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 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 RootOfs 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.