Module multipoly 

Sparse multivariate polynomials over ℚ. Sparse multivariate polynomials over ℚ.

MultiPoly represents polynomials in multiple variables with exact rational coefficients. Monomials are stored sparsely as (exponent_vector, coefficient) pairs.

This module provides:

• Polynomial arithmetic (+, -, ×)
• Degree computation
• Evaluation
• Partial derivatives
• Variable substitution
• Multivariate polynomial division
• S-polynomials for Gröbner basis computation

The monomial ordering is parameterized via the MonomialOrd trait, enabling graded reverse lex (default), lex, and graded lex orderings.

Structs

GrLex

Graded lexicographic ordering.

GrevLex

Graded reverse lexicographic ordering (default for Gröbner computation).

Lex

Pure lexicographic ordering (for elimination/back-substitution).

MonoKey

A monomial exponent vector with ordering determined by type parameter O.

MultiPoly

A sparse multivariate polynomial over ℚ.

Enums

MonomialOrder

A monomial order chosen at run time — the value-level counterpart of the zero-sized order types Lex and GrevLex, for APIs that take the order as an argument (Ex::groebner, Ex::reduce_modulo).

Traits

MonomialOrd

Trait for monomial orderings. Implemented by zero-sized types.

Functions

monomial_coprime

Check if two monomials are coprime (no shared variable).

monomial_div

Divide monomial b by a (component-wise subtraction). Returns None if a doesn’t divide b.

monomial_divides

Check if monomial a divides monomial b (component-wise ≤).

monomial_lcm

Component-wise maximum of two exponent vectors (LCM of monomials).

monomial_mul

Multiply two monomials (component-wise addition).

multipoly_vars

Create variable polynomials for a ring with the given number of variables.

s_polynomial

Compute the S-polynomial of f and g.

Type Aliases

Exponent

An exponent vector representing a monomial x₀^a · x₁^b · x₂^c · … as [a, b, c, …]. The length equals the number of variables.