import { TimeMonzo, TimeReal } from './monzo';
/**
 * Step count vector indexed by strings representing distinct step sizes.
 */
export type StepVector = Record<string, number>;
/**
 * Create a new empty step vector with all counts implicitly zero.
 * @returns The additive identity element.
 */
export declare function zeroVector(): StepVector;
/**
 * Add two {@link StepVector} instances.
 * @param v1 Fist step vector.
 * @param v2 Second step vector.
 * @returns The sum of the step vectors.
 */
export declare function add(v1: StepVector, v2: StepVector): StepVector;
/**
 * Multiply a step vector by a scalar.
 * @param v Step vector to scale.
 * @param scalar A scalar to scale by.
 * @returns The vector multiplied by the given scalar.
 */
export declare function scalarMult(v: StepVector, scalar: number): StepVector;
/**
 * Obtain the additive inverse of a {@link StepVector} instance.
 * @param v Step vector to negate.
 * @returns The negated step vector.
 */
export declare function neg(v: StepVector): StepVector;
/**
 * Subtract two {@link StepVector} instances.
 * @param v1 Step vector to subtract from.
 * @param v2 Step vector to subtract.
 * @returns Difference of the step vectors.
 */
export declare function sub(v1: StepVector, v2: StepVector): StepVector;
/**
 * Rotate a string by moving it by the given offset.
 * @param str String to rotate.
 * @param offset Offset to rotate by.
 * @returns The rotated string.
 */
export declare function rotate(str: string, offset: number): string;
/**
 * Obtain the step vector associated it the given interval class of the given word.
 * @param word A mode of a (periodic) scale given as a string where each character represents a (geometric) step.
 * @param intervalClass Which subtension from root position to calculate (defaults to the whole word).
 * @returns A {@link StepVector} instance representing the interval class in terms of the word characters.
 */
export declare function getStepVector(word: string, intervalClass?: number): StepVector;
/**
 * Calculate the step signature of an entire scale word.
 * @param word A (periodic) scale given as a string where each character represents a (geometric) step.
 * @returns A {@link StepVector} instance representing the size of the entire scale.
 */
export declare function stepSignature(word: string): StepVector;
/**
 * Compute the interval matrix a.k.a. the modes of a scale in terms of {@link StepVector} instances.
 * @param word A (periodic) scale given as a string where each character represents a (geometric) step.
 * @returns An array of arrays of {@link StepVector} instances representing the modes of the scale (j-step on mode i).
 */
export declare function stepVectorMatrix(word: string): StepVector[][];
/**
 * Return the number of distinct letters in a word.
 * @param word A word usually representing a scale where each character represents a step.
 * @returns The number of distinct steps in the scale.
 */
export declare function wordArity(word: string): number;
/**
 * Return the number of distinct letters in a step vector.
 * @param sv Step vector to measure.
 * @returns Arity of the step vector.
 */
export declare function stepVectorArity(sv: StepVector): number;
/**
 * Return the set of letters representing scale steps, sorted in ASCII order.
 * @param sv Step vector to extract letters from.
 * @returns Letters with non-zero count in the step vector.
 */
export declare function letters(sv: StepVector): string[];
/**
 * Return the taxicab norm of a step vector, the sum of the absolute values of the components.
 * @param sv Step vector to measure.
 * @returns Size of the step vector.
 */
export declare function norm(sv: StepVector): number;
/**
 * Break a scale with implicit unison into an implicitly repeating scale word.
 * @param monzos Relative monzos representing intervals of the scale.
 * @returns A scale word where each character represents a step of distinct size.
 */
export declare function stepString(monzos: (TimeMonzo | TimeReal)[]): string;