Crate ocas 

oCAS — open Computer Algebra System.

This crate is the top-level Rust API for oCAS. It re-exports the public items from the lower-level crates so that most users only need one import:

use ocas::prelude::*;

Backends (GMP, MPFR, FLINT, LLVM, Python, GPL) are opt-in via feature flags to keep the default build portable, including on Windows MSVC where GMP is not readily available.

Modules

normalize

Normalization for Atom expression trees.

prelude

Convenience prelude that brings commonly used oCAS types and functions into scope.

simplify

Rule-based simplification for oCAS.

Structs

Arena

A bump-allocated region of memory.

Assumptions

A set of assumptions about a symbolic variable.

Atom

A reference to an expression node allocated in an arena.

AtomArena

A context that allocates Atoms in an Arena.

Bindings

A collection of wildcard bindings produced by a successful match.

Complex

A complex number whose real and imaginary parts live in a base domain.

ComplexDomain

The complex domain over a base domain D.

DenseUnivariatePolynomial

A dense univariate polynomial with coefficients in a domain D.

DiophantineSolution

A solution to a linear Diophantine equation ax + by = c.

ExpressionEvaluator

A compiled expression ready for numeric evaluation.

FiniteField

A prime finite field $\mathbb{Z}/p\mathbb{Z}$.

FiniteFieldElement

An element of a prime finite field.

FunctionMap

A map of named functions that can be called during evaluation.

Grevlex

Graded reverse lexicographic ordering: first by total degree descending, then reverse lexicographic.

GroebnerBasis

A Gröbner basis for a polynomial ideal.

Integer

Arbitrary-precision integer backed by num-bigint.

IntegerDomain

The integer domain.

Lex

Lexicographic ordering: compare exponents left-to-right.

Matrix

A dense matrix with elements from a EuclideanDomain.

Rational

Arbitrary-precision rational number backed by num-rational.

RationalDomain

The rational number domain.

RationalPolynomial

A rational polynomial $\frac{\text{num}}{\text{den}}$ over a domain D.

RealBall

A real ball: midpoint with radius.

RealBallDomain

The real ball domain.

RootInterval

A real interval known to contain exactly one root.

Rule

A rewrite rule.

SparseMultivariatePolynomial

A sparse multivariate polynomial with coefficients in a domain D and monomial ordering O.

Symbol

An interned symbolic name (variable, function, or constant).

SymbolAssumptions

A mapping from symbol names to their domain and assumptions.

Enums

Assumption

A single predicate that can be asserted about a symbolic variable.

AtomNode

The concrete data stored for each expression node.

EvalTree

An owned intermediate representation of a symbolic expression.

EvaluationError

Errors that can occur during expression evaluation.

Instr

An internal, index-based instruction executed by super::ExpressionEvaluator.

Instruction

A public, self-documenting instruction.

MatchError

Errors that can occur during matching.

MatrixError

Errors that can occur during matrix operations.

OcasError

The primary error type returned by oCAS operations.

ParseError

Errors that can occur while parsing an expression.

Pattern

A pattern that can be matched against an Atom.

Slot

A named slot in the evaluator stack.

SolveError

Errors that can occur when solving equations.

WildcardLevel

The scope of a wildcard match.

Traits

Domain

A coefficient domain for generic computer-algebra routines.

EuclideanDomain

Marker trait for domains that support exact division with remainder.

EvaluationDomain

Trait for types that can serve as evaluation domains.

MonomialOrder

A monomial ordering determines how terms are sorted and compared.

PowfExtension

Extension to EvaluationDomain for floating-point exponentiation.

Functions

apart

Perform partial fraction decomposition of num / den.

buchberger

Convenience: compute a Gröbner basis and inter-reduce it.

diff

Differentiate expr with respect to var.

integrate

Integrate expr with respect to var.

match_pattern

Match a pattern against an atom, returning bindings on success.

monomial_are_coprime

Return true if the two monomials are coprime (no variable appears in both).

monomial_divides

Check whether monomial a divides monomial b: a[i] >= b[i] for all i.

monomial_lcm

Compute the least common multiple of two monomials: element-wise max.

parse

Parse an expression string into an Atom.

simplify

Simplify an atom using the supplied rewrite rules.

solve_diophantine

Solve the linear Diophantine equation a*x + b*y = c.

solve_linear_integer

Solve a linear system of equations over the integers.

solve_linear_rational

Solve a linear system of equations over the rational numbers.

solve_polynomial_system

Solve a system of polynomial equations using Gröbner bases.

substitute

Replace every occurrence of var inside expr with replacement.

taylor

Compute the Taylor expansion of expr around point with respect to var, up to the given order (inclusive).

transform

Type Aliases

Result

A convenient result type for oCAS operations.