn latex_relational_gt() {
        let ctx = crate::api::context::Context::new();
        let x = ctx.symbol("x");
        let y = ctx.symbol("y");
        let expr = x.gt(&y);
        assert_eq!(expr.to_latex(), "x > y");
    }

    #[test]
    fn latex_relational_eq() {
        let ctx = crate::api::context::Context::new();
        let x = ctx.symbol("x");
        let expr = x.eq_expr(&ctx.int(0));
        assert_eq!(expr.to_latex(), "x = 0");
    }

    // ── Deep expression (stack safety) ─────────────────────────────

    #[test]
    fn latex_deep_expression_no_stack_overflow() {
        let x = crate::api::context::Context::new().symbol("x");
        let mut expr = x.clone();
        for _ in 0..1000 {
            expr = expr.sin();
        }
        let latex = expr.to_latex();
        assert!(latex.starts_with(r"\sin\left("));
        assert!(latex.ends_with(r"\right)"));
    }

    // ── Add with subtraction ───────────────────────────────────────

    #[test]
    fn latex_add_with_neg_term() {
        let ctx = crate::api::context::Context::new();
        let x = ctx.symbol("x");
        let y = ctx.symbol("y");
        let expr = &x - &y;
        let latex = expr.to_latex();
        assert!(latex == "x - y" || latex == "-y + x", "got: {latex}");
    }

    // ── Binomial ───────────────────────────────────────────────────

    #[test]
    fn latex_binomial() {
        let ctx = Context::new();
        let n = ctx.symbol("n");
        let k = ctx.symbol("k");
        let expr = n.binomial(&k);
        let latex = expr.to_latex();
        assert_eq!(latex, r"\binom{n}{k}");
    }

    // ── Factorial ──────────────────────────────────────────────────

    #[test]
    fn latex_factorial() {
        let ctx = Context::new();
        let n = ctx.symbol("n");
        let expr = n.factorial();
        let latex = expr.to_latex();
        assert_eq!(latex, "n!");
    }

    // ── Mul coefficient spacing ────────────────────────────────────

    #[test]
    fn latex_coefficient_no_space() {
        let x = crate::api::context::Context::new().symbol("x");
        let expr = &x * 3; // 3*x
        let latex = expr.to_latex();
        // Should be "3x" — no "\cdot" for integer coefficient times variable
        assert!(
            !latex.contains(r"\cdot"),
            "coefficient times variable shouldn't use cdot: {latex}"
        );
    }

    // ── 0.2 nodes ──────────────────────────────────────────────────────────

    #[test]
    fn latex_named_constants() {
        let ctx = crate::api::context::Context::new();
        assert_eq!(ctx.euler_gamma().to_latex(), r"\gamma");
        assert_eq!(ctx.catalan().to_latex(), "G");
        assert_eq!(ctx.golden_ratio().to_latex(), r"\phi");
    }

    #[test]
    fn latex_complex_nodes() {
        let ctx = crate::api::context::Context::new();
        let z = ctx.symbol("z");
        assert_eq!(z.re().to_latex(), r"\Re\left(z\right)");
        assert_eq!(z.im().to_latex(), r"\Im\left(z\right)");
        assert_eq!(z.conjugate().to_latex(), r"\overline{z}");
        assert_eq!(z.arg().to_latex(), r"\arg\left(z\right)");
        let sum = &z + 1;
        assert_eq!(sum.conjugate().to_latex(), r"\overline{z} + 1");
    }

    #[test]
    fn latex_special_functions() {
        let ctx = crate::api::context::Context::new();
        let x = ctx.symbol("x");
        let n = ctx.symbol("n");
        assert_eq!(x.si().to_latex(), r"\operatorname{Si}\left(x\right)");
        assert_eq!(x.ci().to_latex(), r"\operatorname{Ci}\left(x\right)");
        assert_eq!(x.ei().to_latex(), r"\operatorname{Ei}\left(x\right)");
        assert_eq!(x.li().to_latex(), r"\operatorname{li}\left(x\right)");
        assert_eq!(x.zeta().to_latex(), r"\zeta\left(x\right)");
        assert_eq!(x.polygamma(&n).to_latex(), r"\psi^{(n)}\left(x\right)");
        assert_eq!(x.kronecker_delta(&n).to_latex(), r"\delta_{n x}");
    }
}