Crate numerica 

Numerica is an open-source mathematics library for Rust, that provides high-performance number types, such as error-tracking floats and finite field elements.

It provides

• Abstractions over rings, Euclidean domains, fields and floats
• High-performance Integer with automatic up-and-downgrading to arbitrary precision types
• Rational numbers with reconstruction algorithms
• Fast finite field arithmetic
• Error-tracking floating point types
• Generic dual numbers for automatic differentiation
• Matrix operations and linear system solving
• Numerical integration using Vegas algorithm with discrete layer support

For operations on symbols, check out the sister project Symbolica.

Example

Solve a linear system over the rationals:

let a = Matrix::from_linear(
    vec![
        1.into(), 2.into(), 3.into(),
        4.into(), 5.into(), 16.into(),
        7.into(), 8.into(), 9.into(),
    ],
    3, 3, Q,
)
.unwrap();

let b = Matrix::from_linear(vec![1.into(), 2.into(), 3.into()], 3, 1, Q).unwrap();

let r = a.solve(&b).unwrap();
assert_eq!(r.into_vec(), [(-1, 3), (2, 3), (0, 1)]);

Solution: $(-1/3, 2/3, 0)$.

Modules

combinatorics

Provides combinatorial utilities for generating combinations, permutations, and partitions of sets.

domains

Defines core algebraic traits and data structures.

numerical_integration

Methods for numerical integration of black-box functions.

printer

Methods for printing rings.

tensors

Methods for tensor manipulation and linear algebra.

utils

Utility traits and structures.

Macros

create_hyperdual_from_components

Create a new hyperdual number, from a specification of the components. The first components must be the real value and the single derivatives of the variables in order.

create_hyperdual_from_depths

Create a new hyperdual number, with a given derivative depth per variable.

create_hyperdual_single_derivative

Create a new hyperdual number, with only single derivatives and with $var variables.