import { scalar } from "./core";
export declare class Monomial extends Array<number> {
    constructor(...v: number[]);
    key(): string;
    map<T>(f: (e: number, i: number, array: Monomial) => T): T[];
    degree(): number;
    without(v: number): Monomial;
    divides(b: Monomial): boolean;
    div(a: Monomial): Monomial | undefined;
    mul(a: Monomial): Monomial;
    static lcm(a: Monomial, b: Monomial): Monomial;
    eq(a: Monomial): boolean;
    toString(): string;
}
type Compare = (a: Monomial, b: Monomial) => number;
declare function compareGrevlex(a: Monomial, b: Monomial): number;
export declare function lexOrder(a: Monomial, b: Monomial): number;
export interface MVTerm<T> {
    coef: T;
    mon: Monomial;
}
export declare class MVPoly<T extends scalar<T>> {
    terms: MVTerm<T>[];
    constructor(terms?: MVTerm<T>[]);
    dup(): MVPoly<T>;
    isZero(): boolean;
    eq(b: MVPoly<T>): boolean;
    sort(ordering: Compare): void;
    contains(v: number): boolean;
    collect(v: number): MVPoly<T>[];
    addTerm(mon: Monomial, coef: T): void;
    leadingTerm(ordering: Compare): MVTerm<T>;
    mulMono(m: Monomial): MVPoly<T>;
    add(b: MVPoly<T>): MVPoly<T>;
    sub(b: MVPoly<T>): MVPoly<T>;
    divCoef(coef: T): MVPoly<T>;
    mulCoef(coef: T): MVPoly<T>;
    mulPoly(b: MVPoly<T>): MVPoly<T>;
    divPoly(divisors: MVPoly<T>[], ordering: Compare): MVTerm<T>[][];
    toString(): string;
}
export declare function groebnerBasis<T extends scalar<T>>(G: MVPoly<T>[], ordering?: typeof compareGrevlex): MVPoly<T>[];
export {};