What’s New in 0.2

symplex 0.2.0 is a large release. This page is the tour; the complete list — including every breaking change and its replacement — is in the CHANGELOG, and the migration guide walks through the code changes you will need.

The theme of the release is never silently wrong. Several 0.1 operations guessed (∫₋₁¹ dx/x² = −2, re(z) = z, solve(x − x) = []); in 0.2 they return an Err, an unevaluated node, or None.

By the numbers

Measured on the release commit:

Complex analysis

New Re, Im, Conjugate, Arg nodes and Ex::{re, im, conjugate, arg, as_real_imag, expand_complex, polar, abs_squared, is_real_valued}. Conjugation distributes over sums, products and integer powers and commutes with real-analytic functions; realness is decided by the assumption system, never assumed. New constants EulerGamma, Catalan, GoldenRatio, and complex infinity (zoo, the value of 1/0).

→ Complex Analysis and Special Functions

Definite, improper and numeric integration

integrate_definite / try_integrate_definite detect interior singularities, handle infinite bounds and endpoint singularities via one-sided limits, exploit symmetry, integrate Abs/Heaviside/DiracDelta/Piecewise, and consult a ~30-entry table of improper integrals (with symbolic parameters under assumptions). integrate_numeric is adaptive Gauss–Kronrod. Residues work at poles of any order and at infinity.

→ Definite Integration and Quadrature

Summation, products and series

summation, product_over, hypergeometric_ratio, is_convergent, series_at_infinity, and an Ex-based FormalPowerSeries with lazy exact coefficients, closed-form general terms, arithmetic, composition, inversion and reversion.

→ Summation and Series

Solving

solve reports identities as Err(InfiniteSolutions) and contradictions/range violations as Err(NoSolution). solve_general returns periodic families with an integer parameter. linsolve returns Unique/Parametric/Inconsistent. Polynomial systems return algebraic solutions. solve_numeric_system is a damped Newton method. ODEs gained nth-order constant-coefficient, Clairaut and Riccati classes, initial-value problems (solve_ode_ivp) and system IVPs. rsolve_linear solves linear recurrences.

→ Solving Equations

Sets and logic

SetEx has a normal form (simplify), set algebra (difference, symmetric_difference, absolute_complement), three-valued queries (contains, is_subset, is_disjoint, is_empty), topology (boundary, closure, interior), and conversion to conditions. BoolEx has to_nnf/to_cnf/to_dnf, is_tautology, satisfiable, truth_table, and eval folds relations through assumptions. reduce_inequalities turns a conjunction of conditions into a set.

→ Sets and Logic

The rule engine is public

Rule, RuleSet, Bindings, RewriteOpts, Step; Ex::{rewrite, rewrite_once, rewrite_traced, rewrite_with, simplify_with_rules, simplify_traced}; AC matching with rest__ sequence wildcards; rule! macro rules via RuleSet::from_macro_rules. Plus new targeted simplifiers: sqrtdenest, signsimp, powdenest(force), expand_with(ExpandOpts), nsimplify, rcollect, subs_algebraic.

→ The Rule Engine

Matrices

The eigen family (eigenvals, eigenvects, diagonalize, jordan_form, matrix_exp) no longer takes a dummy variable. Irreducible cubic/quartic characteristic polynomials give exact, evaluable RootOf eigenvalues instead of Cardano swell. New: qr, ldl, gram_schmidt, matrix_exp_t, matrix_pow_symbolic, matrix_sqrt, hessian, wronskian, structure tests, norms, least squares, Index/IndexMut, scalar operators on both sides.

→ Matrices

Transforms

One-sided limits (limit_left/limit_right/limit_dir), Fourier transforms in three conventions, Mellin transforms with their fundamental strip, Laplace table/inverse extensions and initial/final-value theorems, Fourier series on arbitrary intervals with exact coefficients, Z-transform extensions.

→ Transforms

Number theory and factoring

Berlekamp–Zassenhaus factoring for any degree, multivariate factoring, a polynomial-algebra API on Ex (resultant, discriminant, sqf_list, poly_div, poly_gcdex, nroots, real_roots_isolate, …), factorint with Pollard–Brent rho + ECM, BPSW isprime, sqrt_mod, discrete_log, primitive_root, primepi, continued fractions, Egyptian fractions, Pell equations, sums of squares, Pythagorean triples, and integer sequences.

→ Number Theory and Combinatorics

Code generation

compile() returns Result<CompiledFn> and covers every numerically evaluable node; compile_many shares CSE across a gradient. to_rust_fn embeds only the special-function helpers it needs. New C99 backend (to_c_fn). CodegenOptions::{use_mul_add, checked_domain, emit_runtime} and runtime_module()/c_runtime() for multi-function files.

→ Code Generation

Ergonomics

Context::{from_f64, from_f64_approx, from_f64_nice, from_bigint, from_ratio, from_i128, rational_str, decimal_str, complex, symbols, symbols_indexed, apply, sum, product}; operators with f64/i32/u64/i128/BigInt/Ratio and compound assignment; Ex::{as_rational, as_bigint, as_i64, compare_numeric, is_less_than, probably_equal, eval_at}; Equation arithmetic and solve_for; Debug for Ex prints the expression.

Companion crates

• symplex-wasm: a persistent Session (define names, evaluate, differentiate, solve) plus a full stateless API including integrate_definite and to_c_fn.
• symplex-build: exact DH parameters (0.3 → 3/10), generate_fk_matrix, "fk_matrix" in TOML configs.