simsym 0.1.0

A simple symbolic computation library.
Documentation

simsym

A simple symbolic computation library for Rust, with exact rational arithmetic.

Quick start

use simsym::prelude::*;

let x = symbol("x");
let y = symbol("y");

// Operators
let f = x.pow(2) + rational(2, 1) * x * y + sin(y);

// Macro DSL
let g = expr!(x^2 + 2*x*y + sin(y));

let df_dx = f.clone().diff(x);
let grad = f.gradient(&[x, y]);

let exact = f.eval(&[(x, rational(1, 2)), (y, rational(1, 3))])?;
let approx = f.eval_f64(&[(x, 0.5), (y, 1.0 / 3.0)])?;
let approx32 = f.eval_f32(&[(x, 0.5f32)])?;

let F = f.integrate(x)?; // symbolic when a rule applies
let area = f.integrate_definite(x, rational(0, 1), rational(1, 1), &[])?;

// Numeric fallback
let num = integrate_numeric(&sin(x), x, 0.0, std::f64::consts::PI, &[], NumericOptions::default())?;

Features

  • Expression AST with + - * / ^, full circular & hyperbolic trig (sin…acsch), plus exp, ln
  • Exact Rational constants (i64 ratios); From/TryFrom for all integer primitives and f32/f64
  • Simplification (algebraic folding, some like-term merging)
  • Partial derivatives and gradients / Hessians
  • Symbolic integration for polynomials and common elementary forms
  • Definite integrals (symbolic antiderivative or adaptive Simpson)
  • expr! procedural macro

Limitations

Symbolic integration is rule-based (polynomials, affine trig/exp, e^x×P, parts, sin^n/cos^n reduction, partial fractions for low-degree P/Q including atan terms, sin·cos products, etc.) — not a full Risch algorithm. See docs/INTEGRATION.md for the algorithm stack. When integrate returns IntegrateError::NoRule, use integrate_numeric or integrate_definite (which falls back automatically).

Transcendental functions are not supported in exact eval; use eval_f64 or eval_f32.

Examples

cargo run --example calculus
cargo run --example multivar
cargo run --example numeric_integral

Optional features

Cargo features (enabled by default):

Feature Enables
simplify Expr::simplify
diff Expr::diff, gradient, hessian
integrate Expr::integrate, integrate_definite (implies diff)

Minimal build (AST + rationals + evaluation only):

cargo build --no-default-features

Other optional features: