import { type NumberOps } from "./number-ops";
import { BisectOptions } from "./roots";
export declare enum EvalMethod {
    NORMAL = "normal",
    HORNER = "horner"
}
/**
 * A polynomial instance.
 *
 *     import {Polynomial} from "@erosson/polynomial"
 *     const p = Polynomial.parse([3,2,1])
 *     p.toString()  // "t^2 + 2t + 3"
 */
export declare class Polynomial<T = number> {
    coeffs: readonly T[];
    ops: NumberOps<T>;
    /**
     * @param coeffs The polynomial's coefficients. `coeffs[0]` is the constant term; `coeffs` of `[3,2,1]` are the polynomial `t^2 + 2 t + 3`
     * @param ops Fundamental operations for this polynomial's number type. Used to implement polynomials for {@link https://mikemcl.github.io/decimal.js/ | Decimal.js} or other non-builtin number types. If you're using the builtin number type, feel free to ignore it.
     */
    private constructor();
    /**
     * Given a list of numbers, create a polynomial. The numbers are the polynomial's coefficients.
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *     const p = Polynomial.parse([1,2,3])
     *     p.toString()  // "3 t^2 + 2 t + 1"
     *
     * @group constructors
     */
    static parse(coeffs: readonly number[]): Polynomial<number>;
    /**
     * Given a list of numbers and a `NumberOps`, create a polynomial. The numbers are the polynomial's coefficients.
     *
     *     import {Polynomial, decimalNumberOps} from "@erosson/polynomial"
     *     import Decimal from "decimal.js"
     *     const p = Polynomial.parse([new Decimal(1), new Decimal(2), new Decimal(3)], decimalNumberOps(Decimal))
     *     p.toString()  // "3 t^2 + 2 t + 1"
     *
     * @group constructors
     */
    static parse<T>(coeffs: readonly T[], ops: NumberOps<T>): Polynomial<T>;
    /**
     * The constant-term polynomial zero. Equivalent to `Polynomial.parse(0)`.
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *     Polynomial.zero().toString()  // "0"
     *
     * @group constructors
     */
    static zero(): Polynomial<number>;
    /**
     * The constant-term polynomial zero. Equivalent to `Polynomial.parse(0)`.
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *     Polynomial.zero(decimalNumberOps(Decimal)).toString()  // "0"
     *
     * @group constructors
     */
    static zero<T>(ops: NumberOps<T>): Polynomial<T>;
    /**
     * Return the *degree* of this polynomial - the value of its highest exponent.
     *
     * https://en.wikipedia.org/wiki/Degree_of_a_polynomial
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *     Polynomial.parse([1,2,3]).degree  // 2
     *     Polynomial.parse([9,8,7,6]).degree  // 3
     *     Polynomial.parse([9,8,7,6]).degree  // 3
     *     Polynomial.zero().degree  // 0
     */
    get degree(): number;
    /**
     * Is this polynomial a constant? That is, is its degree equal to zero?
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *     Polynomial.parse([1,2,3]).isConstant  // false
     *     Polynomial.parse([1]).isConstant  // true
     *     Polynomial.zero().isConstant  // true
     */
    get isConstant(): boolean;
    /**
     * Return this polynomial's constant term.
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *     Polynomial.parse([1,2,3]).constantTerm  // 1
     *     Polynomial.parse([1]).constantTerm  // 1
     *     Polynomial.parse([9,8,7,6]).constantTerm  // 9
     *     Polynomial.zero().constantTerm  // 0
     */
    get constantTerm(): T;
    /**
     * Evaluate the polynomial at the given point.
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *     Polynomial.parse([3,2]).evaluate(0)  // 3
     *     Polynomial.parse([3,2]).evaluate(1)  // 5
     *     Polynomial.parse([3,2]).evaluate(2)  // 7
     *     Polynomial.parse([3,2,1]).evaluate(0)  // 3
     *     Polynomial.parse([3,2,1]).evaluate(1)  // 6
     *     Polynomial.parse([3,2,1]).evaluate(2)  // 11
     *
     * @group evaluate
     */
    evaluate(seconds: number, evalMethod?: EvalMethod): T;
    /**
     * Evaluate the polynomial at the given point, with the given degree.
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *     Polynomial.parse([3,2,1]).evaluateDegree(2, 0)  // 11 = 3 + 2*2 + 1*(2^2)
     *     Polynomial.parse([3,2,1]).evaluateDegree(2, 1)  // 6 = 2*2 + 1*(2^2)
     *     Polynomial.parse([3,2,1]).evaluateDegree(2, 2)  // 2 = 1*(2^2)
     *
     * @group evaluate
     */
    evaluateDegree(seconds: number, degree: number, evalMethod?: EvalMethod): T;
    /**
     * Add two polynomials.
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *     Polynomial.parse([3,2,1]).add(Polynomial.parse([1,2,3]))  // [4,4,4]
     *     Polynomial.parse([3,2,1]).add(Polynomial.parse([5]))  // [8,2,1]
     *     Polynomial.parse([3,2,1]).add(Polynomial.zero())  // [3,2,1]
     *
     * @group transforms
     */
    add(b: Polynomial<T>): Polynomial<T>;
    /**
     * Add a polynomial and some polynomial coefficients.
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *     Polynomial.parse([3,2,1]).add([1,2,3])  // [4,4,4]
     *     Polynomial.parse([3,2,1]).add([5])  // [8,2,1]
     *     Polynomial.parse([3,2,1]).add([])  // [3,2,1]
     *
     * @group transforms
     */
    addCoeffs(b: readonly T[]): Polynomial<T>;
    /**
     * Add a list of polynomials.
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *     Polynomial.parse([3,2,1]).sum([Polynomial.parse([1,2,3]), Polynomial.parse([1,1,1])])  // [5,5,5]
     *
     * See also {@link sums}
     *
     * @group transforms
     */
    sum(bs: readonly Polynomial<T>[]): Polynomial<T>;
    /**
     * Add a list of polynomials.
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *     Polynomial.sums([Polynomial.parse([1,2,3]), Polynomial.parse([1,1,1])])  // [5,5,5]
     *     Polynomial.sums([])  // throws error
     *
     * @group transforms
     */
    static sums<T>(ps: readonly Polynomial<T>[]): Polynomial<T>;
    /**
     * Add a list of polynomial-coefficients.
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *     Polynomial.parse([3,2,1]).sumCoeffs([[1,2,3], [1,1,1]])  // [5,5,5]
     *     Polynomial.parse([3,2,1]).sumCoeffs([])  // [3,2,1]
     *
     * @group transforms
     */
    sumCoeffs(bs: readonly (readonly T[])[]): Polynomial<T>;
    /**
     * Multiply a polynomial by a scalar.
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *     Polynomial.parse([3,2,1]).mul(5)  // [15,10,5]
     *     Polynomial.parse([3,2,1]).mul(0)  // [0]
     *
     * @group transforms
     */
    mul(c: number): Polynomial<T>;
    /**
     * Multiply a polynomial by a scalar. Similar to `mul`, but this one supports uses the same number format as your polynomial.
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *     Polynomial.parse([3,2,1]).mulT(5)  // [15,10,5]
     *     Polynomial.parse([3,2,1]).mulT(0)  // [0]
     *
     * @group transforms
     */
    mulT(c: T): Polynomial<T>;
    /**
     * True if the given value is a root of this polynomial - that is, if `evaluate(t) === 0` for this t.
     *
     * @param tolerance floating point imprecision allowed for this to return true
     *
     * @group roots
     */
    isRoot(t: number, tolerance?: number): boolean;
    /**
     * Will `{@link findRootsQuick}` work for this polynomial?
     *
     * True if degree 3 or less, or (trivially) if the constant term is zero.
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *     Polynomial.parse([-3,2,1]).isRootQuick  // true
     *     Polynomial.parse([-64,0,0,1]).isRootQuick  // true
     *     Polynomial.parse([-5,4,3,2,1]).isRootQuick  // false
     *     Polynomial.parse([0]).isRootQuick  // true
     *     Polynomial.parse([1]).isRootQuick  // true
     *
     * @group roots
     */
    get isRootQuick(): boolean;
    /**
     * Try to find at least one root of this polynomial - that is, the values of `t` where `evaluate(t) === 0`.
     *
     * For polynomials with degree <= 3, we use exact formulas to find one. For larger polynomials, we use an iterative method, which will be slower and less accurate.
     *
     * @todo polynomials with degree >= 4 not yet implemented, throw an error
     *
     * https://en.wikipedia.org/wiki/Polynomial_root-finding_algorithms
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *     Polynomial.parse([-3,2,1]).findRootsQuick()  // Set([1,-3])
     *     Polynomial.parse([-64,0,0,1]).findRootsQuick()  // Set([4])
     *     Polynomial.parse([-5,4,3,2,1]).findRootsQuick()  // throws Error - degree too high; isRootQuick was false
     *     Polynomial.parse([0]).findRootsQuick()  // Set([0])
     *     Polynomial.parse([1]).findRootsQuick()  // Set([])
     *
     * @group roots
     */
    findRootsQuick(): ReadonlySet<number>;
    /**
     * Does this polynomial start negative, grow continuously, and eventually become non-negative?
     *
     * - is the constant term `coeffs[0]` negative?
     * - are all non-constant terms `coeffs[1..]` non-negative?
     *
     * That is, does it look like:
     *
     *     -p0 + p1 t + p2 t^2 + p3 t^3 + ...
     *
     * If so, we can bisect it to approximate a root.
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *     Polynomial.parse([-3,2,1]).isRootBisectable  // true
     *     Polynomial.parse([-64,0,0,1]).isRootBisectable  // true
     *     Polynomial.parse([-5,4,3,2,1]).isRootBisectable  // false
     *     Polynomial.parse([0]).isRootBisectable  // false
     *     Polynomial.parse([1]).isRootBisectable  // false
     *
     * @group roots
     */
    get isRootBisectable(): boolean;
    /**
     * Try to approximate exactly one root of this polynomial - that is, the values of `t` where `evaluate(t) === 0`.
     *
     * This uses bisection, which is slower than some other methods. Also, it only works for {@link isRootBisectable | bisectable polynomials}. Also, it's an approximation, not an exact result.
     *
     * You should prefer {@link findRootsQuick} when possible.
     *
     * https://en.wikipedia.org/wiki/Bisection_method#Algorithm
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *     Polynomial.parse([-3,2,1]).findRootBisect()  // 0.999999...
     *     Polynomial.parse([-64,0,0,1]).findRootBisect()  // 3.99999...
     *     Polynomial.parse([-256,0,0,0,1]).findRootBisect()  // 3.99999...
     *     Polynomial.parse([0]).findRootBisect()  // error: not bisectable
     *     Polynomial.parse([1]).isRootBisectable  // error: not bisectable
     *     Polynomial.parse([-1]).isRootBisectable  // error: not bisectable
     *
     * @group roots
     */
    findRootBisect(opts?: BisectOptions): number;
    /**
     * Transform a polynomial to a list of `[formatted-coefficient, degree]`, suitable for string formatting.
     * You could use this to implement an HTML representation, for example.
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *
     *     Polynomial.parse([3,2,1]).format()  // [["",2],["2 ",1],["3 ",0]]
     *     Polynomial.parse([3,2,1]).toString()  // "t^2 + 2 t + 3"
     *
     *     Polynomial.parse([3,0,1]).format()  // [["",2],["0 ",1],["3 ",0]]
     *     Polynomial.parse([3,0,1]).toString()  // "t^2 + 0 t + 3"
     *
     * @group rendering
     */
    format(): readonly (readonly [string, number])[];
    /**
     * Transform a polynomial to a list of `[formatted-coefficient, degree]`, suitable for string formatting.
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *
     *     Polynomial.parse([3,2,1]).formats()  // ["t^2", "2 t", "3"]
     *     Polynomial.parse([3,2,1]).toString()  // "t^2 + 2 t + 3"
     *
     *     Polynomial.parse([3,0,1]).formats()  // ["t^2", "0 t", "3"]
     *     Polynomial.parse([3,0,1]).toString()  // "t^2 + 0 t + 3"
     *
     * @group rendering
     */
    formats(): string[];
    /**
     * Render a polynomial as a string.
     *
     * If you need custom formatting, start with {@link format} instead.
     *
     *     import {Polynomial} from "@erosson/polynomial"
     *     Polynomial.parse([3,2,1]).toString()  // "t^2 + 2 t + 3"
     *     Polynomial.parse([3,0,1]).toString()  // "t^2 + 0 t + 3"
     *
     * @group rendering
     */
    toString(): string;
}