# What's New in 0.9 and 0.10
symplex 0.9.0 is a **comprehensiveness** release — additive over 0.8.2 — driven by a module-by-module survey of the crate against SymPy 1.14. Four areas got a first thorough pass; every new function is tested against reference values from that SymPy. The [CHANGELOG](https://github.com/cgorski/symplex/blob/main/CHANGELOG.md) has the full list.
## Algebraic numbers and polynomial algebra
`Ex::minimal_polynomial(&x)` gives the minimal polynomial over ℚ of an algebraic-number expression (`√2 + √3` → `x⁴ − 10x² + 1`), `gcd_all`/`lcm_all` are the variable-free multivariate gcd and lcm, `Ex::groebner(&polys, &vars, MonomialOrder::Lex)` and `reduce_modulo` expose Gröbner bases and normal forms without the `MultiPoly` dance, `real_roots(&x)` returns the real roots of a rational polynomial as exact `RootOf`s in increasing order, `factor_mod(&x, p)` factors over GF(p), and `resultant_symbolic`/`discriminant_symbolic` handle polynomials whose other coefficients are symbols (`disc(ax² + bx + c) = b² − 4ac`).
## Special functions
Twenty-four functions that appear as integration results or in physics: `erfi`, `erfinv`, `erfcinv`, `expint`/`E1`, `Shi`, `Chi`, `fresnels`, `fresnelc`, `lowergamma`, `uppergamma`, `polylog`, `dirichlet_eta`, the Airy functions and their derivatives, complete and incomplete elliptic integrals (`elliptic_k/e/f/pi`), and the Gegenbauer, Jacobi, associated Legendre and associated Laguerre polynomials. Each has exact special values, a derivative rule, arbitrary-precision `evalf` (checked at 40 digits against mpmath on every branch — series, asymptotic, continued fraction, reflection), `Display`, LaTeX and `parse` support. `integrate` now reaches `∫e^{x²} = (√π/2)·erfi(x)`, `∫sinh(x)/x = Shi(x)`, `∫cosh(x)/x = Chi(x)`.
## Analysing a function
SymPy's `calculus.util` on `Ex`: `singularities`, `stationary_points`, `maximum`/`minimum` on unions of intervals (with one-sided limits at open or infinite endpoints), `is_increasing`/`is_decreasing`/`is_monotonic`/`is_convex` (exact for polynomial and rational derivatives via Sturm sequences; three-valued, never a guess), `periodicity` and `function_range`.
## Matrices
`singular_values`, `condition_number`, a `pinv` that is now defined for every matrix (rank-deficient inputs go through the full-rank factorisation), `rank_decomposition`, `hessenberg`, `companion`, `jordan_block`, `permanent`, row/column insertion, deletion and permutation, `inv_mod`, `matrix_log`, `casoratian`, and an exact `lll` lattice reduction on `ZMatrix` with rational Gram–Schmidt.
## 0.10.0 — budgets, and the rest of the survey
0.10.0 answers a downstream generator's request for **a budget on a single prover call**: `PolyhedronOpts::default().with_time_limit(Duration::from_secs(150))` (or `with_deadline` / `with_max_pivots`) makes a `PolyhedronProver::prove` return `Unknown` — with `budget_exhausted: Some(BudgetHit::Deadline | MaxPivots)` and a `Display` that says so — instead of running on; the deadline is checked at every simplex pivot, across all stages and the `i64 → i128 → BigInt` arithmetic fallback, so a 50 ms limit returns at 50 ms. The same `Budget` is available directly on `LpProblem::with_budget` (status `LpStatus::BudgetExhausted`) and, as a time limit, on `SosOpts`. `prove_poly` now accepts goals carrying unused generators.
The comprehensiveness pass continues: `ntheory` gains `nthroot_mod` for any modulus, `polynomial_congruence`, `quadratic_residues`, `primorial`, `is_carmichael` and friends; a new `discrete` module has exact convolutions, the number-theoretic transform, Walsh–Hadamard and Möbius transforms; `Context::parse_bool` parses relations and Boolean connectives and `parse_implicit` accepts `sin x`/`2 sin x`; and expressions render to Presentation MathML (`to_mathml`), `srepr`/DOT (`to_srepr`, `to_dot`) and executable Python/NumPy/Julia (`to_python`, `to_numpy`, `to_julia`, with `_fn` variants sharing the CSE pass). Two small breaking changes in fresh 0.8 API — `Tactic::Apply`, `Decl.preamble` (use `Decl::new` + builders) — and `LpStatus::BudgetExhausted` are listed first in the CHANGELOG.