/* 0.26.0-alpha2 */
/**
 *
 * ## THEORY OF OPERATIONS
 *
 * A numeric value represents a number literal.
 *
 * It is defined as a functional field over the complex numbers.
 *
 * It includes basic arithmetic operations: addition, subtraction,
 * multiplication, power, division, negation, inversion, square root.
 *
 * Several flavors of numeric values are available:
 * - `NumericValue` is the base class for all numeric values.
 * - `ExactNumericValue` is a numeric value that represents numbers as the
 *    sum of an imaginary number and the product of a rational and a radical
 *    (square root of a integer).
 * - `BigNumericValue` is a numeric value that represents numbers as the
 *   sum of an imaginary number and a decimal (arbitrary precision) number.
 *
 * An exact numeric value may need to be converted to a float one, for
 *   example when calculating the square root of a square root.
 *
 * A float numeric value is never converted to an exact one.
 *
 */
import Decimal from 'decimal.js';
import { SmallInteger } from '../numerics/numeric';
import { Rational } from '../numerics/rationals';
import { NumericType } from '../../common/type/types';
/** The value is equal to `(decimal * rational * sqrt(radical)) + im * i` */
export type ExactNumericValueData = {
    rational?: Rational;
    radical?: number;
};
export type NumericValueData = {
    re?: Decimal | number;
    im?: number;
};
export type NumericValueFactory = (data: number | Decimal | NumericValueData) => NumericValue;
export declare abstract class NumericValue {
    abstract get type(): NumericType;
    /** True if numeric value is the product of a rational and the square root of an integer.
     *
     * This includes: 3/4√5, -2, √2, etc...
     *
     * But it doesn't include 0.5, 3.141592, etc...
     *
     */
    abstract get isExact(): boolean;
    /** If `isExact()`, returns an ExactNumericValue, otherwise returns undefined.
     */
    abstract get asExact(): NumericValue | undefined;
    /** The real part of this numeric value.
     *
     * Can be negative, 0 or positive.
     */
    abstract get re(): number;
    /**  bignum version of .re, if available */
    get bignumRe(): Decimal | undefined;
    /** The imaginary part of this numeric value.
     *
     * Can be negative, zero or positive.
     */
    readonly im: number;
    get bignumIm(): Decimal | undefined;
    abstract get numerator(): NumericValue;
    abstract get denominator(): NumericValue;
    abstract get isNaN(): boolean;
    abstract get isPositiveInfinity(): boolean;
    abstract get isNegativeInfinity(): boolean;
    abstract get isComplexInfinity(): boolean;
    abstract get isZero(): boolean;
    isZeroWithTolerance(_tolerance: number | Decimal): boolean;
    abstract get isOne(): boolean;
    abstract get isNegativeOne(): boolean;
    /** The sign of complex numbers is undefined */
    abstract sgn(): -1 | 0 | 1 | undefined;
    abstract N(): NumericValue;
    abstract neg(): NumericValue;
    abstract inv(): NumericValue;
    abstract add(other: number | NumericValue): NumericValue;
    abstract sub(other: NumericValue): NumericValue;
    abstract mul(other: number | Decimal | NumericValue): NumericValue;
    abstract div(other: SmallInteger | NumericValue): NumericValue;
    abstract pow(n: number | NumericValue | {
        re: number;
        im: number;
    }): NumericValue;
    abstract root(n: number): NumericValue;
    abstract sqrt(): NumericValue;
    abstract gcd(other: NumericValue): NumericValue;
    abstract abs(): NumericValue;
    abstract ln(base?: number): NumericValue;
    abstract exp(): NumericValue;
    abstract floor(): NumericValue;
    abstract ceil(): NumericValue;
    abstract round(): NumericValue;
    abstract eq(other: number | NumericValue): boolean;
    abstract lt(other: number | NumericValue): boolean | undefined;
    abstract lte(other: number | NumericValue): boolean | undefined;
    abstract gt(other: number | NumericValue): boolean | undefined;
    abstract gte(other: number | NumericValue): boolean | undefined;
    /** Object.valueOf(): returns a primitive value */
    valueOf(): number | string;
    /** Object.toPrimitive() */
    [Symbol.toPrimitive](hint: 'number' | 'string' | 'default'): number | string | null;
    /** Object.toJSON */
    toJSON(): any;
    print(): void;
}