mathjs

mathjs

Version 14.6.0
Published 11 days ago
9.57 MB
9 dependencies
Apache-2.0 license

Install

npm i mathjs

yarn add mathjs

pnpm add mathjs

Overview

Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser with support for symbolic computation, comes with a large set of built-in functions and constants, and offers an integrated solution to work with dif

Index

Interfaces

AccessorNode
AccessorNodeCtor
ArrayNode
ArrayNodeCtor
AssignmentNode
AssignmentNodeCtor
BaseUnit
- dimensions
- key
BigNumber
BlockNode
BlockNodeCtor
Complex
ConditionalNode
ConditionalNodeCtor
ConfigOptions
ConstantNode
ConstantNodeCtor
CreateUnitOptions
Distribution
EvalFunction
- evaluate()
FactoryFunctionMap
FormatOptions
FractionDefinition
- a
- b
FunctionAssignmentNode
FunctionAssignmentNodeCtor
FunctionNode
FunctionNodeCtor
- onUndefinedFunction
Help
- toJSON()
- toString()
ImportObject
ImportOptions
Index
IndexNode
IndexNodeCtor
LUDecomposition
- L
- p
- U
MapLike
MathJsChain
MathJsFactory
- create
- factory
MathJsInstance
MathJSON
MathNode
Matrix
MatrixCtor
NodeCtor
ObjectNode
ObjectNodeCtor
ObjectWrappingMap
- wrappedObject
OperatorNode
OperatorNodeCtor
ParenthesisNode
ParenthesisNodeCtor
ParseFunction
ParseOptions
- nodes
Parser
PartitionedMap
- a
- b
PolarCoordinates
- phi
- r
QRDecomposition
- Q
- R
RangeNode
RangeNodeCtor
RelationalNode
RelationalNodeCtor
ResultSet
SchurDecomposition
- T
- U
Simplify
- rules
SimplifyOptions
SLUDecomposition
- q
SymbolNode
SymbolNodeCtor
- onUndefinedSymbol
Unit
UnitComponent
UnitCtor
UnitDefinition
UnitPrefix
UnitStatic

Interfaces

interface AccessorNode

interface AccessorNode<TObject extends MathNode = MathNode> extends MathNode {}

property index

index: IndexNode;

property isAccessorNode

isAccessorNode: true;

property name

name: string;

property object

object: TObject;

property type

type: 'AccessorNode';

interface AccessorNodeCtor

interface AccessorNodeCtor {}

construct signature

new <TObject extends MathNode = MathNode>(
    object: TObject,
    index: IndexNode
): AccessorNode<TObject>;

interface ArrayNode

interface ArrayNode<TItems extends MathNode[] = MathNode[]> extends MathNode {}

property isArrayNode

isArrayNode: true;

property items

items: [...TItems];

property type

type: 'ArrayNode';

interface ArrayNodeCtor

interface ArrayNodeCtor {}

construct signature

new <TItems extends MathNode[] = MathNode[]>(
    items: [...TItems]
): ArrayNode<TItems>;

interface AssignmentNode

interface AssignmentNode<TValue extends MathNode = MathNode> extends MathNode {}

property index

index: IndexNode | null;

property isAssignmentNode

isAssignmentNode: true;

property name

name: string;

property object

object: SymbolNode | AccessorNode;

property type

type: 'AssignmentNode';

property value

value: TValue;

interface AssignmentNodeCtor

interface AssignmentNodeCtor {}

construct signature

new <TValue extends MathNode = MathNode>(
    object: SymbolNode,
    value: TValue
): AssignmentNode<TValue>;

construct signature

new <TValue extends MathNode = MathNode>(
    object: SymbolNode | AccessorNode,
    index: IndexNode,
    value: TValue
): AssignmentNode<TValue>;

interface BaseUnit

interface BaseUnit {}

property dimensions

dimensions: number[];

property key

key: string;

interface BigNumber

interface BigNumber extends Decimal {}

interface BlockNode

interface BlockNode<TNode extends MathNode = MathNode> extends MathNode {}

property blocks

blocks: Array<{ node: TNode; visible: boolean }>;

property isBlockNode

isBlockNode: true;

property type

type: 'BlockNode';

interface BlockNodeCtor

interface BlockNodeCtor {}

construct signature

new <TNode extends MathNode = MathNode>(
    arr: Array<{ node: TNode } | { node: TNode; visible: boolean }>
): BlockNode;

interface Complex

interface Complex {}

property im

im: number;

property re

re: number;

method clone

clone: () => Complex;

method compare

compare: (a: Complex, b: Complex) => number;

method equals

equals: (other: Complex) => boolean;

method format

format: (precision?: number) => string;

method fromJSON

fromJSON: (json: object) => Complex;

method fromPolar

fromPolar: { (polar: object): Complex; (r: number, phi: number): Complex };

method toJSON

toJSON: () => object;

method toPolar

toPolar: () => PolarCoordinates;

method toString

toString: () => string;

interface ConditionalNode

interface ConditionalNode<
    TCond extends MathNode = MathNode,
    TTrueNode extends MathNode = MathNode,
    TFalseNode extends MathNode = MathNode
> extends MathNode {}

property condition

condition: TCond;

property falseExpr

falseExpr: TFalseNode;

property isConditionalNode

isConditionalNode: boolean;

property trueExpr

trueExpr: TTrueNode;

property type

type: 'ConditionalNode';

interface ConditionalNodeCtor

interface ConditionalNodeCtor {}

construct signature

new <
    TCond extends MathNode = MathNode,
    TTrueNode extends MathNode = MathNode,
    TFalseNode extends MathNode = MathNode
>(
    condition: TCond,
    trueExpr: TTrueNode,
    falseExpr: TFalseNode
): ConditionalNode;

interface ConfigOptions

interface ConfigOptions {}

property absTol

absTol?: number;

property epsilon

epsilon?: number;

Deprecated
Use relTol and absTol instead

property matrix

matrix?: 'Matrix' | 'Array';

property number

number?: 'number' | 'BigNumber' | 'bigint' | 'Fraction';

property numberFallback

numberFallback?: 'number' | 'BigNumber';

property precision

precision?: number;

property predictable

predictable?: boolean;

property randomSeed

randomSeed?: string | null;

property relTol

relTol?: number;

interface ConstantNode

interface ConstantNode<
    TValue extends
        | string
        | number
        | boolean
        | null
        | undefined
        | bigint
        | BigNumber
        | Fraction = number
> extends MathNode {}

property isConstantNode

isConstantNode: true;

property type

type: 'ConstantNode';

property value

value: TValue;

interface ConstantNodeCtor

interface ConstantNodeCtor {}

construct signature

new <
    TValue extends
        | string
        | number
        | boolean
        | null
        | undefined
        | bigint
        | BigNumber
        | Fraction = string
>(
    value: TValue
): ConstantNode<TValue>;

interface CreateUnitOptions

interface CreateUnitOptions {}

property aliases

aliases?: string[];

property offset

offset?: number;

property override

override?: boolean;

property prefixes

prefixes?: 'none' | 'short' | 'long' | 'binary_short' | 'binary_long';

interface Distribution

interface Distribution {}

method pickRandom

pickRandom: (array: any) => any;

method random

random: (size: any, min?: any, max?: any) => any;

method randomInt

randomInt: (min: any, max?: any) => any;

interface EvalFunction

interface EvalFunction {}

method evaluate

evaluate: (scope?: MathScope) => any;

interface FactoryFunctionMap

interface FactoryFunctionMap {}

index signature

[key: string]: FactoryFunction<any> | FactoryFunctionMap;

interface FormatOptions

interface FormatOptions {}

property fraction

fraction?: string;

Available values: 'ratio' (default) or 'decimal'. For example format(fraction(1, 3)) will output '1/3' when 'ratio' is configured, and will output 0.(3) when 'decimal' is configured.

property lowerExp

lowerExp?: number | BigNumber;

Exponent determining the lower boundary for formatting a value with an exponent when notation='auto. Default value is -3.

property notation

notation?:
    | 'fixed'
    | 'exponential'
    | 'engineering'
    | 'auto'
    | 'hex'
    | 'bin'
    | 'oct';

Number notation. Choose from: 'fixed' Always use regular number notation. For example '123.40' and '14000000' 'exponential' Always use exponential notation. For example '1.234e+2' and '1.4e+7' 'auto' (default) Regular number notation for numbers having an absolute value between lower and upper bounds, and uses exponential notation elsewhere. Lower bound is included, upper bound is excluded. For example '123.4' and '1.4e7'.

property precision

precision?: number | BigNumber;

A number between 0 and 16 to round the digits of the number. In case of notations 'exponential' and 'auto', precision defines the total number of significant digits returned and is undefined by default. In case of notation 'fixed', precision defines the number of significant digits after the decimal point, and is 0 by default.

property upperExp

upperExp?: number | BigNumber;

Exponent determining the upper boundary for formatting a value with an exponent when notation='auto. Default value is 5.

property wordSize

wordSize?: number | BigNumber;

The word size in bits to use for formatting in binary, octal, or hexadecimal notation. To be used only with 'bin', 'oct', or 'hex' values for notation option. When this option is defined the value is formatted as a signed twos complement integer of the given word size and the size suffix is appended to the output.

interface FractionDefinition

interface FractionDefinition {}

property a

a: number;

property b

b: number;

interface FunctionAssignmentNode

interface FunctionAssignmentNode<TExpr extends MathNode = MathNode>
    extends MathNode {}

property expr

expr: TExpr;

property isFunctionAssignmentNode

isFunctionAssignmentNode: true;

property name

name: string;

property params

params: string[];

property type

type: 'FunctionAssignmentNode';

interface FunctionAssignmentNodeCtor

interface FunctionAssignmentNodeCtor {}

construct signature

new <TExpr extends MathNode = MathNode>(
    name: string,
    params: string[],
    expr: TExpr
): FunctionAssignmentNode<TExpr>;

interface FunctionNode

interface FunctionNode<TFn = SymbolNode, TArgs extends MathNode[] = MathNode[]>
    extends MathNode {}

property args

args: [...TArgs];

property fn

fn: TFn;

property isFunctionNode

isFunctionNode: true;

property type

type: 'FunctionNode';

interface FunctionNodeCtor

interface FunctionNodeCtor {}

property onUndefinedFunction

onUndefinedFunction: (name: string) => any;

construct signature

new <TFn = SymbolNode, TArgs extends MathNode[] = MathNode[]>(
    fn: TFn,
    args: [...TArgs]
): FunctionNode<TFn, TArgs>;

interface Help

interface Help {}

method toJSON

toJSON: () => string;

method toString

toString: () => string;

interface ImportObject

interface ImportObject {}

index signature

[key: string]: any;

interface ImportOptions

interface ImportOptions {}

property override

override?: boolean;

property silent

silent?: boolean;

property wrap

wrap?: boolean;

interface Index

interface Index {}

interface IndexNode

interface IndexNode<TDims extends MathNode[] = MathNode[]> extends MathNode {}

property dimensions

dimensions: [...TDims];

property dotNotation

dotNotation: boolean;

property isIndexNode

isIndexNode: true;

property type

type: 'IndexNode';

interface IndexNodeCtor

interface IndexNodeCtor {}

construct signature

new <TDims extends MathNode[] = MathNode[]>(dimensions: [...TDims]): IndexNode;

construct signature

new <TDims extends MathNode[] = MathNode[]>(
    dimensions: [...TDims],
    dotNotation: boolean
): IndexNode<TDims>;

interface LUDecomposition

interface LUDecomposition {}

property L

L: MathCollection;

property p

p: number[];

property U

U: MathCollection;

interface MapLike

interface MapLike<TKey = string, TValue = unknown> {}

method get

get: (key: TKey) => TValue;

method has

has: (key: TKey) => boolean;

method keys

keys: () => IterableIterator<TKey> | TKey[];

method set

set: (key: TKey, value: TValue) => MapLike<TKey, TValue>;

interface MathJsChain

interface MathJsChain<TValue> {}

property apply

apply: MathJsChain<TValue>['mapSlices'];

Deprecated
backwards-compatibility old name of mapSlices

method abs

abs: <T extends unknown>(this: MathJsChain<T>) => MathJsChain<T>;

Calculate the absolute value of a number. For matrices, the function is evaluated element wise.

method acos

acos: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the inverse cosine of a value. For matrices, the function is evaluated element wise.

method acosh

acosh: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the hyperbolic arccos of a value, defined as acosh(x) = ln(sqrt(x^2 - 1) + x). For matrices, the function is evaluated element wise.

method acot

acot: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the inverse cotangent of a value. For matrices, the function is evaluated element wise.

method acoth

acoth: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the inverse hyperbolic tangent of a value, defined as acoth(x) = (ln((x+1)/x) + ln(x/(x-1))) / 2. For matrices, the function is evaluated element wise.

method acsc

acsc: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the inverse cosecant of a value. For matrices, the function is evaluated element wise.

method acsch

acsch: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the inverse hyperbolic cosecant of a value, defined as acsch(x) = ln(1/x + sqrt(1/x^2 + 1)). For matrices, the function is evaluated element wise.

method add

add: {
    <T extends unknown>(this: MathJsChain<T>, y: T): MathJsChain<T>;
    (this: MathJsChain<any>, y: any): MathJsChain<any>;
};

Add two values, x + y. For matrices, the function is evaluated element wise.
Parameter y
Second value to add

method and

and: (
    this: MathJsChain<
        number | BigNumber | bigint | Complex | Unit | MathCollection
    >,
    y: number | BigNumber | bigint | Complex | Unit | MathCollection
) => MathJsChain<boolean | MathCollection>;

Logical and. Test whether two values are both defined with a nonzero/nonempty value. For matrices, the function is evaluated element wise.
Parameter y
Second value to and

method arg

arg: {
    (this: MathJsChain<number | Complex>): MathJsChain<number>;
    (this: MathJsChain<BigNumber | Complex>): MathJsChain<BigNumber>;
    (this: MathJsChain<MathArray<any>>): MathJsChain<MathArray<any>>;
    (this: MathJsChain<Matrix<any>>): MathJsChain<Matrix<any>>;
};

Compute the argument of a complex value. For a complex number a + bi, the argument is computed as atan2(b, a). For matrices, the function is evaluated element wise.

method asec

asec: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the inverse secant of a value. For matrices, the function is evaluated element wise.

method asech

asech: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the hyperbolic arcsecant of a value, defined as asech(x) = ln(sqrt(1/x^2 - 1) + 1/x). For matrices, the function is evaluated element wise.

method asin

asin: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the inverse sine of a value. For matrices, the function is evaluated element wise.

method asinh

asinh: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the hyperbolic arcsine of a value, defined as asinh(x) = ln(x + sqrt(x^2 + 1)). For matrices, the function is evaluated element wise.

method atan

atan: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the inverse tangent of a value. For matrices, the function is evaluated element wise.

method atan2

atan2: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>,
    x: number
) => MathJsChain<T>;

Calculate the inverse tangent function with two arguments, y/x. By providing two arguments, the right quadrant of the computed angle can be determined. For matrices, the function is evaluated element wise.

method atanh

atanh: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the hyperbolic arctangent of a value, defined as atanh(x) = ln((1 + x)/(1 - x)) / 2. For matrices, the function is evaluated element wise.

method bellNumbers

bellNumbers: {
    (this: MathJsChain<number>): MathJsChain<number>;
    (this: MathJsChain<BigNumber>): MathJsChain<BigNumber>;
};

The Bell Numbers count the number of partitions of a set. A partition is a pairwise disjoint subset of S whose union is S. bellNumbers only takes integer arguments. The following condition must be enforced: n >= 0

method bigint

bigint: {
    (
        this: MathJsChain<
            number | string | Fraction | BigNumber | bigint | boolean | null
        >
    ): MathJsChain<bigint>;
    <T extends MathCollection<any>>(this: MathJsChain<T>): MathJsChain<T>;
};

Create a bigint, which can store integers with arbitrary precision. When a matrix is provided, all elements will be converted to bigint.

method bignumber

bignumber: {
    (
        this: MathJsChain<
            | number
            | string
            | Fraction
            | BigNumber
            | bigint
            | Unit
            | boolean
            | null
        >
    ): MathJsChain<BigNumber>;
    <T extends MathCollection<any>>(this: MathJsChain<T>): MathJsChain<T>;
};

Create a BigNumber, which can store numbers with arbitrary precision. When a matrix is provided, all elements will be converted to BigNumber.

method bitAnd

bitAnd: <T extends number | bigint | BigNumber | MathCollection<any>>(
    this: MathJsChain<T>,
    y: number | BigNumber | bigint | MathCollection
) => MathJsChain<NoLiteralType<T>>;

Bitwise AND two values, x & y. For matrices, the function is evaluated element wise.
Parameter y
Second value to and

method bitNot

bitNot: <T extends number | bigint | BigNumber | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Bitwise NOT value, ~x. For matrices, the function is evaluated element wise. For units, the function is evaluated on the best prefix base.

method bitOr

bitOr: <T extends number | bigint | BigNumber | MathCollection<any>>(
    this: MathJsChain<T>,
    y: T
) => MathJsChain<T>;

Bitwise OR two values, x | y. For matrices, the function is evaluated element wise. For units, the function is evaluated on the lowest print base.
Parameter y
Second value to or

method bitXor

bitXor: <T extends number | bigint | BigNumber | MathCollection<any>>(
    this: MathJsChain<T>,
    y: number | BigNumber | bigint | MathCollection
) => MathJsChain<NoLiteralType<T>>;

Bitwise XOR two values, x ^ y. For matrices, the function is evaluated element wise.
Parameter y
Second value to xor

method boolean

boolean: {
    (this: MathJsChain<string | number | boolean | null>): MathJsChain<boolean>;
    (this: MathJsChain<MathCollection<any>>): MathJsChain<MathCollection<any>>;
};

Create a boolean or convert a string or number to a boolean. In case of a number, true is returned for non-zero numbers, and false in case of zero. Strings can be 'true' or 'false', or can contain a number. When value is a matrix, all elements will be converted to boolean.

method catalan

catalan: {
    (this: MathJsChain<number>): MathJsChain<number>;
    (this: MathJsChain<BigNumber>): MathJsChain<BigNumber>;
};

The Catalan Numbers enumerate combinatorial structures of many different types. catalan only takes integer arguments. The following condition must be enforced: n >= 0

method cbrt

cbrt: <T extends number | BigNumber | Complex | Unit>(
    this: MathJsChain<T>,
    allRoots?: boolean
) => MathJsChain<T>;

Calculate the cubic root of a value. For matrices, the function is evaluated element wise.
Parameter allRoots
Optional, false by default. Only applicable when x is a number or complex number. If true, all complex roots are returned, if false (default) the principal root is returned.

method ceil

ceil: {
    <T extends unknown>(
        this: MathJsChain<T>,
        n?: number | BigNumber | MathCollection
    ): MathJsChain<T>;
    <U extends MathCollection<any>>(
        this: MathJsChain<any>,
        n: U
    ): MathJsChain<U>;
    (this: MathJsChain<Unit>, unit: Unit): MathJsChain<Unit>;
    <U extends MathCollection<Unit>>(
        this: MathJsChain<U>,
        unit: Unit
    ): MathJsChain<U>;
    (
        this: MathJsChain<Unit>,
        n: number | BigNumber,
        unit: Unit
    ): MathJsChain<Unit>;
    <U extends MathCollection<Unit>>(
        this: MathJsChain<U>,
        n: number | BigNumber,
        unit: Unit
    ): MathJsChain<U>;
};

Round a value towards plus infinity If x is complex, both real and imaginary part are rounded towards plus infinity. For matrices, the function is evaluated element wise.
Parameter n
Number of decimals Default value: 0.

method clone

clone: <TValue>(this: MathJsChain<TValue>) => MathJsChain<TValue>;

Clone an object.

method combinations

combinations: <T extends number | BigNumber>(
    n: MathJsChain<T>,
    k: number | BigNumber
) => MathJsChain<NoLiteralType<T>>;

Compute the number of ways of picking k unordered outcomes from n possibilities. Combinations only takes integer arguments. The following condition must be enforced: k <= n.
Parameter k
Number of objects in the subset

method compare

compare: (
    this: MathJsChain<MathType | string>,
    y: MathType | string
) => MathJsChain<number | BigNumber | Fraction | MathCollection>;

Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x == y. x and y are considered equal when the relative difference between x and y is smaller than the configured relTol and absTol. The function cannot be used to compare values smaller than approximately 2.22e-16. For matrices, the function is evaluated element wise.
Parameter y
Second value to compare

method compareNatural

compareNatural: (this: MathJsChain<any>, y: any) => MathJsChain<number>;

Compare two values of any type in a deterministic, natural way. For numeric values, the function works the same as math.compare. For types of values that can’t be compared mathematically, the function compares in a natural way.
Parameter y
Second value to compare

method compareText

compareText: (
    this: MathJsChain<string | MathCollection>,
    y: string | MathCollection
) => MathJsChain<number | MathCollection>;

Compare two strings lexically. Comparison is case sensitive. Returns 1 when x > y, -1 when x < y, and 0 when x == y. For matrices, the function is evaluated element wise.
Parameter y
Second string to compare

method compile

compile: (this: MathJsChain<MathExpression>) => MathJsChain<EvalFunction>;

Parse and compile an expression. Returns a an object with a function evaluate([scope]) to evaluate the compiled expression.

method complex

complex: {
    (
        this: MathJsChain<Complex | string | PolarCoordinates>,
        im?: number
    ): MathJsChain<Complex>;
    (this: MathJsChain<MathCollection<any>>): MathJsChain<MathCollection<any>>;
};

Create a complex value or convert a value to a complex value.
Parameter im
Argument specifying the imaginary part of the complex number

method composition

composition: <T extends number | BigNumber>(
    this: MathJsChain<T>,
    k: number | BigNumber
) => MathJsChain<NoLiteralType<T>>;

The composition counts of n into k parts. Composition only takes integer arguments. The following condition must be enforced: k <= n.
Parameter k
Number of objects in the subset

method concat

concat: (
    this: MathJsChain<Array<MathCollection | number | BigNumber>>
) => MathJsChain<MathCollection>;

Concatenate two or more matrices. dim: number is a zero-based dimension over which to concatenate the matrices. By default the last dimension of the matrices.

method conj

conj: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<NoLiteralType<T>>;

Compute the complex conjugate of a complex value. If x = a+bi, the complex conjugate of x is a - bi. For matrices, the function is evaluated element wise.

method cos

cos: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the cosine of a value. For matrices, the function is evaluated element wise.

method cosh

cosh: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the hyperbolic cosine of a value, defined as cosh(x) = 1/2 * (exp(x) + exp(-x)). For matrices, the function is evaluated element wise.

method cot

cot: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the cotangent of a value. cot(x) is defined as 1 / tan(x). For matrices, the function is evaluated element wise.

method coth

coth: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the hyperbolic cotangent of a value, defined as coth(x) = 1 / tanh(x). For matrices, the function is evaluated element wise.

method count

count: {
    (this: MathJsChain<MathCollection>): MathJsChain<number>;
    (this: MathJsChain<string>): MathJsChain<number>;
};

Count the number of elements of a matrix, array or string.

method createUnit

createUnit: {
    (
        this: MathJsChain<string>,
        definition?: string | UnitDefinition | Unit,
        options?: CreateUnitOptions
    ): MathJsChain<Unit>;
    (
        this: MathJsChain<Record<string, string | Unit | UnitDefinition>>,
        options?: CreateUnitOptions
    ): MathJsChain<Unit>;
};

Create a user-defined unit and register it with the Unit type.
Parameter definition
Definition of the unit in terms of existing units. For example, ‘0.514444444 m / s’.
Parameter options
(optional) An object containing any of the following properties:- prefixes {string} “none”, “short”, “long”, “binary_short”, or “binary_long”. The default is “none”.- aliases {Array} Array of strings. Example: [‘knots’, ‘kt’, ‘kts’]- offset {Numeric} An offset to apply when converting from the unit. For example, the offset for celsius is 273.15. Default is 0.
Create a user-defined unit and register it with the Unit type.
Parameter options
(optional) An object containing any of the following properties:- prefixes {string} “none”, “short”, “long”, “binary_short”, or “binary_long”. The default is “none”.- aliases {Array} Array of strings. Example: [‘knots’, ‘kt’, ‘kts’]- offset {Numeric} An offset to apply when converting from the unit. For example, the offset for celsius is 273.15. Default is 0.

method cross

cross: (
    this: MathJsChain<MathCollection>,
    y: MathCollection
) => MathJsChain<MathCollection>;

Calculate the cross product for two vectors in three dimensional space. The cross product of A = [a1, a2, a3] and B =[b1, b2, b3] is defined as: cross(A, B) = [ a2 * b3 - a3 * b2, a3 * b1 - a1 * b3, a1 * b2 - a2 * b1 ]
Parameter y
Second vector

method csc

csc: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the cosecant of a value, defined as csc(x) = 1/sin(x). For matrices, the function is evaluated element wise.

method csch

csch: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the hyperbolic cosecant of a value, defined as csch(x) = 1 / sinh(x). For matrices, the function is evaluated element wise.

method cube

cube: <T extends unknown>(this: MathJsChain<T>) => MathJsChain<T>;

Compute the cube of a value, x * x * x. For matrices, the function is evaluated element wise.

method deepEqual

deepEqual: (this: MathJsChain<MathType>, y: MathType) => MathJsChain<MathType>;

Test element wise whether two matrices are equal. The function accepts both matrices and scalar values.
Parameter y
Second amtrix to compare

method derivative

derivative: (
    this: MathJsChain<MathNode | string>,
    variable: MathNode | string,
    options?: { simplify: boolean }
) => MathJsChain<MathNode>;

Parameter variable
The variable over which to differentiate
Parameter options
There is one option available, simplify, which is true by default. When false, output will not be simplified.

method det

det: (this: MathJsChain<MathCollection>) => MathJsChain<number>;

Calculate the determinant of a matrix.

method diag

diag: {
    (this: MathJsChain<MathCollection>, format?: string): MathJsChain<Matrix>;
    (
        this: MathJsChain<MathCollection<any>>,
        k: number | BigNumber,
        format?: string
    ): MathJsChain<MathCollection<any>>;
};

Create a diagonal matrix or retrieve the diagonal of a matrix. When x is a vector, a matrix with vector x on the diagonal will be returned. When x is a two dimensional matrix, the matrixes kth diagonal will be returned as vector. When k is positive, the values are placed on the super diagonal. When k is negative, the values are placed on the sub diagonal.
Parameter k
The diagonal where the vector will be filled in or retrieved. Default value: 0.
Parameter format
The matrix storage format. Default value: 'dense'.

method distance

distance: (
    this: MathJsChain<MathCollection | object>,
    y: MathCollection | object
) => MathJsChain<number | BigNumber>;

Calculates: The eucledian distance between two points in 2 and 3 dimensional spaces. Distance between point and a line in 2 and 3 dimensional spaces. Pairwise distance between a set of 2D or 3D points NOTE: When substituting coefficients of a line(a, b and c), use ax + by + c = 0 instead of ax + by = c For parametric equation of a 3D line, x0, y0, z0, a, b, c are from: (x−x0, y−y0, z−z0) = t(a, b, c)
Parameter y
Coordinates of the second point

method divide

divide: {
    (this: MathJsChain<Unit>, y: Unit): MathJsChain<Unit | number>;
    (this: MathJsChain<Unit>, y: number): MathJsChain<Unit>;
    (this: MathJsChain<number>, y: number): MathJsChain<number>;
    (this: MathJsChain<any>, y: any): MathJsChain<any>;
};

Divide two values, x / y. To divide matrices, x is multiplied with the inverse of y: x * inv(y).
Parameter y
Denominator

method done

done: () => TValue;

method dot

dot: (
    this: MathJsChain<MathCollection>,
    y: MathCollection
) => MathJsChain<number>;

Calculate the dot product of two vectors. The dot product of A = [a1, a2, a3, ..., an] and B = [b1, b2, b3, ..., bn] is defined as: dot(A, B) = a1 * b1 + a2 * b2 + a3 * b3 + ... + an * bn
Parameter y
Second vector

method dotDivide

dotDivide: {
    <T extends MathCollection<any>>(
        this: MathJsChain<T>,
        y: MathType
    ): MathJsChain<T>;
    <T extends MathCollection<any>>(
        this: MathJsChain<any>,
        y: T
    ): MathJsChain<T>;
    (this: MathJsChain<Unit>, y: any): MathJsChain<Unit>;
    (this: MathJsChain<any>, y: Unit): MathJsChain<Unit>;
    (this: MathJsChain<any>, y: any): MathJsChain<any>;
};

Divide two matrices element wise. The function accepts both matrices and scalar values.
Parameter y
Denominator

method dotMultiply

dotMultiply: {
    <T extends MathCollection<any>>(
        this: MathJsChain<T>,
        y: MathType
    ): MathJsChain<T>;
    <T extends MathCollection<any>>(
        this: MathJsChain<any>,
        y: T
    ): MathJsChain<T>;
    (this: MathJsChain<Unit>, y: any): MathJsChain<Unit>;
    (this: MathJsChain<any>, y: Unit): MathJsChain<Unit>;
    (this: MathJsChain<any>, y: any): MathJsChain<any>;
};

Multiply two matrices element wise. The function accepts both matrices and scalar values.
Parameter y
Right hand value

method dotPow

dotPow: <T extends unknown>(this: MathJsChain<T>, y: MathType) => MathJsChain<T>;

Calculates the power of x to y element wise.
Parameter y
The exponent

method equal

equal: (
    this: MathJsChain<MathType | string>,
    y: MathType | string
) => MathJsChain<boolean | MathCollection>;

Test whether two values are equal.
The function tests whether the relative difference between x and y is smaller than the configured relTol and absTol. The function cannot be used to compare values smaller than approximately 2.22e-16. For matrices, the function is evaluated element wise. In case of complex numbers, x.re must equal y.re, and x.im must equal y.im. Values null and undefined are compared strictly, thus null is only equal to null and nothing else, and undefined is only equal to undefined and nothing else.
Parameter y
Second value to compare

method equalText

equalText: (
    this: MathJsChain<string | MathCollection>,
    y: string | MathCollection
) => MathJsChain<number | MathCollection>;

Check equality of two strings. Comparison is case sensitive. For matrices, the function is evaluated element wise.
Parameter y
Second string to compare

method erf

erf: <T extends number | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<NoLiteralType<T>>;

Compute the erf function of a value using a rational Chebyshev approximations for different intervals of x.

method evaluate

evaluate: {
    (
        this: MathJsChain<MathExpression | Matrix>,
        scope?: MathScope
    ): MathJsChain<any>;
    (this: MathJsChain<MathExpression[]>, scope?: MathScope<any>): MathJsChain<
        any[]
    >;
};

Evaluate an expression.
Parameter scope
Scope to read/write variables

method exp

exp: <T extends number | BigNumber | Complex>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the exponent of a value. For matrices, the function is evaluated element wise.

method expm

expm: (this: MathJsChain<Matrix>) => MathJsChain<Matrix>;

Compute the matrix exponential, expm(A) = e^A. The matrix must be square. Not to be confused with exp(a), which performs element-wise exponentiation. The exponential is calculated using the Padé approximant with scaling and squaring; see “Nineteen Dubious Ways to Compute the Exponential of a Matrix,” by Moler and Van Loan.

method expm1

expm1: <T extends number | BigNumber | Complex>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the value of subtracting 1 from the exponential value. For matrices, the function is evaluated element wise.

method factorial

factorial: <T extends number | BigNumber | MathCollection<any>>(
    n: MathJsChain<T>
) => MathJsChain<NoLiteralType<T>>;

Compute the factorial of a value Factorial only supports an integer value as argument. For matrices, the function is evaluated element wise.

method filter

filter: (
    this: MathJsChain<MathCollection | string[]>,
    test:
        | RegExp
        | ((
              value: any,
              index: number[],
              matrix: MathCollection | string[]
          ) => boolean)
) => MathJsChain<MathCollection>;

Filter the items in an array or one dimensional matrix.

method fix

fix: {
    <T extends unknown>(
        this: MathJsChain<T>,
        n?: number | BigNumber | MathCollection
    ): MathJsChain<T>;
    <U extends MathCollection<any>>(
        this: MathJsChain<any>,
        n: U
    ): MathJsChain<U>;
    (this: MathJsChain<Unit>, unit: Unit): MathJsChain<Unit>;
    <U extends MathCollection<Unit>>(
        this: MathJsChain<U>,
        unit: Unit
    ): MathJsChain<U>;
    (
        this: MathJsChain<Unit>,
        n: number | BigNumber,
        unit: Unit
    ): MathJsChain<Unit>;
    <U extends MathCollection<Unit>>(
        this: MathJsChain<U>,
        n: number | BigNumber,
        unit: Unit
    ): MathJsChain<U>;
};

Round a value towards zero. For matrices, the function is evaluated element wise.
Parameter n
Number of decimals Default value: 0.

method flatten

flatten: <T extends MathCollection<any>>(x: MathJsChain<T>) => MathJsChain<T>;

Flatten a multi dimensional matrix into a single dimensional matrix.

method floor

floor: {
    <T extends unknown>(
        this: MathJsChain<T>,
        n?: number | BigNumber | MathCollection
    ): MathJsChain<T>;
    <U extends MathCollection<any>>(
        this: MathJsChain<any>,
        n: U
    ): MathJsChain<U>;
    (this: MathJsChain<Unit>, unit: Unit): MathJsChain<Unit>;
    <U extends MathCollection<Unit>>(
        this: MathJsChain<U>,
        unit: Unit
    ): MathJsChain<U>;
    (
        this: MathJsChain<Unit>,
        n: number | BigNumber,
        unit: Unit
    ): MathJsChain<Unit>;
    <U extends MathCollection<Unit>>(
        this: MathJsChain<U>,
        n: number | BigNumber,
        unit: Unit
    ): MathJsChain<U>;
};

Round a value towards minus infinity. For matrices, the function is evaluated element wise.
Parameter n
Number of decimals Default value: 0.

method forEach

forEach: <T extends MathCollection<any>>(
    this: MathJsChain<T>,
    callback: (value: any, index: number[], matrix: T) => void
) => void;

Iterate over all elements of a matrix/array, and executes the given callback function.

method format

format: (
    this: MathJsChain<any>,
    value: any,
    options?: number | FormatOptions | ((item: any) => string),
    callback?: (value: any) => string
) => MathJsChain<string>;

Format a value of any type into a string.
Parameter options
An object with formatting options.
Parameter callback
A custom formatting function, invoked for all numeric elements in value, for example all elements of a matrix, or the real and imaginary parts of a complex number. This callback can be used to override the built-in numeric notation with any type of formatting. Function callback is called with value as parameter and must return a string.
See Also
- http://mathjs.org/docs/reference/functions/format.html

method fraction

fraction: {
    (
        this: MathJsChain<
            | number
            | string
            | BigNumber
            | bigint
            | Unit
            | Fraction
            | FractionDefinition
        >,
        denominator?: number
    ): MathJsChain<Fraction>;
    (this: MathJsChain<MathCollection<any>>): MathJsChain<MathCollection<any>>;
};

Create a fraction convert a value to a fraction.
Parameter denominator
Argument specifying the denominator of the fraction

method freqz

freqz: <T extends number | MathArray<any> | MathArray<any>[]>(
    this: MathJsChain<T>,
    a: T,
    w?: T | number
) => MathJsChain<{ w: T; h: T }>;

Calculates the frequency response of a filter given its numerator and denominator coefficients.

method gamma

gamma: <T extends number | BigNumber | Complex | MathCollection<any>>(
    n: MathJsChain<T>
) => MathJsChain<NoLiteralType<T>>;

Compute the gamma function of a value using Lanczos approximation for small values, and an extended Stirling approximation for large values. For matrices, the function is evaluated element wise.

method gcd

gcd: <T extends unknown>(this: MathJsChain<T[]>, ...args: T[]) => MathJsChain<T>;

Calculate the greatest common divisor for two or more values or arrays. For matrices, the function is evaluated element wise.

method help

help: (this: MathJsChain<unknown>) => MathJsChain<unknown>;

Retrieve help on a function or data type. Help files are retrieved from the documentation in math.expression.docs.

method hypot

hypot: <T extends number | BigNumber>(this: MathJsChain<T[]>) => MathJsChain<T>;

Calculate the hypotenuse of a list with values. The hypotenuse is defined as: hypot(a, b, c, ...) = sqrt(a^2 + b^2 + c^2 + ...) For matrix input, the hypotenuse is calculated for all values in the matrix.

method identity

identity: {
    (
        this: MathJsChain<number | number[] | MathCollection>,
        format?: string
    ): MathJsChain<MathCollection | number>;
    (this: MathJsChain<number>, n: number, format?: string): MathJsChain<
        number | MathCollection<any>
    >;
};

Create a 2-dimensional identity matrix with size m x n or n x n. The matrix has ones on the diagonal and zeros elsewhere.
Parameter format
The Matrix storage format
Parameter n
The y dimension for the matrix
Parameter format
The Matrix storage format

method im

im: {
    (this: MathJsChain<number | Complex>): MathJsChain<number>;
    (this: MathJsChain<BigNumber>): MathJsChain<BigNumber>;
    (this: MathJsChain<MathCollection<any>>): MathJsChain<MathCollection<any>>;
};

Get the imaginary part of a complex number. For a complex number a + bi, the function returns b. For matrices, the function is evaluated element wise.

method index

index: (this: MathJsChain<any[]>) => MathJsChain<Index>;

Create an index. An Index can store ranges having start, step, and end for multiple dimensions. Matrix.get, Matrix.set, and math.subset accept an Index as input.

method intersect

intersect: (
    this: MathJsChain<MathCollection>,
    x: MathCollection,
    y: MathCollection,
    z?: MathCollection
) => MathJsChain<MathArray>;

Calculates the point of intersection of two lines in two or three dimensions and of a line and a plane in three dimensions. The inputs are in the form of arrays or 1 dimensional matrices. The line intersection functions return null if the lines do not meet. Note: Fill the plane coefficients as x + y + z = c and not as x + y + z + c = 0.
Parameter x
Co-ordinates of second end-point of first line
Parameter y
Co-ordinates of first end-point of second line OR Coefficients of the plane's equation
Parameter z
Co-ordinates of second end-point of second line OR null if the calculation is for line and plane

method inv

inv: <T extends number | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<NoLiteralType<T>>;

Calculate the inverse of a square matrix.

method isInteger

isInteger: (
    this: MathJsChain<number | BigNumber | bigint | Fraction | MathCollection>
) => MathJsChain<boolean>;

Test whether a value is an integer number. The function supports number, BigNumber, and Fraction. The function is evaluated element-wise in case of Array or Matrix input.

method isNaN

isNaN: (
    this: MathJsChain<number | BigNumber | Fraction | MathCollection | Unit>
) => MathJsChain<boolean>;

Test whether a value is NaN (not a number). The function supports types number, BigNumber, Fraction, Unit and Complex. The function is evaluated element-wise in case of Array or Matrix input.

method isNegative

isNegative: (
    this: MathJsChain<number | BigNumber | Fraction | MathCollection | Unit>
) => MathJsChain<boolean>;

Test whether a value is negative: smaller than zero. The function supports types number, BigNumber, Fraction, and Unit. The function is evaluated element-wise in case of Array or Matrix input.

method isNumeric

isNumeric: (this: MathJsChain<any>) => MathJsChain<boolean>;

Test whether a value is a numeric value. The function is evaluated element-wise in case of Array or Matrix input.

method isPositive

isPositive: (
    this: MathJsChain<
        number | BigNumber | bigint | Fraction | MathCollection | Unit
    >
) => MathJsChain<boolean>;

Test whether a value is positive: larger than zero. The function supports types number, BigNumber, Fraction, and Unit. The function is evaluated element-wise in case of Array or Matrix input.

method isPrime

isPrime: (
    this: MathJsChain<number | BigNumber | bigint | MathCollection>
) => MathJsChain<boolean>;

Test whether a value is prime: has no divisors other than itself and one. The function supports type number, bignumber. The function is evaluated element-wise in case of Array or Matrix input.

method isZero

isZero: (this: MathJsChain<MathType>) => MathJsChain<boolean>;

Test whether a value is zero. The function can check for zero for types number, BigNumber, Fraction, Complex, and Unit. The function is evaluated element-wise in case of Array or Matrix input.

method kldivergence

kldivergence: (
    this: MathJsChain<MathCollection>,
    p: MathCollection
) => MathJsChain<number>;

Calculate the Kullback-Leibler (KL) divergence between two distributions
Parameter p
Second vector

method kron

kron: (
    this: MathJsChain<MathCollection>,
    y: MathCollection
) => MathJsChain<Matrix>;

Calculate the Kronecker product of two matrices or vectors
Parameter y
Second vector

method larger

larger: (
    this: MathJsChain<MathType | string>,
    y: MathType | string
) => MathJsChain<boolean | MathCollection>;

Test whether value x is larger than y. The function returns true when x is larger than y and the relative difference between x and y is larger than the configured relTol and absTol. The function cannot be used to compare values smaller than approximately 2.22e-16. For matrices, the function is evaluated element wise.
Parameter y
Second value to compare

method largerEq

largerEq: (
    this: MathJsChain<MathType | string>,
    y: MathType | string
) => MathJsChain<boolean | MathCollection>;

Test whether value x is larger or equal to y. The function returns true when x is larger than y or the relative difference between x and y is smaller than the configured relTol and absTol. The function cannot be used to compare values smaller than approximately 2.22e-16. For matrices, the function is evaluated element wise.
Parameter y
Second value to vcompare

method lcm

lcm: <T extends number | BigNumber | MathCollection<any>>(
    this: MathJsChain<T>,
    b: T
) => MathJsChain<T>;

Calculate the least common multiple for two or more values or arrays. lcm is defined as: lcm(a, b) = abs(a * b) / gcd(a, b) For matrices, the function is evaluated element wise.
Parameter b
An integer number

method leafCount

leafCount: (this: MathJsChain<MathNode>) => MathJsChain<number>;

Gives the number of “leaf nodes” in the parse tree of the given expression. A leaf node is one that has no subexpressions, essentially either a symbol or a constant. Note that 5! has just one leaf, the 5; the unary factorial operator does not add a leaf. On the other hand, function symbols do add leaves, so sin(x)/cos(x) has four leaves.

method leftShift

leftShift: <T extends number | bigint | BigNumber | MathCollection<any>>(
    this: MathJsChain<T>,
    y: number | BigNumber | bigint
) => MathJsChain<NoLiteralType<T>>;

Bitwise left logical shift of a value x by y number of bits, x << y. For matrices, the function is evaluated element wise. For units, the function is evaluated on the best prefix base.
Parameter y
Amount of shifts

method log

log: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>,
    base?: number | BigNumber | Complex
) => MathJsChain<NoLiteralType<T>>;

Calculate the logarithm of a value. For matrices, the function is evaluated element wise.
Parameter base
Optional base for the logarithm. If not provided, the natural logarithm of x is calculated. Default value: e.

method log10

log10: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the 10-base of a value. This is the same as calculating log(x, 10). For matrices, the function is evaluated element wise.

method log1p

log1p: {
    (
        this: MathJsChain<number>,
        base?: number | BigNumber | Complex
    ): MathJsChain<number>;
    (
        this: MathJsChain<BigNumber>,
        base?: number | BigNumber | Complex
    ): MathJsChain<BigNumber>;
    (
        this: MathJsChain<Complex>,
        base?: number | BigNumber | Complex
    ): MathJsChain<Complex>;
    (
        this: MathJsChain<MathArray<any>>,
        base?: number | BigNumber | Complex
    ): MathJsChain<MathArray<any>>;
    (
        this: MathJsChain<Matrix<any>>,
        base?: number | BigNumber | Complex
    ): MathJsChain<Matrix<any>>;
};

Calculate the logarithm of a value+1. For matrices, the function is evaluated element wise.

method log2

log2: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the 2-base of a value. This is the same as calculating log(x, 2). For matrices, the function is evaluated element wise.

method lsolve

lsolve: {
    (this: MathJsChain<Matrix>, b: MathCollection): MathJsChain<Matrix>;
    (this: MathJsChain<MathArray<any>>, b: MathCollection<any>): MathJsChain<
        MathArray<any>
    >;
};

Solves the linear equation system by forwards substitution. Matrix must be a lower triangular matrix.
Parameter b
A column vector with the b values

method lup

lup: (this: MathJsChain<MathCollection>) => MathJsChain<LUDecomposition>;

Calculate the Matrix LU decomposition with partial pivoting. Matrix A is decomposed in two matrices (L, U) and a row permutation vector p where A[p,:] = L * U

method lusolve

lusolve: {
    (
        this: MathJsChain<Matrix>,
        b: MathCollection,
        order?: number,
        threshold?: number
    ): MathJsChain<Matrix>;
    (
        this: MathJsChain<MathArray<any>>,
        b: MathCollection<any>,
        order?: number,
        threshold?: number
    ): MathJsChain<MathArray<any>>;
    (this: MathJsChain<LUDecomposition>, b: MathCollection<any>): MathJsChain<
        Matrix<any>
    >;
};

Solves the linear system A * x = b where A is an [n x n] matrix and b is a [n] column vector.
Parameter b
Column Vector
Parameter order
The Symbolic Ordering and Analysis order, see slu for details. Matrix must be a SparseMatrix
Parameter threshold
Partial pivoting threshold (1 for partial pivoting), see slu for details. Matrix must be a SparseMatrix.

method lyap

lyap: (
    this: MathJsChain<MathCollection>,
    Q: MathCollection
) => MathJsChain<MathCollection>;

Solves the Continuous-time Lyapunov equation AP+PA'=Q for P, where Q is a positive semidefinite matrix. https://en.wikipedia.org/wiki/Lyapunov_equation
Parameter Q
Matrix Q
Returns
Matrix P solution to the Continuous-time Lyapunov equation AP+PA'=Q

method mad

mad: (this: MathJsChain<MathCollection>) => MathJsChain<any>;

Compute the median absolute deviation of a matrix or a list with values. The median absolute deviation is defined as the median of the absolute deviations from the median.

method map

map: <T extends MathCollection<any>>(
    this: MathJsChain<T>,
    callback: (value: any, index: number[], matrix: T) => MathType | string
) => MathJsChain<T>;

Iterate over all elements of a matrix/array, and executes the given callback function.
Parameter callback
The callback function is invoked with three parameters: the value of the element, the index of the element, and the Matrix/array being traversed.

method mapSlices

mapSlices: <T extends MathCollection<any>>(
    this: MathJsChain<T>,
    dim: number,
    callback: (array: Array<MathType> | Matrix) => number
) => MathJsChain<T>;

Apply a function that maps an array to a scalar along a given axis of the matrix or array. Returns a new matrix or array with one less dimension than the input.
Parameter dim
The dimension along which the callback is applied
Parameter callback
The callback function that is applied. This Function should take an array or 1-d matrix as an input and return a number.
Returns
The residual matrix with the function applied over some dimension.

method matrix

matrix: (
    this: MathJsChain<MathCollection>,
    format?: 'sparse' | 'dense',
    dataType?: string
) => MathJsChain<Matrix>;

Create a Matrix. The function creates a new math.type.Matrix object from an Array. A Matrix has utility functions to manipulate the data in the matrix, like getting the size and getting or setting values in the matrix. Supported storage formats are 'dense' and 'sparse'.

method max

max: {
    (this: MathJsChain<MathType[]>, dim?: number): MathJsChain<any>;
    (this: MathJsChain<MathCollection<any>>, dim?: number): MathJsChain<any>;
};

Compute the maximum value of a matrix or a list with values. In case of a multi dimensional array, the maximum of the flattened array will be calculated. When dim is provided, the maximum over the selected dimension will be calculated. Parameter dim is zero-based.
Parameter dim
The maximum over the selected dimension

method mean

mean: {
    (this: MathJsChain<MathType[]>, dim?: number): MathJsChain<any>;
    (this: MathJsChain<MathCollection<any>>, dim?: number): MathJsChain<any>;
};

Compute the mean value of matrix or a list with values. In case of a multi dimensional array, the mean of the flattened array will be calculated. When dim is provided, the maximum over the selected dimension will be calculated. Parameter dim is zero-based.
Parameter dim
The mean over the selected dimension

method median

median: {
    (this: MathJsChain<MathType[]>, dim?: number): MathJsChain<any>;
    (this: MathJsChain<MathCollection<any>>, dim?: number): MathJsChain<any>;
};

Compute the median of a matrix or a list with values. The values are sorted and the middle value is returned. In case of an even number of values, the average of the two middle values is returned. Supported types of values are: Number, BigNumber, Unit In case of a (multi dimensional) array or matrix, the median of all elements will be calculated.

method min

min: {
    (this: MathJsChain<MathType[]>): MathJsChain<MathType[]>;
    (this: MathJsChain<MathCollection<any>>, dim?: number): MathJsChain<any>;
};

Compute the minimum value of a matrix or a list of values. In case of a multi dimensional array, the minimum of the flattened array will be calculated. When dim is provided, the minimum over the selected dimension will be calculated. Parameter dim is zero-based.
Parameter dim
The minimum over the selected dimension

method mod

mod: <T extends unknown>(
    this: MathJsChain<T>,
    y: number | BigNumber | bigint | Fraction | MathCollection
) => MathJsChain<NoLiteralType<T>>;

Calculates the modulus, the remainder of an integer division. For matrices, the function is evaluated element wise. The modulus is defined as: x - y * floor(x / y)
Parameter y
Divisor
See Also
- http://en.wikipedia.org/wiki/Modulo_operation.

method mode

mode: (this: MathJsChain<MathType[]>) => MathJsChain<MathType[]>;

Computes the mode of a set of numbers or a list with values(numbers or characters). If there are more than one modes, it returns a list of those values.

method multinomial

multinomial: <T extends number | BigNumber>(
    a: MathJsChain<T[]>
) => MathJsChain<NoLiteralType<T>>;

Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from n possibilities. multinomial takes one array of integers as an argument. The following condition must be enforced: every ai <= 0

method multiply

multiply: {
    <T extends MathCollection<any>>(
        this: MathJsChain<T>,
        y: MathType
    ): MathJsChain<T>;
    (this: MathJsChain<Unit>, y: Unit): MathJsChain<Unit>;
    (this: MathJsChain<number>, y: number): MathJsChain<number>;
    (this: MathJsChain<any>, y: any): MathJsChain<any>;
};

Multiply two values, x * y. The result is squeezed. For matrices, the matrix product is calculated.
Parameter y
The second value to multiply

method norm

norm: (
    this: MathJsChain<number | BigNumber | Complex | MathCollection>,
    p?: number | BigNumber | string
) => MathJsChain<number | BigNumber>;

Calculate the norm of a number, vector or matrix. The second parameter p is optional. If not provided, it defaults to 2.
Parameter p
Vector space. Supported numbers include Infinity and -Infinity. Supported strings are: 'inf', '-inf', and 'fro' (The Frobenius norm) Default value: 2.

method not

not: (
    this: MathJsChain<
        number | BigNumber | bigint | Complex | Unit | MathCollection
    >
) => MathJsChain<boolean | MathCollection>;

Logical not. Flips boolean value of a given parameter. For matrices, the function is evaluated element wise.

method nthRoot

nthRoot: (
    this: MathJsChain<number | BigNumber | MathCollection | Complex>,
    root?: number | BigNumber
) => MathJsChain<number | Complex | MathCollection>;

Calculate the nth root of a value. The principal nth root of a positive real number A, is the positive real solution of the equation x^root = A For matrices, the function is evaluated element wise.
Parameter root
The root. Default value: 2.

method number

number: {
    (
        this: MathJsChain<
            | string
            | number
            | BigNumber
            | bigint
            | Fraction
            | boolean
            | Unit
            | null
        >,
        valuelessUnit?: Unit | string
    ): MathJsChain<number>;
    (
        this: MathJsChain<MathCollection<any>>,
        valuelessUnit?: string | Unit
    ): MathJsChain<MathCollection<any>>;
};

Create a number or convert a string, boolean, or unit to a number. When value is a matrix, all elements will be converted to number.
Parameter valuelessUnit
A valueless unit, used to convert a unit to a number

method numeric

numeric: {
    (
        this: MathJsChain<string | number | BigNumber | bigint | Fraction>,
        outputType: 'number'
    ): MathJsChain<number>;
    (this: MathJsChain<any>, outputType: 'BigNumber'): MathJsChain<BigNumber>;
    (this: MathJsChain<any>, outputType: 'bigint'): MathJsChain<bigint>;
    (this: MathJsChain<any>, outputType: 'Fraction'): MathJsChain<Fraction>;
};

Convert a numeric input to a specific numeric type: number, BigNumber, bigint, or Fraction.
Parameter outputType
The desired numeric output type

method ones

ones: (
    this: MathJsChain<number | number[] | BigNumber | BigNumber[]>,
    format?: string
) => MathJsChain<MathCollection>;

Create a matrix filled with ones. The created matrix can have one or multiple dimensions.
Parameter format
The matrix storage format

method or

or: (
    this: MathJsChain<
        number | BigNumber | bigint | Complex | Unit | MathCollection
    >,
    y: number | BigNumber | bigint | Complex | Unit | MathCollection
) => MathJsChain<boolean | MathCollection>;

Logical or. Test if at least one value is defined with a nonzero/nonempty value. For matrices, the function is evaluated element wise.
Parameter y
Second value to or

method parse

parse: {
    (this: MathJsChain<MathExpression[]>, options?: any): MathJsChain<
        MathNode[]
    >;
    (this: MathJsChain<MathExpression>, options?: any): MathJsChain<MathNode>;
};

Parameter options
Available options: nodes - a set of custome nodes
Parse an expression. Returns a node tree, which can be evaluated by invoking node.evaluate();
Parameter options
Available options: nodes - a set of custome nodes

method partitionSelect

partitionSelect: (
    this: MathJsChain<MathCollection>,
    k: number,
    compare?: 'asc' | 'desc' | ((a: any, b: any) => number)
) => MathJsChain<MathCollection>;

Partition-based selection of an array or 1D matrix. Will find the kth smallest value, and mutates the input array. Uses Quickselect.
Parameter k
The kth smallest value to be retrieved; zero-based index
Parameter compare
An optional comparator function. The function is called as compare(a, b), and must return 1 when a > b, -1 when a < b, and 0 when a == b. Default value: 'asc'.

method permutations

permutations: <T extends number | BigNumber>(
    n: MathJsChain<T>,
    k?: number | BigNumber
) => MathJsChain<NoLiteralType<T>>;

Compute the number of ways of obtaining an ordered subset of k elements from a set of n elements. Permutations only takes integer arguments. The following condition must be enforced: k <= n.
Parameter k
The number of objects in the subset

method pickRandom

pickRandom: {
    <T>(this: MathJsChain<T[]>): MathJsChain<T>;
    <T>(this: MathJsChain<T[]>, number: number): MathJsChain<T[]>;
    <T>(this: MathJsChain<T[]>, number: number, weights: number[]): MathJsChain<
        T[]
    >;
};

Random pick a value from a one dimensional array. Array element is picked using a random function with uniform distribution.
Parameter number
An int or float
Parameter weights
An array of ints or floats

method pow

pow: (
    this: MathJsChain<MathType>,
    y: number | BigNumber | bigint | Complex
) => MathJsChain<MathType>;

Calculates the power of x to y, x ^ y. Matrix exponentiation is supported for square matrices x, and positive integer exponents y.
Parameter y
The exponent

method print

print: (
    this: MathJsChain<string>,
    values: any,
    precision?: number,
    options?: number | object
) => MathJsChain<string>;

Interpolate values into a string template.
Parameter values
An object containing variables which will be filled in in the template.
Parameter precision
Number of digits to format numbers. If not provided, the value will not be rounded.
Parameter options
Formatting options, or the number of digits to format numbers. See function math.format for a description of all options.

method prod

prod: (this: MathJsChain<MathType[]>) => MathJsChain<any>;

Compute the product of a matrix or a list with values. In case of a (multi dimensional) array or matrix, the sum of all elements will be calculated.

method qr

qr: (this: MathJsChain<MathCollection>) => MathJsChain<QRDecomposition>;

Calculate the Matrix QR decomposition. Matrix A is decomposed in two matrices (Q, R) where Q is an orthogonal matrix and R is an upper triangular matrix.

method quantileSeq

quantileSeq: (
    A: MathJsChain<MathCollection>,
    prob: number | BigNumber | MathArray,
    sorted?: boolean
) => MathJsChain<number | BigNumber | Unit | MathArray>;

Compute the prob order quantile of a matrix or a list with values. The sequence is sorted and the middle value is returned. Supported types of sequence values are: Number, BigNumber, Unit Supported types of probability are: Number, BigNumber In case of a (multi dimensional) array or matrix, the prob order quantile of all elements will be calculated.
Parameter probOrN
prob is the order of the quantile, while N is the amount of evenly distributed steps of probabilities; only one of these options can be provided
Parameter sorted
=false is data sorted in ascending order

method random

random: {
    (this: MathJsChain<number>, max?: number): MathJsChain<number>;
    <T extends MathCollection<any>>(
        this: MathJsChain<T>,
        min?: number,
        max?: number
    ): MathJsChain<T>;
};

Return a random number larger or equal to min and smaller than max using a uniform distribution.
Parameter min
Minimum boundary for the random value, included
Parameter max
Maximum boundary for the random value, excluded

method randomInt

randomInt: {
    <T extends MathCollection<any>>(
        this: MathJsChain<T>,
        max?: number
    ): MathJsChain<T>;
    <T extends MathCollection<any>>(
        this: MathJsChain<T>,
        max?: number
    ): MathJsChain<T>;
    <T extends MathCollection<any>>(
        this: MathJsChain<T>,
        min: number,
        max: number
    ): MathJsChain<T>;
};

Return a random integer number larger or equal to min and smaller than max using a uniform distribution.
Parameter min
Minimum boundary for the random value, included
Parameter max
Maximum boundary for the random value, excluded

method range

range: {
    (this: MathJsChain<string>, includeEnd?: boolean): MathJsChain<Matrix>;
    (
        this: MathJsChain<number | BigNumber>,
        end: number | BigNumber,
        includeEnd?: boolean
    ): MathJsChain<Matrix<any>>;
    (
        this: MathJsChain<number | BigNumber | Unit>,
        end: number | BigNumber | Unit,
        step: number | BigNumber | Unit,
        includeEnd?: boolean
    ): MathJsChain<Matrix<any>>;
};

Create an array from a range. By default, the range end is excluded. This can be customized by providing an extra parameter includeEnd.
Parameter end
End of the range, excluded by default, included when parameter includeEnd=true
Parameter step
Step size. Default value is 1.
Parameter includeEnd
: Option to specify whether to include the end or not. False by default

method rationalize

rationalize: (
    this: MathJsChain<MathNode | string>,
    optional?: object | boolean,
    detailed?: boolean
) => MathJsChain<MathNode>;

Transform a rationalizable expression in a rational fraction. If rational fraction is one variable polynomial then converts the numerator and denominator in canonical form, with decreasing exponents, returning the coefficients of numerator.
Parameter optional
scope of expression or true for already evaluated rational expression at input
Parameter detailed
optional True if return an object, false if return expression node (default)

method re

re: {
    (this: MathJsChain<number | Complex>): MathJsChain<number>;
    (this: MathJsChain<BigNumber>): MathJsChain<BigNumber>;
    (this: MathJsChain<MathCollection<any>>): MathJsChain<MathCollection<any>>;
};

Get the real part of a complex number. For a complex number a + bi, the function returns a. For matrices, the function is evaluated element wise.

method reshape

reshape: <T extends MathCollection<any>>(
    this: MathJsChain<T>,
    sizes: number[]
) => MathJsChain<T>;

Reshape a multi dimensional array to fit the specified dimensions
Parameter sizes
One dimensional array with integral sizes for each dimension

method resize

resize: <T extends MathCollection<any>>(
    this: MathJsChain<T>,
    size: MathCollection,
    defaultValue?: number | string
) => MathJsChain<T>;

Resize a matrix
Parameter size
One dimensional array with numbers
Parameter defaultValue
Zero by default, except in case of a string, in that case defaultValue = ' ' Default value: 0.

method resolve

resolve: {
    (this: MathJsChain<MathNode>, scope?: MathScope): MathJsChain<MathNode>;
    (this: MathJsChain<MathNode[]>, scope?: MathScope<any>): MathJsChain<
        MathNode[]
    >;
};

Replaces variable nodes with their scoped values
Parameter scope
Scope to read/write variables

method rightArithShift

rightArithShift: <T extends number | bigint | BigNumber | MathCollection<any>>(
    this: MathJsChain<T>,
    y: number | BigNumber | bigint
) => MathJsChain<NoLiteralType<T>>;

Bitwise right arithmetic shift of a value x by y number of bits, x >> y. For matrices, the function is evaluated element wise. For units, the function is evaluated on the best prefix base.
Parameter y
Amount of shifts

method rightLogShift

rightLogShift: <T extends number | MathCollection<any>>(
    this: MathJsChain<T>,
    y: number
) => MathJsChain<NoLiteralType<T>>;

Bitwise right logical shift of value x by y number of bits, x >>> y. For matrices, the function is evaluated element wise. For units, the function is evaluated on the best prefix base.
Parameter y
Amount of shifts

method round

round: {
    <T extends unknown>(
        this: MathJsChain<T>,
        n?: number | BigNumber | MathCollection
    ): MathJsChain<T>;
    <U extends MathCollection<any>>(
        this: MathJsChain<any>,
        n: U
    ): MathJsChain<U>;
    (this: MathJsChain<Unit>, unit: Unit): MathJsChain<Unit>;
    <U extends MathCollection<Unit>>(
        this: MathJsChain<U>,
        unit: Unit
    ): MathJsChain<U>;
    (
        this: MathJsChain<Unit>,
        n: number | BigNumber,
        unit: Unit
    ): MathJsChain<Unit>;
    <U extends MathCollection<Unit>>(
        this: MathJsChain<U>,
        n: number | BigNumber,
        unit: Unit
    ): MathJsChain<U>;
};

Round a value towards the nearest integer. For matrices, the function is evaluated element wise.
Parameter n
Number of decimals Default value: 0.

method schur

schur: (this: MathJsChain<MathCollection>) => SchurDecomposition;

Performs a real Schur decomposition of the real matrix A = UTU' where U is orthogonal and T is upper quasi-triangular. https://en.wikipedia.org/wiki/Schur_decomposition
Returns
Object containing both matrix U and T of the Schur Decomposition A=UTU'

method sec

sec: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the secant of a value, defined as sec(x) = 1/cos(x). For matrices, the function is evaluated element wise.

method sech

sech: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the hyperbolic secant of a value, defined as sech(x) = 1 / cosh(x). For matrices, the function is evaluated element wise.

method setCartesian

setCartesian: <T extends MathCollection<any>>(
    this: MathJsChain<T>,
    a2: MathCollection
) => MathJsChain<T>;

Create the cartesian product of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays and the values will be sorted in ascending order before the operation.
Parameter a2
A (multi)set

method setDifference

setDifference: <T extends MathCollection<any>>(
    this: MathJsChain<T>,
    a2: MathCollection
) => MathJsChain<T>;

Create the difference of two (multi)sets: every element of set1, that is not the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation
Parameter a2
A (multi)set

method setDistinct

setDistinct: <T extends MathCollection<any>>(
    a: MathJsChain<T>
) => MathJsChain<T>;

Collect the distinct elements of a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.

method setIntersect

setIntersect: <T extends MathCollection<any>>(
    this: MathJsChain<T>,
    a2: MathCollection
) => MathJsChain<T>;

Create the intersection of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.
Parameter a2
A (multi)set

method setIsSubset

setIsSubset: (
    this: MathJsChain<MathCollection>,
    a2: MathCollection
) => MathJsChain<boolean>;

Check whether a (multi)set is a subset of another (multi)set. (Every element of set1 is the element of set2.) Multi-dimension arrays will be converted to single-dimension arrays before the operation.
Parameter a2
A (multi)set

method setMultiplicity

setMultiplicity: (
    e: MathJsChain<MathNumericType>,
    a: MathCollection
) => MathJsChain<number>;

Count the multiplicity of an element in a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.
Parameter a
A multiset

method setPowerset

setPowerset: <T extends MathCollection<any>>(
    a: MathJsChain<T>
) => MathJsChain<T>;

Create the powerset of a (multi)set. (The powerset contains very possible subsets of a (multi)set.) A multi-dimension array will be converted to a single-dimension array before the operation.

method setSize

setSize: (this: MathJsChain<MathCollection>) => MathJsChain<number>;

Count the number of elements of a (multi)set. When a second parameter is ‘true’, count only the unique values. A multi-dimension array will be converted to a single-dimension array before the operation.

method setSymDifference

setSymDifference: <T extends MathCollection<any>>(
    this: MathJsChain<T>,
    a2: MathCollection
) => MathJsChain<T>;

Create the symmetric difference of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.
Parameter a2
A (multi)set

method setUnion

setUnion: <T extends MathCollection<any>>(
    this: MathJsChain<T>,
    a2: MathCollection
) => MathJsChain<T>;

Create the union of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.
Parameter a2
A (multi)set

method sign

sign: <T extends unknown>(this: MathJsChain<T>) => MathJsChain<T>;

Compute the sign of a value. The sign of a value x is: 1 when x > 1 -1 when x < 0 0 when x == 0 For matrices, the function is evaluated element wise.
Parameter x
The number for which to determine the sign
Returns
The sign of x

method simplify

simplify: (
    this: MathJsChain<MathNode | string>,
    rules?: SimplifyRule[],
    scope?: Map<string, MathType> | object,
    options?: SimplifyOptions
) => MathJsChain<MathNode>;

Simplify an expression tree.
Parameter rules
A list of rules are applied to an expression, repeating over the list until no further changes are made. It’s possible to pass a custom set of rules to the function as second argument. A rule can be specified as an object, string, or function.
Parameter scope
Scope to variables
Parameter options
Options to configure the behavior of simplify

method simplifyConstant

simplifyConstant: (
    this: MathJsChain<MathNode | string>,
    options?: SimplifyOptions
) => MathJsChain<MathNode>;

method simplifyCore

simplifyCore: (
    this: MathJsChain<MathNode | string>,
    options?: SimplifyOptions
) => MathJsChain<MathNode>;

method sin

sin: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the sine of a value. For matrices, the function is evaluated element wise.

method sinh

sinh: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the hyperbolic sine of a value, defined as sinh(x) = 1/2 * (exp(x) - exp(-x)). For matrices, the function is evaluated element wise.

method size

size: (
    this: MathJsChain<
        boolean | number | Complex | Unit | string | MathCollection
    >
) => MathJsChain<MathCollection>;

Calculate the size of a matrix or scalar.

method slu

slu: (
    this: MathJsChain<Matrix>,
    order: number,
    threshold: number
) => MathJsChain<SLUDecomposition>;

Calculate the Sparse Matrix LU decomposition with full pivoting. Sparse Matrix A is decomposed in two matrices (L, U) and two permutation vectors (pinv, q) where P * A * Q = L * U
Parameter order
The Symbolic Ordering and Analysis order: 0 - Natural ordering, no permutation vector q is returned 1 - Matrix must be square, symbolic ordering and analisis is performed on M = A + A' 2 - Symbolic ordering and analysis is performed on M = A' * A. Dense columns from A' are dropped, A recreated from A'. This is appropriate for LU factorization of non-symmetric matrices. 3 - Symbolic ordering and analysis is performed on M = A' * A. This is best used for LU factorization is matrix M has no dense rows. A dense row is a row with more than 10*sqr(columns) entries.
Parameter threshold
Partial pivoting threshold (1 for partial pivoting)

method smaller

smaller: (
    this: MathJsChain<MathType | string>,
    y: MathType | string
) => MathJsChain<boolean | MathCollection>;

Test whether value x is smaller than y. The function returns true when x is smaller than y and the relative difference between x and y is smaller than the configured relTol and absTol. The function cannot be used to compare values smaller than approximately 2.22e-16. For matrices, the function is evaluated element wise.
Parameter y
Second value to vcompare

method smallerEq

smallerEq: (
    this: MathJsChain<MathType | string>,
    y: MathType | string
) => MathJsChain<boolean | MathCollection>;

Test whether value x is smaller or equal to y. The function returns true when x is smaller than y or the relative difference between x and y is smaller than the configured relTol and absTol. The function cannot be used to compare values smaller than approximately 2.22e-16. For matrices, the function is evaluated element wise.
Parameter y
Second value to compare

method sort

sort: <T extends MathCollection<any>>(
    this: MathJsChain<T>,
    compare: 'asc' | 'desc' | 'natural' | ((a: any, b: any) => number)
) => MathJsChain<T>;

Sort the items in a matrix
Parameter compare
An optional _comparator function or name. The function is called as compare(a, b), and must return 1 when a > b, -1 when a < b, and 0 when a == b. Default value: ‘asc’

method sparse

sparse: (
    this: MathJsChain<MathCollection>,
    dataType?: string
) => MathJsChain<Matrix>;

Create a Sparse Matrix. The function creates a new math.type.Matrix object from an Array. A Matrix has utility functions to manipulate the data in the matrix, like getting the size and getting or setting values in the matrix.
Parameter dataType
Sparse Matrix data type

method splitUnit

splitUnit: (this: MathJsChain<Unit>, parts: Unit[]) => MathJsChain<Unit[]>;

Split a unit in an array of units whose sum is equal to the original unit.
Parameter parts
An array of strings or valueless units

method sqrt

sqrt: <T extends number | BigNumber | Complex | MathCollection<any> | Unit>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the square root of a value. For matrices, the function is evaluated element wise.

method sqrtm

sqrtm: <T extends MathCollection<any>>(A: MathJsChain<T>) => MathJsChain<T>;

Calculate the principal square root of a square matrix. The principal square root matrix X of another matrix A is such that X * X = A.

method square

square: <T extends unknown>(this: MathJsChain<T>) => MathJsChain<T>;

Compute the square of a value, x * x. For matrices, the function is evaluated element wise.

method squeeze

squeeze: <T extends MathCollection<any>>(x: MathJsChain<T>) => MathJsChain<T>;

Squeeze a matrix, remove inner and outer singleton dimensions from a matrix.

method std

std: {
    (
        this: MathJsChain<number[]>,
        dim?: number,
        normalization?: 'unbiased' | 'uncorrected' | 'biased'
    ): MathJsChain<number>;
    (
        this: MathJsChain<MathCollection<any>>,
        dimension?: number,
        normalization?: 'unbiased' | 'uncorrected' | 'biased'
    ): MathJsChain<number[]>;
    (
        this: MathJsChain<MathCollection<any>>,
        normalization: 'unbiased' | 'uncorrected' | 'biased'
    ): MathJsChain<number>;
};

Compute the standard deviation of a matrix or a list with values. The standard deviations is defined as the square root of the variance: std(A) = sqrt(variance(A)). In case of a (multi dimensional) array or matrix, the standard deviation over all elements will be calculated. Optionally, the type of normalization can be specified as second parameter. The parameter normalization can be one of the following values: 'unbiased' (default) The sum of squared errors is divided by (n - 1) 'uncorrected' The sum of squared errors is divided by n 'biased' The sum of squared errors is divided by (n + 1)
Parameter dim
A dimension to compute standard deviation.
Parameter normalization
Determines how to normalize the variance. Choose ‘unbiased’ (default), ‘uncorrected’, or ‘biased’. Default value: ‘unbiased’.
Returns
The standard deviation
Compute the standard deviation of a matrix or a list with values. The standard deviations is defined as the square root of the variance: std(A) = sqrt(variance(A)). In case of a (multi dimensional) array or matrix, the standard deviation over all elements will be calculated. Optionally, the type of normalization can be specified as second parameter. The parameter normalization can be one of the following values: 'unbiased' (default) The sum of squared errors is divided by (n - 1) 'uncorrected' The sum of squared errors is divided by n 'biased' The sum of squared errors is divided by (n + 1)
Parameter normalization
Determines how to normalize the variance. Choose ‘unbiased’ (default), ‘uncorrected’, or ‘biased’. Default value: ‘unbiased’.
Returns
The standard deviation
Compute the sum of a matrix or a list with values. In case of a (multi dimensional) array or matrix, the sum of all elements will be calculated.

method stirlingS2

stirlingS2: <T extends number | BigNumber>(
    this: MathJsChain<T>,
    k: number | BigNumber
) => MathJsChain<NoLiteralType<T>>;

The Stirling numbers of the second kind, counts the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets. stirlingS2 only takes integer arguments. The following condition must be enforced: k <= n. If n = k or k = 1, then s(n,k) = 1
Parameter k
Number of objects in the subset

method string

string: {
    (
        this: MathJsChain<MathNumericType | string | Unit | null>
    ): MathJsChain<string>;
    (this: MathJsChain<MathCollection<any>>): MathJsChain<MathCollection<any>>;
};

Create a string or convert any object into a string. Elements of Arrays and Matrices are processed element wise.

method subset

subset: <T extends string | MathCollection<any>>(
    this: MathJsChain<T>,
    index: Index,
    replacement?: any,
    defaultValue?: any
) => MathJsChain<T>;

Get or set a subset of a matrix or string.
Parameter index
For each dimension, an index or list of indices to get or set
Parameter replacement
An array, matrix, or scalar. If provided, the subset is replaced with replacement. If not provided, the subset is returned
Parameter defaultValue
Default value, filled in on new entries when the matrix is resized. If not provided, math.matrix elements will be left undefined. Default value: undefined.

method subtract

subtract: <T extends unknown>(this: MathJsChain<T>, y: T) => MathJsChain<T>;

Subtract two values, x - y. For matrices, the function is evaluated element wise.
Parameter y
Value to subtract from x

method sum

sum: {
    (
        this: MathJsChain<Array<number | BigNumber | Fraction>>
    ): MathJsChain<number>;
    (this: MathJsChain<MathCollection<any>>): MathJsChain<number>;
};

Compute the sum of a matrix or a list with values. In case of a (multi dimensional) array or matrix, the sum of all elements will be calculated.

method symbolicEqual

symbolicEqual: (
    this: MathJsChain<MathNode>,
    expr2: MathNode,
    options?: SimplifyOptions
) => MathJsChain<boolean>;

Determines if two expressions are symbolically equal, i.e. one is the result of valid algebraic manipulations on the other.
Parameter expr2
The second expression to compare
Parameter options
Optional option object, passed to simplify
Returns
{boolean} Returns true if a valid manipulation making the expressions equal is found.

method tan

tan: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the tangent of a value. tan(x) is equal to sin(x) / cos(x). For matrices, the function is evaluated element wise.

method tanh

tanh: <T extends number | BigNumber | Complex | MathCollection<any>>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Calculate the hyperbolic tangent of a value, defined as tanh(x) = (exp(2 * x) - 1) / (exp(2 * x) + 1). For matrices, the function is evaluated element wise.

method to

to: (
    this: MathJsChain<Unit | MathCollection>,
    unit: Unit | string
) => MathJsChain<Unit | MathCollection>;

Change the unit of a value. For matrices, the function is evaluated element wise.
Parameter unit
New unit. Can be a string like "cm" or a unit without value.

method toBest

toBest: {
    (this: MathJsChain<Unit>): MathJsChain<Unit>;
    (
        this: MathJsChain<Unit>,
        units: string[] | Unit[],
        options: object
    ): MathJsChain<Unit>;
};

Converts a unit to the most appropriate display unit. When no preferred units are provided, the function automatically find the best prefix. When preferred units are provided, it converts to the unit that gives a value closest to 1.
Parameter preferredUnits
Optional preferred target units
Parameter options
Optional options object

method trace

trace: (this: MathJsChain<MathCollection>) => MathJsChain<number>;

Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.

method transpose

transpose: <T extends MathCollection<any>>(x: MathJsChain<T>) => MathJsChain<T>;

Transpose a matrix. All values of the matrix are reflected over its main diagonal. Only two dimensional matrices are supported.

method typeOf

typeOf: (this: MathJsChain<any>) => MathJsChain<string>;

Determine the type of a variable.

method unaryMinus

unaryMinus: <T extends unknown>(this: MathJsChain<T>) => MathJsChain<T>;

Inverse the sign of a value, apply a unary minus operation. For matrices, the function is evaluated element wise. Boolean values and strings will be converted to a number. For complex numbers, both real and complex value are inverted.

method unaryPlus

unaryPlus: <T extends unknown>(this: MathJsChain<T>) => MathJsChain<T>;

Unary plus operation. Boolean values and strings will be converted to a number, numeric values will be returned as is. For matrices, the function is evaluated element wise.

method unequal

unequal: (
    this: MathJsChain<MathType | string>,
    y: MathType | string
) => MathJsChain<boolean | MathCollection>;

Test whether two values are unequal. The function tests whether the relative difference between x and y is larger than the configured relTol and absTol. The function cannot be used to compare values smaller than approximately 2.22e-16. For matrices, the function is evaluated element wise. In case of complex numbers, x.re must unequal y.re, or x.im must unequal y.im. Values null and undefined are compared strictly, thus null is unequal with everything except null, and undefined is unequal with everything except undefined.
Parameter y
Second value to vcompare

method unit

unit: {
    (this: MathJsChain<string>, unit?: string): MathJsChain<Unit>;
    (this: MathJsChain<any>, unit?: string): MathJsChain<Unit>;
    (this: MathJsChain<MathCollection<any>>): MathJsChain<Unit[]>;
};

Create a unit. Depending on the passed arguments, the function will create and return a new math.type.Unit object. When a matrix is provided, all elements will be converted to units.
Parameter unit
The unit to be created

method usolve

usolve: {
    (this: MathJsChain<Matrix>, b: MathCollection): MathJsChain<Matrix>;
    (this: MathJsChain<MathArray<any>>, b: MathCollection<any>): MathJsChain<
        MathArray<any>
    >;
};

Solves the linear equation system by backward substitution. Matrix must be an upper triangular matrix. U * x = b
Parameter b
A column vector with the b values

method variance

variance: {
    (
        this: MathJsChain<Array<Array<number | BigNumber | Fraction>>>
    ): MathJsChain<number>;
    (
        this: MathJsChain<MathCollection<any>>,
        dimension?: number,
        normalization?: 'unbiased' | 'uncorrected' | 'biased'
    ): MathJsChain<number[]>;
    (
        this: MathJsChain<MathCollection<any>>,
        normalization: 'unbiased' | 'uncorrected' | 'biased'
    ): MathJsChain<number>;
};

Compute the variance of a matrix or a list with values. In case of a (multi dimensional) array or matrix, the variance over all elements will be calculated. Optionally, the type of normalization can be specified as second parameter. The parameter normalization can be one of the following values: 'unbiased' (default) The sum of squared errors is divided by (n - 1) 'uncorrected' The sum of squared errors is divided by n 'biased' The sum of squared errors is divided by (n + 1) Note that older browser may not like the variable name var. In that case, the function can be called as math['var'](...) instead of math.variance(...).
Parameter dim
a dimension to compute variance.
Parameter normalization
normalization Determines how to normalize the variance. Choose ‘unbiased’ (default), ‘uncorrected’, or ‘biased’. Default value: ‘unbiased’.
Returns
The variance
Compute the variance of a matrix or a list with values. In case of a (multi dimensional) array or matrix, the variance over all elements will be calculated. Optionally, the type of normalization can be specified as second parameter. The parameter normalization can be one of the following values: 'unbiased' (default) The sum of squared errors is divided by (n - 1) 'uncorrected' The sum of squared errors is divided by n 'biased' The sum of squared errors is divided by (n + 1) Note that older browser may not like the variable name var. In that case, the function can be called as math['var'](...) instead of math.variance(...).
Parameter normalization
normalization Determines how to normalize the variance. Choose ‘unbiased’ (default), ‘uncorrected’, or ‘biased’. Default value: ‘unbiased’.
Returns
The variance

method xgcd

xgcd: (
    this: MathJsChain<number | BigNumber>,
    b: number | BigNumber
) => MathJsChain<MathArray>;

Calculate the extended greatest common divisor for two values. See http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm.
Parameter b
An integer number

method xor

xor: (
    this: MathJsChain<
        number | BigNumber | bigint | Complex | Unit | MathCollection
    >,
    y: number | BigNumber | bigint | Complex | Unit | MathCollection
) => MathJsChain<boolean | MathCollection>;

Logical xor. Test whether one and only one value is defined with a nonzero/nonempty value. For matrices, the function is evaluated element wise.
Parameter y
Second value to xor

method zeros

zeros: (
    this: MathJsChain<number | number[] | BigNumber | BigNumber[]>,
    format?: string
) => MathJsChain<MathCollection>;

Create a matrix filled with zeros. The created matrix can have one or multiple dimensions.
Parameter format
The matrix storage format
Returns
A matrix filled with zeros

method zeta

zeta: <T extends number | BigNumber | Complex>(
    this: MathJsChain<T>
) => MathJsChain<T>;

Compute the Riemann Zeta function of a value using an infinite series and Riemann's Functional equation.

method zpk2tf

zpk2tf: <T extends MathCollection<any>>(
    this: MathJsChain<T>,
    p: T,
    k?: number
) => MathJsChain<T>;

Compute the transfer function of a zero-pole-gain model.

interface MathJsFactory

interface MathJsFactory {}

*********************************************************************** Factory and Dependencies **********************************************************************

property create

create: (
    factories: FactoryFunctionMap,
    config?: ConfigOptions
) => MathJsInstance;

property factory

factory: <T, TDeps extends readonly MathJsFunctionName[]>(
    name: string,
    dependencies: TDeps,
    create: (
        injected: Pick<
            MathJsInstance,
            Extract<MathJsFunctionName, TDeps[number]>
        >
    ) => T,
    // eslint-disable-next-line @typescript-eslint/no-explicit-any
    meta?: any
) => FactoryFunction<T>;

interface MathJsInstance

interface MathJsInstance extends MathJsFactory {}

property AccessorNode

AccessorNode: AccessorNodeCtor;

property apply

apply: MathJsInstance['mapSlices'];

Deprecated
backwards-compatibility old name of mapSlices

property ArrayNode

ArrayNode: ArrayNodeCtor;

property AssignmentNode

AssignmentNode: AssignmentNodeCtor;

property BlockNode

BlockNode: BlockNodeCtor;

property ConditionalNode

ConditionalNode: ConditionalNodeCtor;

property config

config: (options: ConfigOptions) => ConfigOptions;

Set configuration options for math.js, and get current options. Will emit a ‘config’ event, with arguments (curr, prev, changes).
Parameter options
Available options: {number} relTol Minimum relative difference between two compared values, used by all comparison functions. {number} absTol Minimum absolute difference between two compared values, used by all comparison functions. {string} matrix A string ‘Matrix’ (default) or ‘Array’. {string} number A string ‘number’ (default), ‘BigNumber’, or ‘Fraction’ {number} precision The number of significant digits for BigNumbers. Not applicable for Numbers. {string} parenthesis How to display parentheses in LaTeX and string output. {string} randomSeed Random seed for seeded pseudo random number generator. Set to null to randomly seed.
Returns
Returns the current configuration

property ConstantNode

ConstantNode: ConstantNodeCtor;

property e

e: number;

property expression

expression: MathNode;

property FunctionAssignmentNode

FunctionAssignmentNode: FunctionAssignmentNodeCtor;

property FunctionNode

FunctionNode: FunctionNodeCtor;

property i

i: number;

property IndexNode

IndexNode: IndexNodeCtor;

property Infinity

Infinity: number;

property isArray

isArray: ArrayConstructor['isArray'];

property LN10

LN10: number;

property LN2

LN2: number;

property LOG10E

LOG10E: number;

property LOG2E

LOG2E: number;

property Matrix

Matrix: MatrixCtor;

property NaN

NaN: number;

property Node

Node: NodeCtor;

property ObjectNode

ObjectNode: ObjectNodeCtor;

property OperatorNode

OperatorNode: OperatorNodeCtor;

property ParenthesisNode

ParenthesisNode: ParenthesisNodeCtor;

property parse

parse: ParseFunction;

Parse an expression. Returns a node tree, which can be evaluated by invoking node.evaluate();

property phi

phi: number;

property pi

pi: number;

property RangeNode

RangeNode: RangeNodeCtor;

property RelationalNode

RelationalNode: RelationalNodeCtor;

property simplify

simplify: Simplify;

Simplify an expression tree.
Parameter expr
The expression to be simplified
Parameter rules
(optional) A list of rules are applied to an expression, repeating over the list until no further changes are made. It’s possible to pass a custom set of rules to the function as second argument. A rule can be specified as an object, string, or function.
Parameter scope
(optional) Scope to variables
Parameter options
(optional) An object with simplify options
Returns
Returns the simplified form of expr

property SQRT1_2

SQRT1_2: number;

property SQRT2

SQRT2: number;

property SymbolNode

SymbolNode: SymbolNodeCtor;

property tau

tau: number;

property typed

typed: (
    name: string,
    // eslint-disable-next-line @typescript-eslint/no-explicit-any
    signatures: Record<string, (...args: any[]) => any>
    // eslint-disable-next-line @typescript-eslint/no-explicit-any
) => (...args: any[]) => any;

Create a typed-function which checks the types of the arguments and can match them against multiple provided signatures. The typed-function automatically converts inputs in order to find a matching signature. Typed functions throw informative errors in case of wrong input arguments.
Parameter name
Optional name for the typed-function
Parameter signatures
Object with one or multiple function signatures
Returns
The created typed-function.

property uninitialized

uninitialized: any;

If null were to be included in this interface, it would be auto-suggested as an import in VSCode. This causes issues because null is not a valid label.
See Also
- https://github.com/josdejong/mathjs/issues/2019

property Unit

Unit: UnitCtor;

property version

version: string;

method abs

abs: <T extends unknown>(x: T) => T;

Calculate the absolute value of a number. For matrices, the function is evaluated element wise.
Parameter x
A number or matrix for which to get the absolute value
Returns
Absolute value of x

method acos

acos: {
    (x: number): number | Complex;
    <T extends BigNumber | Complex>(x: T): T;
};

Calculate the inverse cosine of a value.
Parameter x
Function input
Returns
The arc cosine of x

method acosh

acosh: {
    (x: number): number | Complex;
    <T extends BigNumber | Complex>(x: T): T;
};

Calculate the hyperbolic arccos of a value, defined as acosh(x) = ln(sqrt(x^2 - 1) + x).
Parameter x
Function input
Returns
The hyperbolic arccosine of x

method acot

acot: { (x: number): number; <T extends BigNumber | Complex>(x: T): T };

Calculate the inverse cotangent of a value.
Parameter x
Function input
Returns
The arc cotangent of x

method acoth

acoth: { (x: number): number; <T extends BigNumber | Complex>(x: T): T };

Calculate the inverse hyperbolic tangent of a value, defined as acoth(x) = (ln((x+1)/x) + ln(x/(x-1))) / 2.
Parameter x
Function input
Returns
The inverse hyperbolic tangent of x

method acsc

acsc: {
    (x: number): number | Complex;
    <T extends BigNumber | Complex>(x: T): T;
};

Calculate the inverse cosecant of a value.
Parameter x
Function input
Returns
The arc cosecant of x

method acsch

acsch: { (x: number): number; <T extends BigNumber | Complex>(x: T): T };

Calculate the inverse hyperbolic cosecant of a value, defined as acsch(x) = ln(1/x + sqrt(1/x^2 + 1)).
Parameter x
Function input
Returns
The inverse hyperbolic cosecant of x

method add

add: {
    <T extends unknown>(x: T, y: T): T;
    <T extends unknown>(x: T, y: T, ...values: T[]): T;
    (x: any, y: any): any;
    (x: any, y: any, ...values: any[]): any;
};

Add two values, x + y. For matrices, the function is evaluated element wise.
Parameter x
First value to add
Parameter y
Second value to add
Returns
Sum of x and y

method and

and: (
    x: number | BigNumber | bigint | Complex | Unit | MathCollection,
    y: number | BigNumber | bigint | Complex | Unit | MathCollection
) => boolean | MathCollection;

Logical and. Test whether two values are both defined with a nonzero/nonempty value. For matrices, the function is evaluated element wise.
Parameter x
First value to and
Parameter y
Second value to and
Returns
Returns true when both inputs are defined with a nonzero/nonempty value.

method arg

arg: {
    (x: number | Complex): number;
    (x: BigNumber | Complex): BigNumber;
    <T extends MathCollection<any>>(x: T): T;
};

Compute the argument of a complex value. For a complex number a + bi, the argument is computed as atan2(b, a). For matrices, the function is evaluated element wise.
Parameter x
A complex number or array with complex numbers
Returns
The argument of x

method asec

asec: {
    (x: number): number | Complex;
    <T extends BigNumber | Complex>(x: T): T;
};

Calculate the inverse secant of a value.
Parameter x
Function input
Returns
The arc secant of x

method asech

asech: {
    (x: number): number | Complex;
    <T extends BigNumber | Complex>(x: T): T;
};

Calculate the hyperbolic arcsecant of a value, defined as asech(x) = ln(sqrt(1/x^2 - 1) + 1/x).
Parameter x
Function input
Returns
The hyperbolic arcsecant of x

method asin

asin: {
    (x: number): number | Complex;
    <T extends BigNumber | Complex>(x: T): T;
};

Calculate the inverse sine of a value.
Parameter x
Function input
Returns
The arc sine of x

method asinh

asinh: <T extends number | BigNumber | Complex>(x: T) => T;

Calculate the hyperbolic arcsine of a value, defined as asinh(x) = ln(x + sqrt(x^2 + 1)).
Parameter x
Function input
Returns
The hyperbolic arcsine of x

method atan

atan: <T extends number | BigNumber | Complex>(x: T) => T;

Calculate the inverse tangent of a value.
Parameter x
Function input
Returns
The arc tangent of x

method atan2

atan2: <T extends number | MathCollection<any>>(y: T, x: T) => T;

Calculate the inverse tangent function with two arguments, y/x. By providing two arguments, the right quadrant of the computed angle can be determined. For matrices, the function is evaluated element wise.
Parameter x
Function input
Returns
Four quadrant inverse tangent

method atanh

atanh: {
    (x: number): number | Complex;
    <T extends BigNumber | Complex>(x: T): T;
};

Calculate the hyperbolic arctangent of a value, defined as atanh(x) = ln((1 + x)/(1 - x)) / 2.
Parameter x
Function input
Returns
The hyperbolic arctangent of x

method bellNumbers

bellNumbers: <T extends number | BigNumber>(n: T) => T;

The Bell Numbers count the number of partitions of a set. A partition is a pairwise disjoint subset of S whose union is S. bellNumbers only takes integer arguments. The following condition must be enforced: n >= 0
Parameter n
Total number of objects in the set
Returns
B(n)

method bigint

bigint: {
    (
        x?: number | string | Fraction | BigNumber | bigint | boolean | null
    ): bigint;
    <T extends MathCollection<any>>(x: T): T;
};

Create a bigint, which can store integers with arbitrary precision. When a matrix is provided, all elements will be converted to bigint.
Parameter x
Value for the integer, 0 by default.
Returns
The created bigint

method bignumber

bignumber: {
    (
        x?:
            | number
            | string
            | Fraction
            | BigNumber
            | bigint
            | Unit
            | boolean
            | null
    ): BigNumber;
    <T extends MathCollection<any>>(x: T): T;
};

Create a BigNumber, which can store numbers with arbitrary precision. When a matrix is provided, all elements will be converted to BigNumber.
Parameter x
Value for the big number, 0 by default.
Returns
The created bignumber

method bitAnd

bitAnd: <T extends number | bigint | BigNumber | MathCollection<any>>(
    x: T,
    y: number | BigNumber | bigint | MathCollection
) => NoLiteralType<T>;

Bitwise AND two values, x & y. For matrices, the function is evaluated element wise.
Parameter x
First value to and
Parameter y
Second value to and
Returns
AND of x and y

method bitNot

bitNot: <T extends number | bigint | BigNumber | MathCollection<any>>(x: T) => T;

Bitwise NOT value, ~x. For matrices, the function is evaluated element wise. For units, the function is evaluated on the best prefix base.
Parameter x
Value to not
Returns
NOT of x

method bitOr

bitOr: <T extends number | bigint | BigNumber | MathCollection<any>>(
    x: T,
    y: T
) => T;

Bitwise OR two values, x | y. For matrices, the function is evaluated element wise. For units, the function is evaluated on the lowest print base.
Parameter x
First value to or
Parameter y
Second value to or
Returns
OR of x and y

method bitXor

bitXor: <T extends number | bigint | BigNumber | MathCollection<any>>(
    x: T,
    y: number | BigNumber | bigint | MathCollection
) => NoLiteralType<T>;

Bitwise XOR two values, x ^ y. For matrices, the function is evaluated element wise.
Parameter x
First value to xor
Parameter y
Second value to xor
Returns
XOR of x and y

method boolean

boolean: {
    (x: string | number | boolean | null): boolean;
    (x: MathCollection<any>): MathCollection<any>;
};

Create a boolean or convert a string or number to a boolean. In case of a number, true is returned for non-zero numbers, and false in case of zero. Strings can be 'true' or 'false', or can contain a number. When value is a matrix, all elements will be converted to boolean.
Parameter x
A value of any type
Returns
The boolean value

method catalan

catalan: <T extends number | BigNumber>(n: T) => T;

The Catalan Numbers enumerate combinatorial structures of many different types. catalan only takes integer arguments. The following condition must be enforced: n >= 0
Parameter n
nth Catalan number
Returns
Cn(n)

method cbrt

cbrt: {
    (x: Complex, allRoots?: boolean): Complex;
    <T extends number | BigNumber | Unit>(x: T): T;
};

Calculate the cubic root of a value.
Parameter x
Value for which to calculate the cubic root.
Parameter allRoots
Optional, false by default. Only applicable when x is a number or complex number. If true, all complex roots are returned, if false (default) the principal root is returned.
Returns
Returns the cubic root of x

method ceil

ceil: {
    <T extends unknown>(x: T, n?: number | BigNumber): NoLiteralType<T>;
    <U extends MathCollection<any>>(x: any, n: U): U;
    <U extends MathCollection<Unit>>(x: U, unit: Unit): U;
    (x: Unit, unit: Unit): Unit;
    (x: Unit, n: number | BigNumber, unit: Unit): Unit;
    <U extends MathCollection<Unit>>(x: U, n: number | BigNumber, unit: Unit): U;
};

Round a value towards plus infinity If x is complex, both real and imaginary part are rounded towards plus infinity. For matrices, the function is evaluated element wise.
Parameter x
Number to be rounded
Parameter n
Number of decimals Default value: 0.
Returns
Rounded value

method chain

chain: <TValue>(value?: TValue) => MathJsChain<TValue>;

Wrap any value in a chain, allowing to perform chained operations on the value. All methods available in the math.js library can be called upon the chain, and then will be evaluated with the value itself as first argument. The chain can be closed by executing chain.done(), which returns the final value. The chain has a number of special functions: done() Finalize the chain and return the chain's value. valueOf() The same as done() toString() Executes math.format() onto the chain's value, returning a string representation of the value.
Parameter value
A value of any type on which to start a chained operation.
Returns
The created chain

method clone

clone: <TType>(x: TType) => TType;

Clone an object.
Parameter x
Object to be cloned
Returns
A clone of object x

method column

column: <T extends MathCollection<any>>(value: T, column: number) => T;

Return a column from a Matrix.
Parameter value
An array or matrix
Parameter column
The index of the column
Returns
The retrieved column

method combinations

combinations: <T extends number | BigNumber>(
    n: T,
    k: number | BigNumber
) => NoLiteralType<T>;

Compute the number of ways of picking k unordered outcomes from n possibilities. Combinations only takes integer arguments. The following condition must be enforced: k <= n.
Parameter n
Total number of objects in the set
Parameter k
Number of objects in the subset
Returns
Number of possible combinations

method compare

compare: (
    x: MathType | string,
    y: MathType | string
) => number | BigNumber | Fraction | MathCollection;

Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x == y. x and y are considered equal when the relative difference between x and y is smaller than the configured relTol and absTol. The function cannot be used to compare values smaller than approximately 2.22e-16. For matrices, the function is evaluated element wise.
Parameter x
First value to compare
Parameter y
Second value to compare
Returns
Returns the result of the comparison: 1 when x > y, -1 when x < y, and 0 when x == y.

method compareNatural

compareNatural: (x: any, y: any) => number;

Compare two values of any type in a deterministic, natural way. For numeric values, the function works the same as math.compare. For types of values that can’t be compared mathematically, the function compares in a natural way.
Parameter x
First value to compare
Parameter y
Second value to compare
Returns
Returns the result of the comparison: 1 when x > y, -1 when x < y, and 0 when x == y.

method compareText

compareText: (
    x: string | MathCollection,
    y: string | MathCollection
) => number | MathCollection;

Compare two strings lexically. Comparison is case sensitive. Returns 1 when x > y, -1 when x < y, and 0 when x == y. For matrices, the function is evaluated element wise.
Parameter x
First string to compare
Parameter y
Second string to compare
Returns
Returns the result of the comparison: 1 when x > y, -1 when x < y, and 0 when x == y.

method compile

compile: {
    (expr: MathExpression): EvalFunction;
    (exprs: MathExpression[]): EvalFunction[];
};

Parse and compile an expression. Returns a an object with a function evaluate([scope]) to evaluate the compiled expression.
Parameter expr
The expression to be compiled
Returns
An object with the compiled expression
Parameter exprs
The expressions to be compiled
Returns
An array of objects with the compiled expressions

method complex

complex: {
    (arg?: MathNumericType | string | PolarCoordinates): Complex;
    (arg?: MathCollection<any>): MathCollection<any>;
    (re: number, im: number): Complex;
};

Create a complex value or convert a value to a complex value.
Parameter args
Arguments specifying the real and imaginary part of the complex number
Returns
Returns a complex value
Parameter re
Argument specifying the real part of the complex number
Parameter im
Argument specifying the imaginary part of the complex number
Returns
Returns a complex value

method composition

composition: <T extends number | BigNumber>(
    n: T,
    k: number | BigNumber
) => NoLiteralType<T>;

The composition counts of n into k parts. Composition only takes integer arguments. The following condition must be enforced: k <= n.
Parameter n
Total number of objects in the set
Parameter k
Number of objects in the subset
Returns
Returns the composition counts of n into k parts.

method concat

concat: (...args: Array<MathCollection | number | BigNumber>) => MathCollection;

Concatenate two or more matrices. dim: number is a zero-based dimension over which to concatenate the matrices. By default the last dimension of the matrices.
Parameter args
Two or more matrices
Returns
Concatenated matrix

method conj

conj: <T extends number | BigNumber | Complex | MathCollection<any>>(
    x: T
) => NoLiteralType<T>;

Compute the complex conjugate of a complex value. If x = a+bi, the complex conjugate of x is a - bi. For matrices, the function is evaluated element wise.
Parameter x
A complex number or array with complex numbers
Returns
The complex conjugate of x

method corr

corr: (x: MathCollection, y: MathCollection) => MathType;

Calculate the correlation coefficient between two matrix.
Parameter x
The first array or matrix to compute correlation coefficient
Parameter y
The second array or matrix to compute correlation coefficient
Returns
correlation coefficient

method cos

cos: { (x: number | Unit): number; <T extends BigNumber | Complex>(x: T): T };

Calculate the cosine of a value.
Parameter x
Function input
Returns
The cosine of x

method cosh

cosh: { (x: number | Unit): number; <T extends BigNumber | Complex>(x: T): T };

Calculate the hyperbolic cosine of a value, defined as cosh(x) = 1/2 * (exp(x) + exp(-x)).
Parameter x
Function input
Returns
The hyperbolic cosine of x

method cot

cot: { (x: number | Unit): number; <T extends BigNumber | Complex>(x: T): T };

Calculate the cotangent of a value. cot(x) is defined as 1 / tan(x).
Parameter x
Function input
Returns
The cotangent of x

method coth

coth: { (x: number | Unit): number; <T extends BigNumber | Complex>(x: T): T };

Calculate the hyperbolic cotangent of a value, defined as coth(x) = 1 / tanh(x).
Parameter x
Function input
Returns
The hyperbolic cotangent of x

method count

count: (x: MathCollection | string) => number;

Count the number of elements of a matrix, array or string.
Parameter x
A matrix, array or string.
Returns
The number of members passed in parameters

method createUnit

createUnit: {
    (
        name: string,
        definition?: string | UnitDefinition | Unit,
        options?: CreateUnitOptions
    ): Unit;
    (
        units: Record<string, string | Unit | UnitDefinition>,
        options?: CreateUnitOptions
    ): Unit;
};

Create a user-defined unit and register it with the Unit type.
Parameter name
The name of the new unit. Must be unique. Example: ‘knot’
Parameter definition
Definition of the unit in terms of existing units. For example, ‘0.514444444 m / s’.
Parameter options
(optional) An object containing any of the following properties:- prefixes {string} “none”, “short”, “long”, “binary_short”, or “binary_long”. The default is “none”.- aliases {Array} Array of strings. Example: [‘knots’, ‘kt’, ‘kts’]- offset {Numeric} An offset to apply when converting from the unit. For example, the offset for celsius is 273.15. Default is 0.
Returns
The new unit
Create a user-defined unit and register it with the Unit type.
Parameter units
Definition of the unit
Parameter options
Returns
The new unit

method cross

cross: (x: MathCollection, y: MathCollection) => MathCollection;

Calculate the cross product for two vectors in three dimensional space. The cross product of A = [a1, a2, a3] and B =[b1, b2, b3] is defined as: cross(A, B) = [ a2 * b3 - a3 * b2, a3 * b1 - a1 * b3, a1 * b2 - a2 * b1 ]
Parameter x
First vector
Parameter y
Second vector
Returns
Returns the cross product of x and y

method csc

csc: { (x: number | Unit): number; <T extends BigNumber | Complex>(x: T): T };

Calculate the cosecant of a value, defined as csc(x) = 1/sin(x).
Parameter x
Function input
Returns
The cosecant hof x

method csch

csch: { (x: number | Unit): number; <T extends BigNumber | Complex>(x: T): T };

Calculate the hyperbolic cosecant of a value, defined as csch(x) = 1 / sinh(x).
Parameter x
Function input
Returns
The hyperbolic cosecant of x

method cube

cube: <T extends unknown>(x: T) => T;

Compute the cube of a value, x * x * x. For matrices, the function is evaluated element wise.
Parameter x
Number for which to calculate the cube
Returns
Cube of x

method cumsum

cumsum: {
    (...args: MathType[]): MathType[];
    (array: MathCollection<any>, dim?: number): MathCollection<any>;
};

Compute the cumulative sum of a matrix or a list with values. In case of a (multi dimensional) array or matrix, the cumulative sums along a specified dimension (defaulting to the first) will be calculated.
Parameter args
A single matrix or multiple scalar values
Returns
The cumulative sums of the the values.
Parameter array
A single matrix
Parameter dim
The dimension along which to sum (defaults to 0)
Returns
The cumulative sums along the given dimension

method deepEqual

deepEqual: (x: MathType, y: MathType) => MathType;

Test element wise whether two matrices are equal. The function accepts both matrices and scalar values.
Parameter x
First matrix to compare
Parameter y
Second amtrix to compare
Returns
Returns true when the input matrices have the same size and each of their elements is equal.

method derivative

derivative: (
    expr: MathNode | string,
    variable: MathNode | string,
    options?: { simplify: boolean }
) => MathNode;

Parameter expr
The expression to differentiate
Parameter variable
The variable over which to differentiate
Parameter options
There is one option available, simplify, which is true by default. When false, output will not be simplified.
Returns
The derivative of expr

method det

det: (x: MathCollection) => number;

Calculate the determinant of a matrix.
Parameter x
A Matrix
Returns
the determinant of x

method diag

diag: {
    (X: MathCollection, format?: string): Matrix;
    (
        X: MathCollection<any>,
        k: number | BigNumber,
        format?: string
    ): MathCollection<any>;
};

Create a diagonal matrix or retrieve the diagonal of a matrix. When x is a vector, a matrix with vector x on the diagonal will be returned. When x is a two dimensional matrix, the matrixes kth diagonal will be returned as vector. When k is positive, the values are placed on the super diagonal. When k is negative, the values are placed on the sub diagonal.
Parameter X
A two dimensional matrix or a vector
Parameter k
The diagonal where the vector will be filled in or retrieved. Default value: 0.
Parameter format
The matrix storage format. Default value: 'dense'.
Returns
Diagonal matrix from input vector, or diagonal from input matrix

method distance

distance: (
    x: MathCollection | object,
    y: MathCollection | object,
    z?: MathCollection | object
) => number | BigNumber;

Calculates: The eucledian distance between two points in 2 and 3 dimensional spaces. Distance between point and a line in 2 and 3 dimensional spaces. Pairwise distance between a set of 2D or 3D points NOTE: When substituting coefficients of a line(a, b and c), use ax + by + c = 0 instead of ax + by = c For parametric equation of a 3D line, x0, y0, z0, a, b, c are from: (x−x0, y−y0, z−z0) = t(a, b, c)
Parameter x
Coordinates of the first point
Parameter y
Coordinates of the second point OR coefficients of a line in 3D OR first end-point of a line if the calculation is for distance between point and a line in 2D
Parameter z
Coordinates of second end-point of a line if the calculation is for distance between point and a line in 2D
Returns
Returns the distance from two/three points

method divide

divide: {
    (x: Unit, y: Unit): Unit | number;
    (x: Unit, y: number): Unit;
    (x: number, y: number): number;
    (x: any, y: any): any;
};

Divide two values, x / y. To divide matrices, x is multiplied with the inverse of y: x * inv(y).
Parameter x
Numerator
Parameter y
Denominator
Returns
Quotient, x / y

method dot

dot: (x: MathCollection, y: MathCollection) => number;

Calculate the dot product of two vectors. The dot product of A = [a1, a2, a3, ..., an] and B = [b1, b2, b3, ..., bn] is defined as: dot(A, B) = a1 * b1 + a2 * b2 + a3 * b3 + ... + an * bn
Parameter x
First vector
Parameter y
Second vector
Returns
Returns the dot product of x and y

method dotDivide

dotDivide: {
    <T extends MathCollection<any>>(x: T, y: MathType): T;
    <T extends MathCollection<any>>(x: any, y: T): T;
    (x: Unit, y: any): Unit;
    (x: any, y: Unit): Unit;
    (x: any, y: any): any;
};

Divide two matrices element wise. The function accepts both matrices and scalar values.
Parameter x
Numerator
Parameter y
Denominator
Returns
Quotient, x ./ y

method dotMultiply

dotMultiply: {
    <T extends MathCollection<any>>(x: T, y: MathType): T;
    <T extends MathCollection<any>>(x: any, y: T): T;
    (x: Unit, y: any): Unit;
    (x: any, y: Unit): Unit;
    (x: any, y: any): any;
};

Multiply two matrices element wise. The function accepts both matrices and scalar values.
Parameter x
Left hand value
Parameter y
Right hand value
Returns
Multiplication of x and y

method dotPow

dotPow: <T extends unknown>(x: T, y: MathType) => T;

Calculates the power of x to y element wise.
Parameter x
The base
Parameter y
The exponent
Returns
The value of x to the power y

method eigs

eigs: {
    (
        x: MathCollection,
        opts?:
            | number
            | BigNumber
            | { precision?: number | BigNumber; eigenvectors?: true }
    ): {
        values: MathCollection;
        eigenvectors: { value: number | BigNumber; vector: MathCollection }[];
    };
    (
        x: MathCollection<any>,
        opts: { eigenvectors: false; precision?: number | BigNumber }
    ): { values: MathCollection<any> };
};

Compute eigenvalues and eigenvectors of a matrix. The eigenvalues are sorted by their absolute value, ascending. An eigenvalue with multiplicity k will be listed k times. The eigenvectors are returned as an array of objects, each with a value and a vector. If the algorithm fails to converge, it will throw an error – in that case, however, you may still find useful information in err.values and err.vectors
Parameter x
Matrix to be diagonalized
Parameter prec
Precision, default value: 1e-15
Returns
Object containing an array of eigenvalues and a matrix with eigenvectors as columns.

method equal

equal: (x: MathType | string, y: MathType | string) => boolean | MathCollection;

Test whether two values are equal.
The function tests whether the relative difference between x and y is smaller than the configured relTol and absTol. The function cannot be used to compare values smaller than approximately 2.22e-16. For matrices, the function is evaluated element wise. In case of complex numbers, x.re must equal y.re, and x.im must equal y.im. Values null and undefined are compared strictly, thus null is only equal to null and nothing else, and undefined is only equal to undefined and nothing else.
Parameter x
First value to compare
Parameter y
Second value to compare
Returns
Returns true when the compared values are equal, else returns false

method equalText

equalText: (
    x: string | MathCollection,
    y: string | MathCollection
) => number | MathCollection;

Check equality of two strings. Comparison is case sensitive. For matrices, the function is evaluated element wise.
Parameter x
First string to compare
Parameter y
Second string to compare
Returns
Returns true if the values are equal, and false if not.

method erf

erf: <T extends number | MathCollection<any>>(x: T) => NoLiteralType<T>;

Compute the erf function of a value using a rational Chebyshev approximations for different intervals of x.
Parameter x
A real number
Returns
The erf of x

method evaluate

evaluate: {
    (expr: MathExpression | Matrix, scope?: MathScope): any;
    (expr: MathExpression[], scope?: MathScope<any>): any[];
};

Evaluate an expression.
Parameter expr
The expression to be evaluated
Parameter scope
Scope to read/write variables
Returns
The result of the expression

method exp

exp: <T extends number | BigNumber | Complex>(x: T) => T;

Calculate the exponent of a value. For matrices, the function is evaluated element wise.
Parameter x
A number or matrix to exponentiate
Returns
Exponent of x

method expm

expm: (x: Matrix) => Matrix;

Compute the matrix exponential, expm(A) = e^A. The matrix must be square. Not to be confused with exp(a), which performs element-wise exponentiation. The exponential is calculated using the Padé approximant with scaling and squaring; see “Nineteen Dubious Ways to Compute the Exponential of a Matrix,” by Moler and Van Loan.
Parameter x
A square matrix
Returns
The exponential of x

method expm1

expm1: <T extends number | BigNumber | Complex>(x: T) => T;

Calculate the value of subtracting 1 from the exponential value. For matrices, the function is evaluated element wise.
Parameter x
A number or matrix to apply expm1
Returns
Exponent of x

method factorial

factorial: <T extends number | BigNumber | MathCollection<any>>(
    n: T
) => NoLiteralType<T>;

Compute the factorial of a value Factorial only supports an integer value as argument. For matrices, the function is evaluated element wise.
Parameter n
An integer number
Returns
The factorial of n

method fft

fft: <T extends MathCollection<any>>(arr: T) => T;

Calculate N-dimensional Fourier transform
Parameter arr
An array or matrix {Array | Matrix} N-dimensional Fourier transformation of the array

method filter

filter: (
    x: MathCollection | string[],
    test:
        | RegExp
        | ((
              value: any,
              index: number[],
              matrix: MathCollection | string[]
          ) => boolean)
) => MathCollection;

Filter the items in an array or one dimensional matrix.
Parameter x
A one dimensional matrix or array to filter
Parameter test
A function or regular expression to test items. All entries for which test returns true are returned. When test is a function, it is invoked with three parameters: the value of the element, the index of the element, and the matrix/array being traversed. The function must return a boolean.

method fix

fix: {
    <T extends unknown>(x: T, n?: number | BigNumber): NoLiteralType<T>;
    <U extends MathCollection<any>>(x: any, n: U): U;
    <U extends MathCollection<Unit>>(x: U, unit: Unit): U;
    (x: Unit, unit: Unit): Unit;
    (x: Unit, n: number | BigNumber, unit: Unit): Unit;
    <U extends MathCollection<Unit>>(x: U, n: number | BigNumber, unit: Unit): U;
};

Round a value towards zero. For matrices, the function is evaluated element wise.
Parameter x
Number to be rounded
Parameter n
Number of decimals Default value: 0.
Returns
Rounded value

method flatten

flatten: <T extends MathCollection<any>>(x: T) => T;

Flatten a multi dimensional matrix into a single dimensional matrix.
Parameter x
Matrix to be flattened
Returns
Returns the flattened matrix

method floor

floor: {
    <T extends unknown>(x: T, n?: number | BigNumber): NoLiteralType<T>;
    <U extends MathCollection<any>>(x: any, n: U): U;
    <U extends MathCollection<Unit>>(x: U, unit: Unit): U;
    (x: Unit, unit: Unit): Unit;
    (x: Unit, n: number | BigNumber, unit: Unit): Unit;
    <U extends MathCollection<Unit>>(x: U, n: number | BigNumber, unit: Unit): U;
};

Round a value towards minus infinity. For matrices, the function is evaluated element wise.
Parameter x
Number to be rounded
Parameter n
Number of decimals Default value: 0.
Returns
Rounded value

method forEach

forEach: <T extends MathCollection<any>>(
    x: T,
    callback: (value: any, index: number[], matrix: T) => void
) => void;

Iterate over all elements of a matrix/array, and executes the given callback function.
Parameter x
The matrix to iterate on.
Parameter callback
The callback function is invoked with three parameters: the value of the element, the index of the element, and the Matrix/array being traversed.

method format

format: (
    value: any,
    options?: number | BigNumber | FormatOptions | ((item: any) => string),
    callback?: (value: any) => string
) => string;

Format a value of any type into a string.
Parameter value
The value to be formatted
Parameter options
An object with formatting options.
Parameter callback
A custom formatting function, invoked for all numeric elements in value, for example all elements of a matrix, or the real and imaginary parts of a complex number. This callback can be used to override the built-in numeric notation with any type of formatting. Function callback is called with value as parameter and must return a string.
Returns
The formatted value
See Also
- http://mathjs.org/docs/reference/functions/format.html

method fraction

fraction: {
    (
        value:
            | number
            | string
            | BigNumber
            | bigint
            | Unit
            | Fraction
            | FractionDefinition
    ): Fraction;
    (values: MathCollection<any>): MathCollection<any>;
    (numerator: bigint, denominator: bigint): Fraction;
    (numerator: number, denominator: number): Fraction;
};

Create a fraction convert a value to a fraction.
Parameter value
Arguments specifying the numerator and denominator of the fraction
Returns
Returns a fraction
Parameter numerator
Argument specifying the numerator of the fraction
Parameter denominator
Argument specifying the denominator of the fraction
Returns
Returns a fraction

method freqz

freqz: <T extends MathCollection<any>>(
    b: T,
    a: T,
    w?: number | T
) => { w: T; h: T };

Calculates the frequency response of a filter given its numerator and denominator coefficients.
Parameter b
The numerator polynomial of the filter
Parameter a
The denominator polynomial of the filter
Parameter w
The range of frequencies in which the response is to be calculated
Returns
The frequency response

method gamma

gamma: <T extends number | BigNumber | Complex>(n: T) => NoLiteralType<T>;

Compute the gamma function of a value using Lanczos approximation for small values, and an extended Stirling approximation for large values.
Parameter n
A real or complex number
Returns
The gamma of n

method gcd

gcd: { <T extends unknown>(...args: T[]): T; <T extends unknown>(args: T[]): T };

Calculate the greatest common divisor for two or more values or arrays. For matrices, the function is evaluated element wise.
Parameter args
Two or more integer numbers
Returns
The greatest common divisor

method hasNumericValue

hasNumericValue: (x: any) => boolean | boolean[];

Test whether a value is an numeric value. In case of a string, true is returned if the string contains a numeric value.
Parameter x
Value to be tested
Returns
Returns true when x is a number, BigNumber, bigint, Fraction, Boolean, or a String containing number. Returns false for other types. Throws an error in case of unknown types.

method help

help: (search: () => any) => Help;

Retrieve help on a function or data type. Help files are retrieved from the documentation in math.expression.docs.
Parameter search
A function or function name for which to get help
Returns
A help object

method hypot

hypot: {
    <T extends number | BigNumber>(...args: T[]): T;
    <T extends number | BigNumber>(args: T[]): T;
};

Calculate the hypotenuse of a list with values. The hypotenuse is defined as: hypot(a, b, c, ...) = sqrt(a^2 + b^2 + c^2 + ...) For matrix input, the hypotenuse is calculated for all values in the matrix.
Parameter args
A list with numeric values or an Array or Matrix. Matrix and Array input is flattened and returns a single number for the whole matrix.
Returns
Returns the hypothenuse of the input values.

method identity

identity: {
    (size: number | number[] | MathCollection, format?: string):
        | MathCollection
        | number;
    (m: number, n: number, format?: string): number | MathCollection<any>;
};

Create a 2-dimensional identity matrix with size m x n or n x n. The matrix has ones on the diagonal and zeros elsewhere.
Parameter size
The size for the matrix
Parameter format
The Matrix storage format
Returns
A matrix with ones on the diagonal
Parameter m
The x dimension for the matrix
Parameter n
The y dimension for the matrix
Parameter format
The Matrix storage format
Returns
A matrix with ones on the diagonal

method ifft

ifft: <T extends MathCollection<any>>(arr: T) => T;

Calculate N-dimensional inverse Fourier transform
Parameter arr
An array or matrix {Array | Matrix} N-dimensional Fourier transformation of the array

method im

im: {
    (x: MathJsChain<number | Complex>): MathJsChain<number>;
    <T extends BigNumber | MathCollection<any>>(
        x: MathJsChain<T>
    ): MathJsChain<T>;
};

Get the imaginary part of a complex number. For a complex number a + bi, the function returns b. For matrices, the function is evaluated element wise.
Parameter x
A complex number or array with complex numbers
Returns
The imaginary part of x

method import

import: (object: ImportObject | ImportObject[], options?: ImportOptions) => void;

Import functions from an object or a module To avoid errors when using one of the imported functions extend module like this:
Parameter object
An object with functions to be imported.
Parameter options
An object with import options.
Example 1
// imported_math_functions.ts declare module 'mathjs' { interface MathJsInterface { hello(a: number): number; } }

method index

index: (...ranges: any[]) => Index;

Create an index. An Index can store ranges having start, step, and end for multiple dimensions. Matrix.get, Matrix.set, and math.subset accept an Index as input.
Parameter ranges
Zero or more ranges or numbers.
Returns
Returns the created index

method intersect

intersect: (
    w: MathCollection,
    x: MathCollection,
    y: MathCollection,
    z?: MathCollection
) => MathArray;

Calculates the point of intersection of two lines in two or three dimensions and of a line and a plane in three dimensions. The inputs are in the form of arrays or 1 dimensional matrices. The line intersection functions return null if the lines do not meet. Note: Fill the plane coefficients as x + y + z = c and not as x + y + z + c = 0.
Parameter w
Co-ordinates of first end-point of first line
Parameter x
Co-ordinates of second end-point of first line
Parameter y
Co-ordinates of first end-point of second line OR Coefficients of the plane's equation
Parameter z
Co-ordinates of second end-point of second line OR null if the calculation is for line and plane
Returns
Returns the point of intersection of lines/lines-planes

method inv

inv: <T extends number | Complex | MathCollection<any>>(
    x: T
) => NoLiteralType<T>;

Calculate the inverse of a square matrix.
Parameter x
Matrix to be inversed
Returns
The inverse of x

method isAccessorNode

isAccessorNode: (x: unknown) => x is AccessorNode<MathNode>;

method isArrayNode

isArrayNode: (x: unknown) => x is ArrayNode<MathNode[]>;

method isAssignmentNode

isAssignmentNode: (x: unknown) => x is AssignmentNode<MathNode>;

method isBigInt

isBigInt: (x: unknown) => x is bigint;

method isBigNumber

isBigNumber: (x: unknown) => x is BigNumber;

method isBlockNode

isBlockNode: (x: unknown) => x is BlockNode<MathNode>;

method isBoolean

isBoolean: (x: unknown) => x is boolean;

method isChain

isChain: (x: unknown) => x is MathJsChain<unknown>;

method isCollection

isCollection: (x: unknown) => x is any[] | Matrix<any>;

method isComplex

isComplex: (x: unknown) => x is Complex;

method isConditionalNode

isConditionalNode: (
    x: unknown
) => x is ConditionalNode<MathNode, MathNode, MathNode>;

method isConstantNode

isConstantNode: (x: unknown) => x is ConstantNode<number>;

method isDate

isDate: (x: unknown) => x is Date;

method isDenseMatrix

isDenseMatrix: (x: unknown) => x is Matrix<any>;

method isFraction

isFraction: (x: unknown) => x is Fraction;

method isFunction

isFunction: (x: unknown) => boolean;

method isFunctionAssignmentNode

isFunctionAssignmentNode: (x: unknown) => x is FunctionAssignmentNode<MathNode>;

method isFunctionNode

isFunctionNode: (x: unknown) => x is FunctionNode<SymbolNode, MathNode[]>;

method isHelp

isHelp: (x: unknown) => x is Help;

method isIndex

isIndex: (x: unknown) => x is Index;

method isIndexNode

isIndexNode: (x: unknown) => x is IndexNode<MathNode[]>;

method isInteger

isInteger: (x: number | BigNumber | Fraction | MathCollection) => boolean;

Test whether a value is an integer number. The function supports number, BigNumber, and Fraction. The function is evaluated element-wise in case of Array or Matrix input.
Parameter x
Value to be tested
Returns
Returns true when x contains a numeric, integer value. Throws an error in case of an unknown data type.

method isMap

isMap: <T, U>(x: unknown) => x is Map<T, U>;

method isMatrix

isMatrix: (x: unknown) => x is Matrix<any>;

method isNaN

isNaN: (
    x: number | BigNumber | bigint | Fraction | MathCollection | Unit
) => boolean;

Test whether a value is NaN (not a number). The function supports types number, BigNumber, Fraction, Unit and Complex. The function is evaluated element-wise in case of Array or Matrix input.
Parameter x
Value to be tested
Returns
Returns true when x is NaN. Throws an error in case of an unknown data type.

method isNegative

isNegative: (
    x: number | BigNumber | bigint | Fraction | MathCollection | Unit
) => boolean;

Test whether a value is negative: smaller than zero. The function supports types number, BigNumber, Fraction, and Unit. The function is evaluated element-wise in case of Array or Matrix input.
Parameter x
Value to be tested
Returns
Returns true when x is larger than zero. Throws an error in case of an unknown data type.

method isNode

isNode: (x: unknown) => x is MathNode;

method isNull

isNull: (x: unknown) => x is null;

method isNumber

isNumber: (x: unknown) => x is number;

*********************************************************************** Utils **********************************************************************

method isNumeric

isNumeric: (x: any) => x is any;

Test whether a value is an numeric value. The function is evaluated element-wise in case of Array or Matrix input.
Parameter x
Value to be tested
Returns
Returns true when x is a number, BigNumber, bigint, Fraction, or boolean. Returns false for other types. Throws an error in case of unknown types.

method isObject

isObject: (x: unknown) => boolean;

method isObjectNode

isObjectNode: (x: unknown) => x is ObjectNode<Record<string, MathNode>>;

method isObjectWrappingMap

isObjectWrappingMap: <T extends string | number | symbol, U>(
    x: unknown
) => x is ObjectWrappingMap<T, U>;

method isOperatorNode

isOperatorNode: (
    x: unknown
) => x is OperatorNode<OperatorNodeOp, keyof OperatorNodeMap, MathNode[]>;

method isParenthesisNode

isParenthesisNode: (x: unknown) => x is ParenthesisNode<MathNode>;

method isPartitionedMap

isPartitionedMap: <T, U>(x: unknown) => x is PartitionedMap<T, U>;

method isPositive

isPositive: (
    x: number | BigNumber | bigint | Fraction | MathCollection | Unit
) => boolean;

Test whether a value is positive: larger than zero. The function supports types number, BigNumber, Fraction, and Unit. The function is evaluated element-wise in case of Array or Matrix input.
Parameter x
Value to be tested
Returns
Returns true when x is larger than zero. Throws an error in case of an unknown data type.

method isPrime

isPrime: (x: number | BigNumber | MathCollection) => boolean;

Test whether a value is prime: has no divisors other than itself and one. The function supports type number, bignumber. The function is evaluated element-wise in case of Array or Matrix input.
Parameter x
Value to be tested
Returns
Returns true when x is larger than zero. Throws an error in case of an unknown data type.

method isRange

isRange: (x: unknown) => boolean;

method isRangeNode

isRangeNode: (x: unknown) => x is RangeNode<MathNode, MathNode, MathNode>;

method isRegExp

isRegExp: (x: unknown) => x is RegExp;

method isRelationalNode

isRelationalNode: (x: unknown) => x is RelationalNode<MathNode[]>;

method isResultSet

isResultSet: (x: unknown) => x is ResultSet;

method isSparseMatrix

isSparseMatrix: (x: unknown) => x is Matrix<any>;

method isString

isString: (x: unknown) => x is string;

method isSymbolNode

isSymbolNode: (x: unknown) => x is SymbolNode;

method isUndefined

isUndefined: (x: unknown) => x is undefined;

method isUnit

isUnit: (x: unknown) => x is Unit;

method isZero

isZero: (x: MathType) => boolean;

Test whether a value is zero. The function can check for zero for types number, BigNumber, Fraction, Complex, and Unit. The function is evaluated element-wise in case of Array or Matrix input.
Parameter x
Value to be tested
Returns
Returns true when x is zero. Throws an error in case of an unknown data type.

method kldivergence

kldivergence: (q: MathCollection, p: MathCollection) => number;

Calculate the Kullback-Leibler (KL) divergence between two distributions
Parameter q
First vector
Parameter p
Second vector
Returns
Returns disance between q and p

method kron

kron: (x: MathCollection, y: MathCollection) => Matrix;

Calculate the Kronecker product of two matrices or vectors
Parameter x
First vector
Parameter y
Second vector
Returns
Returns the Kronecker product of x and y

method larger

larger: (x: MathType | string, y: MathType | string) => boolean | MathCollection;

Test whether value x is larger than y. The function returns true when x is larger than y and the relative difference between x and y is larger than the configured relTol and absTol. The function cannot be used to compare values smaller than approximately 2.22e-16. For matrices, the function is evaluated element wise.
Parameter x
First value to compare
Parameter y
Second value to vcompare
Returns
Returns true when x is larger than y, else returns false

method largerEq

largerEq: (
    x: MathType | string,
    y: MathType | string
) => boolean | MathCollection;

Test whether value x is larger or equal to y. The function returns true when x is larger than y or the relative difference between x and y is smaller than the configured relTol and absTol. The function cannot be used to compare values smaller than approximately 2.22e-16. For matrices, the function is evaluated element wise.
Parameter x
First value to compare
Parameter y
Second value to vcompare
Returns
Returns true when x is larger than or equal to y, else returns false

method lcm

lcm: <T extends number | BigNumber | MathCollection<any>>(a: T, b: T) => T;

Calculate the least common multiple for two or more values or arrays. lcm is defined as: lcm(a, b) = abs(a * b) / gcd(a, b) For matrices, the function is evaluated element wise.
Parameter a
An integer number
Parameter b
An integer number
Returns
The least common multiple

method leafCount

leafCount: (expr: MathNode) => number;

Gives the number of “leaf nodes” in the parse tree of the given expression. A leaf node is one that has no subexpressions, essentially either a symbol or a constant. Note that 5! has just one leaf, the 5; the unary factorial operator does not add a leaf. On the other hand, function symbols do add leaves, so sin(x)/cos(x) has four leaves.

method leftShift

leftShift: <T extends number | bigint | BigNumber | MathCollection<any>>(
    x: T,
    y: number | BigNumber | bigint
) => NoLiteralType<T>;

Bitwise left logical shift of a value x by y number of bits, x << y. For matrices, the function is evaluated element wise. For units, the function is evaluated on the best prefix base.
Parameter x
Value to be shifted
Parameter y
Amount of shifts
Returns
x shifted left y times

method lgamma

lgamma: <T extends number | Complex>(n: T) => NoLiteralType<T>;

Compute the log gamma function of a value, using Lanczos approximation for numbers and Stirling series for complex numbers.
Parameter n
A real or complex number
Returns
The log gamma of n

method log

log: <T extends number | BigNumber | Complex>(
    x: T,
    base?: number | BigNumber | Complex
) => NoLiteralType<T>;

Calculate the logarithm of a value.
Parameter x
Value for which to calculate the logarithm.
Parameter base
Optional base for the logarithm. If not provided, the natural logarithm of x is calculated. Default value: e.
Returns
Returns the logarithm of x

method log10

log10: <T extends number | BigNumber | Complex | MathCollection<any>>(x: T) => T;

Calculate the 10-base of a value. This is the same as calculating log(x, 10). For matrices, the function is evaluated element wise.
Parameter x
Value for which to calculate the logarithm.
Returns
Returns the 10-base logarithm of x

method log1p

log1p: <T extends number | BigNumber | Complex | MathCollection<any>>(
    x: T,
    base?: number | BigNumber | Complex
) => T;

Calculate the logarithm of a value+1. For matrices, the function is evaluated element wise.
Parameter x
Value for which to calculate the logarithm.
Returns
Returns the logarithm of x+1

method log2

log2: <T extends number | BigNumber | Complex | MathCollection<any>>(x: T) => T;

Calculate the 2-base of a value. This is the same as calculating log(x, 2). For matrices, the function is evaluated element wise.
Parameter x
Value for which to calculate the logarithm.
Returns
Returns the 2-base logarithm of x

method lsolve

lsolve: {
    (L: Matrix, b: MathCollection): Matrix;
    (L: MathArray<any>, b: MathCollection<any>): MathArray<any>;
};

Solves the linear equation system by forwards substitution. Matrix must be a lower triangular matrix.
Parameter L
A N x N matrix or array (L)
Parameter b
A column vector with the b values
Returns
A column vector with the linear system solution (x)

method lup

lup: (A?: MathCollection) => LUDecomposition;

Calculate the Matrix LU decomposition with partial pivoting. Matrix A is decomposed in two matrices (L, U) and a row permutation vector p where A[p,:] = L * U
Parameter A
A two dimensional matrix or array for which to get the LUP decomposition.
Returns
The lower triangular matrix, the upper triangular matrix and the permutation matrix.

method lusolve

lusolve: {
    (A: Matrix, b: MathCollection, order?: number, threshold?: number): Matrix;
    (
        A: MathArray<any>,
        b: MathCollection<any>,
        order?: number,
        threshold?: number
    ): MathArray<any>;
    (A: LUDecomposition, b: MathCollection<any>): Matrix<any>;
};

Solves the linear system A * x = b where A is an [n x n] matrix and b is a [n] column vector.
Parameter A
Invertible Matrix or the Matrix LU decomposition
Parameter b
Column Vector
Parameter order
The Symbolic Ordering and Analysis order, see slu for details. Matrix must be a SparseMatrix
Parameter threshold
Partial pivoting threshold (1 for partial pivoting), see slu for details. Matrix must be a SparseMatrix.
Returns
Column vector with the solution to the linear system A * x = b

method lyap

lyap: (A: MathCollection, Q: MathCollection) => MathCollection;

Solves the Continuous-time Lyapunov equation AP+PA'=Q for P, where Q is a positive semidefinite matrix. https://en.wikipedia.org/wiki/Lyapunov_equation
Parameter A
Matrix A
Parameter Q
Matrix Q
Returns
Matrix P solution to the Continuous-time Lyapunov equation AP+PA'=Q

method mad

mad: (array: MathCollection) => any;

Compute the median absolute deviation of a matrix or a list with values. The median absolute deviation is defined as the median of the absolute deviations from the median.
Parameter array
A single matrix or multiple scalar values.
Returns
The median absolute deviation

method map

map: {
    <T extends MathCollection<any>>(
        x: T,
        callback: (value: any, index: number[], matrix: T) => MathType | string
    ): T;
    <T extends MathCollection<any>>(
        x: T,
        ...args: (T | ((value: any, ...args: any[]) => any))[]
    ): T;
};

Iterate over all elements of a matrix/array, and executes the given callback function.
Parameter x
The matrix to iterate on.
Parameter callback
The callback function is invoked with three parameters: the value of the element, the index of the element, and the Matrix/array being traversed.
Returns
Transformed map of x
Iterate over all elements of multiple matrices/arrays, and executes the given callback function.
Parameter x
The first matrix to iterate on.
Parameter args
The rest of the matrices and at the end the callback function is invoked with multiple parameters: the values of the elements, the indices of the elements, and the matrices/arrays being traversed.
Returns
Transformed map of matrices

method mapSlices

mapSlices: <T extends MathCollection<any>>(
    array: T,
    dim: number,
    callback: (array: MathCollection) => number
) => T;

Apply a function that maps an array to a scalar along a given axis of a matrix or array. Returns a new matrix or array with one less dimension than the input.
Parameter array
The input Matrix
Parameter dim
The dimension along which the callback is applied
Parameter callback
The callback function that is applied. This Function should take an array or 1-d matrix as an input and return a number.
Returns
The residual matrix with the function applied over some dimension.

method matrix

matrix: {
    (format?: MatrixStorageFormat): Matrix;
    (
        data: string[] | MathCollection<any>,
        format?: MatrixStorageFormat,
        dataType?: string
    ): Matrix<any>;
    <T extends unknown>(
        data: MathCollection<T>,
        format?: MatrixStorageFormat,
        dataType?: string
    ): Matrix<T>;
};

Create a Matrix. The function creates a new math.type.Matrix object from an Array. A Matrix has utility functions to manipulate the data in the matrix, like getting the size and getting or setting values in the matrix. Supported storage formats are 'dense' and 'sparse'.
Parameter format
The Matrix storage format
Returns
The created Matrix
Parameter data
A multi dimensional array
Parameter format
The Matrix storage format
Parameter dataType
The Matrix data type
Returns
The created Matrix

method matrixFromColumns

matrixFromColumns: {
    (...cols: Matrix[]): Matrix;
    <T extends unknown>(...cols: (Matrix<any> | T[] | [T][])[]): T[][];
};

Create a dense matrix from vectors as individual columns. If you pass row vectors, they will be transposed (but not conjugated!)
Parameter cols
a multi-dimensional number array or matrix

method matrixFromFunction

matrixFromFunction: {
    <T extends unknown>(size: [number], fn: MatrixFromFunctionCallback<T>): T[];
    <T extends unknown>(
        size: [number, number],
        fn: MatrixFromFunctionCallback<T>
    ): T[][];
    <T extends unknown>(
        size: number[],
        fn: MatrixFromFunctionCallback<T>
    ): MathArray<T>;
    (size: Matrix<number>, fn: MatrixFromFunctionCallback<any>): Matrix<any>;
    (
        size: number[] | Matrix<number>,
        fn: MatrixFromFunctionCallback<any>,
        format: MatrixStorageFormat,
        datatype?: string
    ): Matrix<any>;
    (
        size: number[] | Matrix<number>,
        format: MatrixStorageFormat,
        fn: MatrixFromFunctionCallback<any>,
        datatype?: string
    ): Matrix<any>;
};

Create a matrix by evaluating a generating function at each index. The simplest overload returns a multi-dimensional array as long as size is an array. Passing size as a Matrix or specifying a format will result in returning a Matrix.
Parameter size
the size of the matrix to be created
Parameter fn
Callback function invoked for every entry in the matrix
Parameter format
The Matrix storage format, either 'dense' or 'sparse'
Parameter datatype
Type of the values

method matrixFromRows

matrixFromRows: {
    (...rows: Matrix[]): Matrix;
    <T extends unknown>(...rows: (Matrix<any> | T[] | [T][])[]): T[][];
};

Create a dense matrix from vectors as individual rows. If you pass column vectors, they will be transposed (but not conjugated!)
Parameter rows
a multi-dimensional number array or matrix

method max

max: {
    <T extends unknown>(...args: T[]): T;
    (...args: any[]): any;
    <T extends unknown>(A: T[] | T[][], dimension?: number | BigNumber): T;
    (A: MathCollection<any>, dimension?: number | BigNumber): any;
};

Compute the maximum value of a matrix or a list with values. In case of a multi dimensional array, the maximum of the flattened array will be calculated. When dim is provided, the maximum over the selected dimension will be calculated. Parameter dim is zero-based.
Parameter args
Multiple scalar values
Returns
The maximum value
Parameter args
Multiple scalar values
Returns
The maximum value
Parameter A
A single matrix
Parameter dimension
The maximum over the selected dimension
Returns
The maximum value

method mean

mean: {
    <T extends unknown>(...args: T[]): T;
    (...args: any[]): any;
    <T extends unknown>(A: T[] | T[][], dimension?: number | BigNumber): T;
    (A: MathCollection<any>, dimension?: number | BigNumber): any;
};

Compute the mean value of matrix or a list with values. In case of a multi dimensional array, the mean of the flattened array will be calculated. When dim is provided, the maximum over the selected dimension will be calculated. Parameter dim is zero-based.
Parameter args
Multiple scalar values
Returns
The mean of all values
Parameter args
Multiple scalar values
Returns
The mean value
Parameter A
A single matrix
Parameter dimension
The mean over the selected dimension
Returns
The mean value

method median

median: {
    <T extends unknown>(...args: T[]): T;
    (...args: any[]): any;
    <T extends unknown>(A: T[] | T[][]): T;
    (A: MathCollection<any>): any;
};

Compute the median of a matrix or a list with values. The values are sorted and the middle value is returned. In case of an even number of values, the average of the two middle values is returned. Supported types of values are: Number, BigNumber, Unit In case of a (multi dimensional) array or matrix, the median of all elements will be calculated.
Parameter args
Multiple scalar values
Returns
The median value
Parameter args
Multiple scalar values
Returns
The median value
Parameter A
A single matrix
Returns
The median value

method min

min: {
    <T extends unknown>(...args: T[]): T;
    (...args: any[]): any;
    <T extends unknown>(A: T[] | T[][], dimension?: number | BigNumber): T;
    (A: MathCollection<any>, dimension?: number | BigNumber): any;
};

Compute the minimum value of a matrix or a list of values. In case of a multi dimensional array, the minimum of the flattened array will be calculated. When dim is provided, the minimum over the selected dimension will be calculated. Parameter dim is zero-based.
Parameter args
multiple scalar values
Returns
The minimum value
Parameter args
Multiple scalar values
Returns
The minimum value
Parameter A
A single matrix
Parameter dimension
The minimum over the selected dimension
Returns
The minimum value

method mod

mod: <T extends unknown>(
    x: T,
    y: number | BigNumber | bigint | Fraction | MathCollection
) => NoLiteralType<T>;

Calculates the modulus, the remainder of an integer division. For matrices, the function is evaluated element wise. The modulus is defined as: x - y * floor(x / y)
Parameter x
Dividend
Parameter y
Divisor
Returns
Returns the remainder of x divided by y
See Also
- http://en.wikipedia.org/wiki/Modulo_operation.

method mode

mode: {
    <T extends unknown>(...args: T[]): T[];
    (...args: any[]): any[];
    <T extends unknown>(A: T[] | T[][]): T[];
    (A: MathCollection<any>): any[];
};

Computes the mode of a set of numbers or a list with values(numbers or characters). If there are more than one modes, it returns a list of those values.
Parameter args
Multiple scalar values
Returns
The mode of all values
Parameter args
Multiple scalar values
Returns
The mode of all values
Parameter A
A single matrix
Returns
The mode value
Parameter A
A single matrix
Returns
The mode of all values

method multinomial

multinomial: <T extends number | BigNumber>(a: T[]) => NoLiteralType<T>;

Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from n possibilities. multinomial takes one array of integers as an argument. The following condition must be enforced: every ai <= 0
Parameter a
Integer number of objects in the subset
Returns
multinomial coefficent

method multiply

multiply: {
    <T extends Matrix<any>>(x: T, y: MathType): Matrix;
    <T extends Matrix<any>>(x: any, y: T): Matrix<any>;
    <T extends MathArray<any>>(x: T, y: T[]): T;
    <T extends MathArray<any>>(x: T[], y: T): T;
    <T extends MathArray<any>>(x: T[], y: T[]): T[];
    <T extends MathArray<any>>(x: T, y: T): any;
    (x: Unit, y: Unit): Unit;
    (x: number, y: number): number;
    (x: any, y: any, ...values: any[]): any;
    <T extends unknown>(x: T, y: T, ...values: T[]): T;
};

Multiply two values, x * y. The result is squeezed. For matrices, the matrix product is calculated.
Parameter x
The first value to multiply
Parameter y
The second value to multiply
Returns
Multiplication of x and y

method norm

norm: (
    x: number | BigNumber | Complex | MathCollection,
    p?: number | BigNumber | string
) => number | BigNumber;

Calculate the norm of a number, vector or matrix. The second parameter p is optional. If not provided, it defaults to 2.
Parameter x
Value for which to calculate the norm
Parameter p
Vector space. Supported numbers include Infinity and -Infinity. Supported strings are: 'inf', '-inf', and 'fro' (The Frobenius norm) Default value: 2.
Returns
the p-norm

method not

not: (
    x: number | BigNumber | bigint | Complex | Unit | MathCollection
) => boolean | MathCollection;

Logical not. Flips boolean value of a given parameter. For matrices, the function is evaluated element wise.
Parameter x
First value to not
Returns
Returns true when input is a zero or empty value.

method nthRoot

nthRoot: (
    a: number | BigNumber | MathCollection | Complex,
    root?: number | BigNumber
) => number | Complex | MathCollection;

Calculate the nth root of a value. The principal nth root of a positive real number A, is the positive real solution of the equation x^root = A For matrices, the function is evaluated element wise.
Parameter a
Value for which to calculate the nth root
Parameter root
The root. Default value: 2. The nth root of a

method number

number: {
    (
        value?:
            | string
            | number
            | BigNumber
            | bigint
            | Fraction
            | boolean
            | Unit
            | null
    ): number;
    (value?: MathCollection<any>): number | MathCollection<any>;
    (unit: Unit, valuelessUnit: string | Unit): number;
};

Create a number or convert a string, boolean, or unit to a number. When value is a matrix, all elements will be converted to number.
Parameter value
Value to be converted
Returns
The created number
Parameter value
Value to be converted
Parameter valuelessUnit
A valueless unit, used to convert a unit to a number
Returns
The created number

method numeric

numeric: {
    (
        value: string | number | BigNumber | bigint | Fraction,
        outputType: 'number'
    ): number;
    (value: any, outputType: 'BigNumber'): BigNumber;
    (value: any, outputType: 'bigint'): bigint;
    (value: any, outputType: 'Fraction'): Fraction;
};

Convert a numeric input to a specific numeric type: number, BigNumber, bigint, or Fraction.
Parameter value
The value to be converted
Parameter outputType
The desired numeric output type

method ones

ones: {
    (
        size?: number | number[] | BigNumber | BigNumber[],
        format?: string
    ): MathCollection;
    (
        m: number | BigNumber,
        n: number | BigNumber,
        format?: string
    ): MathCollection<any>;
    (
        m: number | BigNumber,
        n: number | BigNumber,
        p: number | BigNumber,
        format?: string
    ): MathCollection<any>;
};

Create a matrix filled with ones. The created matrix can have one or multiple dimensions.
Parameter size
The size of each dimension of the matrix
Parameter format
The matrix storage format
Returns
A matrix filled with ones
Parameter m
The x dimension of the matrix
Parameter n
The y dimension of the matrix
Parameter format
The matrix storage format
Returns
A matrix filled with ones
Parameter m
The x dimension of the matrix
Parameter n
The y dimension of the matrix
Parameter p
The z dimension of the matrix
Parameter format
The matrix storage format
Returns
A matrix filled with ones

method or

or: (
    x: number | BigNumber | bigint | Complex | Unit | MathCollection,
    y: number | BigNumber | bigint | Complex | Unit | MathCollection
) => boolean | MathCollection;

Logical or. Test if at least one value is defined with a nonzero/nonempty value. For matrices, the function is evaluated element wise.
Parameter x
First value to or
Parameter y
Second value to or
Returns
Returns true when one of the inputs is defined with a nonzero/nonempty value.

method parser

parser: () => Parser;

Create a parser. The function creates a new math.expression.Parser object.
Returns
A Parser object

method partitionSelect

partitionSelect: (
    x: MathCollection,
    k: number,
    compare?: 'asc' | 'desc' | ((a: any, b: any) => number)
) => any;

Partition-based selection of an array or 1D matrix. Will find the kth smallest value, and mutates the input array. Uses Quickselect.
Parameter x
A one dimensional matrix or array to sort
Parameter k
The kth smallest value to be retrieved; zero-based index
Parameter compare
An optional comparator function. The function is called as compare(a, b), and must return 1 when a > b, -1 when a < b, and 0 when a == b. Default value: 'asc'.
Returns
Returns the kth lowest value.

method permutations

permutations: <T extends number | BigNumber>(
    n: T,
    k?: number | BigNumber
) => NoLiteralType<T>;

Compute the number of ways of obtaining an ordered subset of k elements from a set of n elements. Permutations only takes integer arguments. The following condition must be enforced: k <= n.
Parameter n
The number of objects in total
Parameter k
The number of objects in the subset
Returns
The number of permutations

method pickRandom

pickRandom: {
    <T>(array: T[]): T;
    <T>(array: T[], number: number): T[];
    <T>(array: T[], number: number, weights: number[]): T[];
};

Random pick a value from a one dimensional array. Array element is picked using a random function with uniform distribution.
Parameter array
A one dimensional array
Parameter number
An int or float
Parameter weights
An array of ints or floats
Returns
Returns a single random value from array when number is undefined. Returns an array with the configured number of elements when number is defined.

method pinv

pinv: <T extends unknown>(x: T) => T;

Calculate the Moore–Penrose inverse of a matrix.
Parameter x
Matrix to be inversed The inverse of x.

method polynomialRoot

polynomialRoot: (
    constantCoeff: number | Complex,
    linearCoeff: number | Complex,
    quadraticCoeff?: number | Complex,
    cubicCoeff?: number | Complex
) => (number | Complex)[];

method pow

pow: (x: MathType, y: number | BigNumber | bigint | Complex) => MathType;

Calculates the power of x to y, x ^ y. Matrix exponentiation is supported for square matrices x, and positive integer exponents y.
Parameter x
The base
Parameter y
The exponent
Returns
x to the power y

method print

print: (
    template: string,
    values: any,
    precision?: number,
    options?: number | object
) => void;

Interpolate values into a string template.
Parameter template
A string containing variable placeholders.
Parameter values
An object containing variables which will be filled in in the template.
Parameter precision
Number of digits to format numbers. If not provided, the value will not be rounded.
Parameter options
Formatting options, or the number of digits to format numbers. See function math.format for a description of all options.
Returns
Interpolated string

method prod

prod: {
    <T extends unknown>(...args: T[]): T;
    (...args: any[]): any;
    <T extends unknown>(A: T[] | T[][]): T;
    (A: MathCollection<any>): any;
};

Compute the product of a matrix or a list with values. In case of a (multi dimensional) array or matrix, the sum of all elements will be calculated.
Parameter args
Multiple scalar values
Returns
The product of all values
Parameter args
Multiple scalar values
Returns
The product of all values
Parameter A
A single matrix
Returns
The product of all values

method qr

qr: (A: MathCollection) => QRDecomposition;

Calculate the Matrix QR decomposition. Matrix A is decomposed in two matrices (Q, R) where Q is an orthogonal matrix and R is an upper triangular matrix.
Parameter A
A two dimensional matrix or array for which to get the QR decomposition.
Returns
Q: the orthogonal matrix and R: the upper triangular matrix

method quantileSeq

quantileSeq: {
    <T extends unknown>(
        A: T[] | T[][],
        prob: number | BigNumber,
        sorted?: boolean
    ): T;
    (
        A: MathCollection<any>,
        prob: number | BigNumber | MathArray<any>,
        sorted?: boolean
    ): any;
};

Parameter A
A single matrix
Parameter probOrN
prob is the order of the quantile, while N is the amount of evenly distributed steps of probabilities; only one of these options can be provided
Parameter sorted
=false is data sorted in ascending order
Returns
Quantile(s)
Compute the prob order quantile of a matrix or a list with values. The sequence is sorted and the middle value is returned. Supported types of sequence values are: Number, BigNumber, Unit Supported types of probability are: Number, BigNumber In case of a (multi dimensional) array or matrix, the prob order quantile of all elements will be calculated.
Parameter A
A single matrix or array
Parameter probOrN
prob is the order of the quantile, while N is the amount of evenly distributed steps of probabilities; only one of these options can be provided
Parameter sorted
=false is data sorted in ascending order
Returns
Quantile(s)

method random

random: {
    (min?: number, max?: number): number;
    <T extends MathCollection<any>>(size: T, min?: number, max?: number): T;
};

Return a random number larger or equal to min and smaller than max using a uniform distribution.
Parameter size
If provided, an array or matrix with given size and filled with random values is returned
Parameter min
Minimum boundary for the random value, included
Parameter max
Maximum boundary for the random value, excluded
Returns
A random number

method randomInt

randomInt: {
    (min: number, max?: number): number;
    <T extends MathCollection<any>>(size: T, min?: number, max?: number): T;
};

Return a random integer number larger or equal to min and smaller than max using a uniform distribution.
Parameter size
If provided, an array or matrix with given size and filled with random values is returned
Parameter min
Minimum boundary for the random value, included
Parameter max
Maximum boundary for the random value, excluded
Returns
A random number

method range

range: {
    (str: string, includeEnd?: boolean): Matrix;
    (
        start: number | BigNumber,
        end: number | BigNumber,
        includeEnd?: boolean
    ): Matrix<any>;
    (
        start: number | BigNumber | Unit,
        end: number | BigNumber | Unit,
        step: number | BigNumber | Unit,
        includeEnd?: boolean
    ): Matrix<any>;
};

Create an array from a range. By default, the range end is excluded. This can be customized by providing an extra parameter includeEnd.
Parameter str
A string 'start:end' or 'start:step:end'
Parameter start
Start of the range
Parameter end
End of the range, excluded by default, included when parameter includeEnd=true
Parameter step
Step size. Default value is 1.
Parameter includeEnd
: Option to specify whether to include the end or not. False by default
Returns
Parameters describing the ranges start, end, and optional step.

method rationalize

rationalize: {
    (
        expr: MathNode | string,
        optional?: object | boolean,
        detailed?: false
    ): MathNode;
    (expr: string | MathNode, optional?: boolean | object, detailed?: true): {
        expression: string | MathNode;
        variables: string[];
        coefficients: any[];
    };
};

Transform a rationalizable expression in a rational fraction. If rational fraction is one variable polynomial then converts the numerator and denominator in canonical form, with decreasing exponents, returning the coefficients of numerator.
Parameter expr
The expression to check if is a polynomial expression
Parameter optional
scope of expression or true for already evaluated rational expression at input
Parameter detailed
optional True if return an object, false if return expression node (default)
Returns
The rational polynomial of expr

method re

re: {
    (x: MathJsChain<number | Complex>): MathJsChain<number>;
    <T extends BigNumber | MathCollection<any>>(
        x: MathJsChain<T>
    ): MathJsChain<T>;
};

Get the real part of a complex number. For a complex number a + bi, the function returns a. For matrices, the function is evaluated element wise.
Parameter x
A complex number or array of complex numbers
Returns
The real part of x

method replacer

replacer: () => (key: any, value: any) => any;

Returns replacer function that can be used as replacer in JSON.stringify function.

method reshape

reshape: <T extends MathCollection<any>>(x: T, sizes: number[]) => T;

Reshape a multi dimensional array to fit the specified dimensions
Parameter x
Matrix to be reshaped
Parameter sizes
One dimensional array with integral sizes for each dimension
Returns
A reshaped clone of matrix x

method resize

resize: <T extends MathCollection<any>>(
    x: T,
    size: MathCollection,
    defaultValue?: number | string
) => T;

Resize a matrix
Parameter x
Matrix to be resized
Parameter size
One dimensional array with numbers
Parameter defaultValue
Zero by default, except in case of a string, in that case defaultValue = ' ' Default value: 0.
Returns
A resized clone of matrix x

method resolve

resolve: {
    (node: MathNode | string, scope?: MathScope): MathNode;
    (node: (string | MathNode)[], scope?: MathScope<any>): MathNode[];
    (node: Matrix<any>, scope?: MathScope<any>): Matrix<any>;
};

Replaces variable nodes with their scoped values
Parameter node
Tree to replace variable nodes in
Parameter scope
Scope to read/write variables

method reviver

reviver: () => (key: any, value: any) => any;

Returns reviver function that can be used as reviver in JSON.parse function.

method rightArithShift

rightArithShift: <T extends number | bigint | BigNumber | MathCollection<any>>(
    x: T,
    y: number | BigNumber | bigint
) => NoLiteralType<T>;

Bitwise right arithmetic shift of a value x by y number of bits, x >> y. For matrices, the function is evaluated element wise. For units, the function is evaluated on the best prefix base.
Parameter x
Value to be shifted
Parameter y
Amount of shifts
Returns
x sign-filled shifted right y times

method rightLogShift

rightLogShift: <T extends number | MathCollection<any>>(
    x: T,
    y: number
) => NoLiteralType<T>;

Bitwise right logical shift of value x by y number of bits, x >>> y. For matrices, the function is evaluated element wise. For units, the function is evaluated on the best prefix base.
Parameter x
Value to be shifted
Parameter y
Amount of shifts
Returns
x zero-filled shifted right y times

method rotate

rotate: <T extends MathCollection<any>>(
    w: T,
    theta: number | BigNumber | Complex | Unit,
    v?: T
) => T;

Return a rotated matrix.
Parameter w
Vector to rotate
Parameter theta
Rotation angle
Parameter v
Rotation axis {Array | Matrix} Multiplication of the rotation matrix and w

method rotationMatrix

rotationMatrix: <T extends MathCollection<any>>(
    theta?: number | BigNumber | Complex | Unit,
    axis?: T,
    format?: 'sparse' | 'dense'
) => T;

Return a Rotation Matrix for a given angle in radians
Parameter theta
Rotation angle
Parameter v
Rotation axis
Parameter format
Result Matrix storage format. Default value: 'dense'. {Matrix} Rotation Matrix

method round

round: {
    <T extends unknown>(x: T, n?: number | BigNumber): NoLiteralType<T>;
    <U extends MathCollection<any>>(x: any, n: U): U;
    <U extends MathCollection<Unit>>(x: U, unit: Unit): U;
    (x: Unit, unit: Unit): Unit;
    (x: Unit, n: number | BigNumber, unit: Unit): Unit;
    <U extends MathCollection<Unit>>(x: U, n: number | BigNumber, unit: Unit): U;
};

Round a value towards the nearest integer. For matrices, the function is evaluated element wise.
Parameter x
Number to be rounded
Parameter n
Number of decimals Default value: 0.
Returns
Rounded value of x

method row

row: <T extends MathCollection<any>>(value: T, row: number) => T;

Return a row from a Matrix.
Parameter value
An array or matrix
Parameter row
The index of the row
Returns
The retrieved row

method schur

schur: (A: MathCollection) => SchurDecomposition;

Performs a real Schur decomposition of the real matrix A = UTU' where U is orthogonal and T is upper quasi-triangular. https://en.wikipedia.org/wiki/Schur_decomposition
Parameter A
Matrix A
Returns
Object containing both matrix U and T of the Schur Decomposition A=UTU'

method sec

sec: { (x: number | Unit): number; <T extends BigNumber | Complex>(x: T): T };

Calculate the secant of a value, defined as sec(x) = 1/cos(x).
Parameter x
Function input
Returns
The secant of x

method sech

sech: { (x: number | Unit): number; <T extends BigNumber | Complex>(x: T): T };

Calculate the hyperbolic secant of a value, defined as sech(x) = 1 / cosh(x).
Parameter x
Function input
Returns
The hyperbolic secant of x

method setCartesian

setCartesian: <T extends MathCollection<any>>(a1: T, a2: MathCollection) => T;

Create the cartesian product of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays and the values will be sorted in ascending order before the operation.
Parameter a1
A (multi)set
Parameter a2
A (multi)set
Returns
The cartesian product of two (multi)sets

method setDifference

setDifference: <T extends MathCollection<any>>(a1: T, a2: MathCollection) => T;

Create the difference of two (multi)sets: every element of set1, that is not the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation
Parameter a1
A (multi)set
Parameter a2
A (multi)set
Returns
The difference of two (multi)sets

method setDistinct

setDistinct: <T extends MathCollection<any>>(a: T) => T;

Collect the distinct elements of a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.
Parameter a
A multiset
Returns
A set containing the distinct elements of the multiset

method setIntersect

setIntersect: <T extends MathCollection<any>>(a1: T, a2: MathCollection) => T;

Create the intersection of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.
Parameter a1
A (multi)set
Parameter a2
A (multi)set
Returns
The intersection of two (multi)sets

method setIsSubset

setIsSubset: (a1: MathCollection, a2: MathCollection) => boolean;

Check whether a (multi)set is a subset of another (multi)set. (Every element of set1 is the element of set2.) Multi-dimension arrays will be converted to single-dimension arrays before the operation.
Parameter a1
A (multi)set
Parameter a2
A (multi)set
Returns
True if a1 is subset of a2, else false

method setMultiplicity

setMultiplicity: (e: MathNumericType, a: MathCollection) => number;

Count the multiplicity of an element in a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.
Parameter e
An element in the multiset
Parameter a
A multiset
Returns
The number of how many times the multiset contains the element

method setPowerset

setPowerset: <T extends MathCollection<any>>(a: T) => T;

Create the powerset of a (multi)set. (The powerset contains very possible subsets of a (multi)set.) A multi-dimension array will be converted to a single-dimension array before the operation.
Parameter a
A multiset
Returns
The powerset of the (multi)set

method setSize

setSize: (a: MathCollection) => number;

Count the number of elements of a (multi)set. When a second parameter is ‘true’, count only the unique values. A multi-dimension array will be converted to a single-dimension array before the operation.
Parameter a
A multiset
Returns
The number of elements of the (multi)set

method setSymDifference

setSymDifference: <T extends MathCollection<any>>(
    a1: T,
    a2: MathCollection
) => T;

Create the symmetric difference of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.
Parameter a1
A (multi)set
Parameter a2
A (multi)set
Returns
The symmetric difference of two (multi)sets

method setUnion

setUnion: <T extends MathCollection<any>>(a1: T, a2: MathCollection) => T;

Create the union of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.
Parameter a1
A (multi)set
Parameter a2
A (multi)set
Returns
The union of two (multi)sets

method sign

sign: <T extends unknown>(x: T) => T;

Compute the sign of a value. The sign of a value x is: 1 when x > 1 -1 when x < 0 0 when x == 0 For matrices, the function is evaluated element wise.
Parameter x
The number for which to determine the sign
Returns
The sign of x

method simplifyConstant

simplifyConstant: (
    expr: MathNode | string,
    options?: SimplifyOptions
) => MathNode;

method simplifyCore

simplifyCore: (expr: MathNode | string, options?: SimplifyOptions) => MathNode;

method sin

sin: { (x: number | Unit): number; <T extends BigNumber | Complex>(x: T): T };

Calculate the sine of a value.
Parameter x
Function input
Returns
The sine of x

method sinh

sinh: { (x: number | Unit): number; <T extends BigNumber | Complex>(x: T): T };

Calculate the hyperbolic sine of a value, defined as sinh(x) = 1/2 * (exp(x) - exp(-x)).
Parameter x
Function input
Returns
The hyperbolic sine of x

method size

size: (
    x: boolean | number | Complex | Unit | string | MathCollection
) => MathCollection;

Calculate the size of a matrix or scalar.
Parameter A
matrix
Returns
A vector with the size of x

method slu

slu: (A: Matrix, order: number, threshold: number) => SLUDecomposition;

Calculate the Sparse Matrix LU decomposition with full pivoting. Sparse Matrix A is decomposed in two matrices (L, U) and two permutation vectors (pinv, q) where P * A * Q = L * U
Parameter A
A two dimensional sparse matrix for which to get the LU decomposition.
Parameter order
The Symbolic Ordering and Analysis order: 0 - Natural ordering, no permutation vector q is returned 1 - Matrix must be square, symbolic ordering and analisis is performed on M = A + A' 2 - Symbolic ordering and analysis is performed on M = A' * A. Dense columns from A' are dropped, A recreated from A'. This is appropriate for LU factorization of non-symmetric matrices. 3 - Symbolic ordering and analysis is performed on M = A' * A. This is best used for LU factorization is matrix M has no dense rows. A dense row is a row with more than 10*sqr(columns) entries.
Parameter threshold
Partial pivoting threshold (1 for partial pivoting)
Returns
The lower triangular matrix, the upper triangular matrix and the permutation vectors.

method smaller

smaller: (
    x: MathType | string,
    y: MathType | string
) => boolean | MathCollection;

Test whether value x is smaller than y. The function returns true when x is smaller than y and the relative difference between x and y is smaller than the configured relTol and absTol. The function cannot be used to compare values smaller than approximately 2.22e-16. For matrices, the function is evaluated element wise.
Parameter x
First value to compare
Parameter y
Second value to vcompare
Returns
Returns true when x is smaller than y, else returns false

method smallerEq

smallerEq: (
    x: MathType | string,
    y: MathType | string
) => boolean | MathCollection;

Test whether value x is smaller or equal to y. The function returns true when x is smaller than y or the relative difference between x and y is smaller than the configured relTol and absTol. The function cannot be used to compare values smaller than approximately 2.22e-16. For matrices, the function is evaluated element wise.
Parameter x
First value to compare
Parameter y
Second value to vcompare
Returns
Returns true when x is smaller than or equal to y, else returns false

method sort

sort: <T extends MathCollection<any>>(
    x: T,
    compare: 'asc' | 'desc' | ((a: any, b: any) => number) | 'natural'
) => T;

Sort the items in a matrix
Parameter x
A one dimensional matrix or array to sort
Parameter compare
An optional _comparator function or name. The function is called as compare(a, b), and must return 1 when a > b, -1 when a < b, and 0 when a == b. Default value: ‘asc’
Returns
Returns the sorted matrix

method sparse

sparse: (data?: MathCollection, dataType?: string) => Matrix;

Create a Sparse Matrix. The function creates a new math.type.Matrix object from an Array. A Matrix has utility functions to manipulate the data in the matrix, like getting the size and getting or setting values in the matrix.
Parameter data
A two dimensional array
Parameter dataType
Sparse Matrix data type
Returns
The created matrix

method splitUnit

splitUnit: (unit: Unit, parts: Unit[]) => Unit[];

Split a unit in an array of units whose sum is equal to the original unit.
Parameter unit
A unit to be split
Parameter parts
An array of strings or valueless units
Returns
An array of units

method sqrt

sqrt: {
    (x: number): number | Complex;
    <T extends BigNumber | Complex | Unit>(x: T): T;
};

Calculate the square root of a value. For matrices, use either sqrtm for the matrix square root, or map(M, sqrt) to take the square root element wise.
Parameter x
Value for which to calculate the square root
Returns
Returns the square root of x

method sqrtm

sqrtm: <T extends MathCollection<any>>(A: T) => T;

Calculate the principal square root of a square matrix. The principal square root matrix X of another matrix A is such that X * X = A.
Parameter A
The square matrix A
Returns
The principal square root of matrix A

method square

square: <T extends unknown>(x: T) => T;

Compute the square of a value, x * x.
Parameter x
Number for which to calculate the square
Returns
Squared value

method squeeze

squeeze: <T extends MathCollection<any>>(x: T) => T;

Squeeze a matrix, remove inner and outer singleton dimensions from a matrix.
Parameter x
Matrix to be squeezed
Returns
Squeezed matrix

method std

std: {
    <T extends unknown>(...args: T[]): T;
    (...args: any[]): any;
    (
        array: MathCollection<any>,
        dimension?: number,
        normalization?: 'unbiased' | 'uncorrected' | 'biased'
    ): any[];
    (
        array: MathCollection<any>,
        normalization: 'unbiased' | 'uncorrected' | 'biased'
    ): any;
};

Compute the standard deviation of a matrix or a list with values. The standard deviations is defined as the square root of the variance: std(A) = sqrt(variance(A)). In case of a (multi dimensional) array or matrix, the standard deviation over all elements will be calculated. Optionally, the type of normalization can be specified as second parameter. The parameter normalization can be one of the following values: 'unbiased' (default) The sum of squared errors is divided by (n - 1) 'uncorrected' The sum of squared errors is divided by n 'biased' The sum of squared errors is divided by (n + 1)
Parameter args
variadic argument of number to calculate standard deviation
Returns
The standard deviation
Parameter args
Multiple scalar values
Returns
The standard deviation
Compute the standard deviation of a matrix or a list with values. The standard deviations is defined as the square root of the variance: std(A) = sqrt(variance(A)). In case of a (multi dimensional) array or matrix, the standard deviation over all elements will be calculated. Optionally, the type of normalization can be specified as second parameter. The parameter normalization can be one of the following values: 'unbiased' (default) The sum of squared errors is divided by (n - 1) 'uncorrected' The sum of squared errors is divided by n 'biased' The sum of squared errors is divided by (n + 1)
Parameter array
A single matrix to compute standard deviation.
Parameter dimension
A dimension to calculate standard deviation
Parameter normalization
Determines how to normalize the variance. Choose ‘unbiased’ (default), ‘uncorrected’, or ‘biased’. Default value: ‘unbiased’.
Returns
The standard deviation array
Compute the standard deviation of a matrix or a list with values. The standard deviations is defined as the square root of the variance: std(A) = sqrt(variance(A)). In case of a (multi dimensional) array or matrix, the standard deviation over all elements will be calculated. Optionally, the type of normalization can be specified as second parameter. The parameter normalization can be one of the following values: 'unbiased' (default) The sum of squared errors is divided by (n - 1) 'uncorrected' The sum of squared errors is divided by n 'biased' The sum of squared errors is divided by (n + 1)
Parameter array
A single matrix or multiple scalar values
Parameter normalization
Determines how to normalize the variance. Choose ‘unbiased’ (default), ‘uncorrected’, or ‘biased’. Default value: ‘unbiased’.
Returns
The standard deviation

method stirlingS2

stirlingS2: <T extends number | BigNumber>(
    n: T,
    k: number | BigNumber
) => NoLiteralType<T>;

The Stirling numbers of the second kind, counts the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets. stirlingS2 only takes integer arguments. The following condition must be enforced: k <= n. If n = k or k = 1, then s(n,k) = 1
Parameter n
Total number of objects in the set
Parameter k
Number of objects in the subset
Returns
S(n,k)

method string

string: {
    (value: MathNumericType | string | Unit | null): string;
    (value: MathCollection<any>): MathCollection<any>;
};

Create a string or convert any object into a string. Elements of Arrays and Matrices are processed element wise.
Parameter value
A value to convert to a string
Returns
The created string

method subset

subset: <T extends string | MathCollection<any>>(
    value: T,
    index: Index,
    replacement?: any,
    defaultValue?: any
) => T;

Get or set a subset of a matrix or string.
Parameter value
An array, matrix, or string
Parameter index
For each dimension, an index or list of indices to get or set.
Parameter replacement
An array, matrix, or scalar. If provided, the subset is replaced with replacement. If not provided, the subset is returned
Parameter defaultValue
Default value, filled in on new entries when the matrix is resized. If not provided, math.matrix elements will be left undefined. Default value: undefined.
Returns
Either the retrieved subset or the updated matrix

method subtract

subtract: { <T extends unknown>(x: T, y: T): T; (x: any, y: any): any };

Subtract two values, x - y. For matrices, the function is evaluated element wise.
Parameter x
Initial value
Parameter y
Value to subtract from x
Returns
Subtraction of x and y

method sum

sum: {
    <T extends unknown>(...args: T[]): T;
    (...args: any[]): any;
    <T extends unknown>(A: T[] | T[][], dimension?: number | BigNumber): T;
    (A: MathCollection<any>, dimension?: number | BigNumber): any;
};

Compute the sum of a matrix or a list with values. In case of a (multi dimensional) array or matrix, the sum of all elements will be calculated.
Parameter args
A single matrix or multiple scalar values
Returns
The sum of all values
Parameter args
Multiple scalar values
Returns
The sum of all values
Parameter A
A single matrix
Parameter dimension
The sum over the selected dimension
Returns
The sum of all values

method sylvester

sylvester: (
    A: MathCollection,
    B: MathCollection,
    C: MathCollection
) => MathCollection;

Solves the real-valued Sylvester equation AX-XB=C for X, where A, B and C are matrices of appropriate dimensions, being A and B squared. The method used is the Bartels-Stewart algorithm. https://en.wikipedia.org/wiki/Sylvester_equation
Parameter A
Matrix A
Parameter B
Matrix B
Parameter C
Matrix C
Returns
Matrix X, solving the Sylvester equation

method symbolicEqual

symbolicEqual: (
    expr1: MathNode,
    expr2: MathNode,
    options?: SimplifyOptions
) => boolean;

Determines if two expressions are symbolically equal, i.e. one is the result of valid algebraic manipulations on the other.
Parameter expr1
The first expression to compare
Parameter expr2
The second expression to compare
Parameter options
Optional option object, passed to simplify
Returns
{boolean} Returns true if a valid manipulation making the expressions equal is found.

method tan

tan: { (x: number | Unit): number; <T extends BigNumber | Complex>(x: T): T };

Calculate the tangent of a value. tan(x) is equal to sin(x) / cos(x).
Parameter x
Function input
Returns
The tangent of x

method tanh

tanh: { (x: number | Unit): number; <T extends BigNumber | Complex>(x: T): T };

Calculate the hyperbolic tangent of a value, defined as tanh(x) = (exp(2 * x) - 1) / (exp(2 * x) + 1).
Parameter x
Function input
Returns
The hyperbolic tangent of x

method to

to: (x: Unit | MathCollection, unit: Unit | string) => Unit | MathCollection;

Change the unit of a value. For matrices, the function is evaluated element wise.
Parameter x
The unit to be converted.
Parameter unit
New unit. Can be a string like "cm" or a unit without value.
Returns
Value with changed, fixed unit

method toBest

toBest: { (): Unit; (units: string[] | Unit[], options: object): Unit };

Converts a unit to the most appropriate display unit. When no preferred units are provided, the function automatically find the best prefix. When preferred units are provided, it converts to the unit that gives a value closest to 1.
Parameter preferredUnits
Optional preferred target units
Parameter options
Optional options object
Returns
Unit with optimized prefix/unit

method trace

trace: (x: MathCollection) => number;

Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.
Parameter x
A matrix
Returns
The trace of x

method transpose

transpose: <T extends MathCollection<any>>(x: T) => T;

Transpose a matrix. All values of the matrix are reflected over its main diagonal. Only two dimensional matrices are supported.
Parameter x
Matrix to be transposed
Returns
The transposed matrix

method typeOf

typeOf: (x: any) => string;

Determine the type of a variable.
Parameter x
The variable for which to test the type
Returns
Returns the name of the type. Primitive types are lower case, non-primitive types are upper-camel-case. For example ‘number’, ‘string’, ‘Array’, ‘Date’.

method unaryMinus

unaryMinus: <T extends unknown>(x: T) => T;

Inverse the sign of a value, apply a unary minus operation. For matrices, the function is evaluated element wise. Boolean values and strings will be converted to a number. For complex numbers, both real and complex value are inverted.
Parameter x
Number to be inverted
Returns
Retursn the value with inverted sign

method unaryPlus

unaryPlus: <T extends unknown>(x: T) => T;

Unary plus operation. Boolean values and strings will be converted to a number, numeric values will be returned as is. For matrices, the function is evaluated element wise.
Parameter x
Input value
Returns
Returns the input value when numeric, converts to a number when input is non-numeric.

method unequal

unequal: (
    x: MathType | string,
    y: MathType | string
) => boolean | MathCollection;

Test whether two values are unequal. The function tests whether the relative difference between x and y is larger than the configured relTol and absTol. The function cannot be used to compare values smaller than approximately 2.22e-16. For matrices, the function is evaluated element wise. In case of complex numbers, x.re must unequal y.re, or x.im must unequal y.im. Values null and undefined are compared strictly, thus null is unequal with everything except null, and undefined is unequal with everything except undefined.
Parameter x
First value to compare
Parameter y
Second value to vcompare
Returns
Returns true when the compared values are unequal, else returns false

method unit

unit: {
    (unit: string): Unit;
    (unit: Unit): Unit;
    (value: any, unit?: string): Unit;
    (value: MathCollection<any>): Unit[];
};

Create a unit. Depending on the passed arguments, the function will create and return a new math.type.Unit object. When a matrix is provided, all elements will be converted to units.
Parameter unit
The unit to be created
Returns
The created unit
Parameter unit
The unit to be created
Returns
The created unit
Parameter value
The value of the unit to be created
Parameter unit
The unit to be created
Returns
The created unit

method usolve

usolve: {
    (U: Matrix, b: MathCollection): Matrix;
    (U: MathArray<any>, b: MathCollection<any>): MathArray<any>;
};

Solves the linear equation system by backward substitution. Matrix must be an upper triangular matrix. U * x = b
Parameter U
A N x N matrix or array (U)
Parameter b
A column vector with the b values
Returns
A column vector with the linear system solution (x)

method variance

variance: {
    (...args: MathNumericType[]): MathNumericType;
    (
        array: MathCollection<any>,
        dimension?: number,
        normalization?: 'unbiased' | 'uncorrected' | 'biased'
    ): any[];
    (
        array: MathCollection<any>,
        normalization: 'unbiased' | 'uncorrected' | 'biased'
    ): any;
};

Compute the variance of a matrix or a list with values. In case of a (multi dimensional) array or matrix, the variance over all elements will be calculated. Optionally, the type of normalization can be specified as second parameter. The parameter normalization can be one of the following values: 'unbiased' (default) The sum of squared errors is divided by (n - 1) 'uncorrected' The sum of squared errors is divided by n 'biased' The sum of squared errors is divided by (n + 1) Note that older browser may not like the variable name var. In that case, the function can be called as math['var'](...) instead of math.variance(...).
Parameter args
A single matrix or multiple scalar values
Returns
The variance
Compute the variance of a matrix or a list with values. In case of a (multi dimensional) array or matrix, the variance over all elements will be calculated. Optionally, the type of normalization can be specified as second parameter. The parameter normalization can be one of the following values: 'unbiased' (default) The sum of squared errors is divided by (n - 1) 'uncorrected' The sum of squared errors is divided by n 'biased' The sum of squared errors is divided by (n + 1) Note that older browser may not like the variable name var. In that case, the function can be called as math['var'](...) instead of math.variance(...).
Parameter array
A matrix to compute variance.
Parameter dimension
A dimension to compute variance on
Parameter normalization
normalization Determines how to normalize the variance. Choose ‘unbiased’ (default), ‘uncorrected’, or ‘biased’. Default value: ‘unbiased’.
Returns
variance matrix.
Parameter array
A single matrix
Parameter normalization
normalization Determines how to normalize the variance. Choose ‘unbiased’ (default), ‘uncorrected’, or ‘biased’. Default value: ‘unbiased’.
Returns
The variance

method xgcd

xgcd: (a: number | BigNumber, b: number | BigNumber) => MathArray;

Calculate the extended greatest common divisor for two values. See http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm.
Parameter a
An integer number
Parameter b
An integer number
Returns
Returns an array containing 3 integers [div, m, n] where div = gcd(a, b) and a*m + b*n = div

method xor

xor: (
    x: number | BigNumber | bigint | Complex | Unit | MathCollection,
    y: number | BigNumber | bigint | Complex | Unit | MathCollection
) => boolean | MathCollection;

Logical xor. Test whether one and only one value is defined with a nonzero/nonempty value. For matrices, the function is evaluated element wise.
Parameter x
First value to xor
Parameter y
Second value to xor
Returns
Returns true when one and only one input is defined with a nonzero/nonempty value.

method zeros

zeros: {
    (
        size?: number | number[] | BigNumber | BigNumber[],
        format?: string
    ): MathCollection;
    (
        m: number | BigNumber,
        n: number | BigNumber,
        format?: string
    ): MathCollection<any>;
    (
        m: number | BigNumber,
        n: number | BigNumber,
        p: number | BigNumber,
        format?: string
    ): MathCollection<any>;
};

Create a matrix filled with zeros. The created matrix can have one or multiple dimensions.
Parameter size
The size of each dimension of the matrix
Parameter format
The matrix storage format
Returns
A matrix filled with zeros
Parameter m
The x dimension of the matrix
Parameter n
The y dimension of the matrix
Parameter format
The matrix storage format
Returns
A matrix filled with zeros
Parameter m
The x dimension of the matrix
Parameter n
The y dimension of the matrix
Parameter p
The z dimension of the matrix
Parameter format
The matrix storage format
Returns
A matrix filled with zeros

method zeta

zeta: <T extends number | BigNumber | Complex>(s: T) => T;

Compute the Riemann Zeta function of a value using an infinite series and Riemann's Functional equation.
Parameter s
A real, complex or BigNumber
Returns
The Riemann Zeta of s

method zpk2tf

zpk2tf: <T extends MathCollection<any>>(z: T, p: T, k?: number) => T;

Compute the transfer function of a zero-pole-gain model.
Parameter z
Zeroes of the model
Parameter p
Poles of the model
Parameter k
Gain of the model
Returns
The transfer function as array of numerator and denominator

interface MathJSON

interface MathJSON {}

property fixPrefix

fixPrefix?: boolean;

property mathjs

mathjs?: string;

property unit

unit: string;

property value

value: number;

interface MathNode

interface MathNode {}

property comment

comment: string;

property isNode

isNode: true;

property isUpdateNode

isUpdateNode?: boolean;

property type

type: string;

method clone

clone: () => this;

Create a shallow clone of the node. The node itself is cloned, its childs are not cloned.

method cloneDeep

cloneDeep: () => this;

Create a deep clone of the node. Both the node as well as all its childs are cloned recursively.

method compile

compile: () => EvalFunction;

Compile an expression into optimized JavaScript code. compile returns an object with a function evaluate([scope]) to evaluate. Example:

method equals

equals: (other: MathNode) => boolean;

Test whether this node equals an other node. Does a deep comparison of the values of both nodes.

method evaluate

evaluate: (scope?: MathScope) => any;

Compile and eval an expression, this is the equivalent of doing node.compile().evaluate(scope). Example:

method filter

filter: (
    callback: (node: MathNode, path: string, parent: MathNode) => any
) => MathNode[];

Filter nodes in an expression tree. The callback function is called as callback(node: MathNode, path: string, parent: MathNode) : boolean for every node in the tree, and must return a boolean. The function filter returns an array with nodes for which the test returned true. Parameter path is a string containing a relative JSON Path.
Example:
var node = math.parse('x^2 + x/4 + 3*y'); var filtered = node.filter(function (node) { return node.isSymbolMathNode && node.name == 'x'; }); // returns an array with two entries: two SymbolMathNodes 'x'
The callback function is called as callback(node: MathNode, path: string, parent: MathNode) : boolean for every node in the tree, and must return a boolean. The function filter returns an array with nodes for which the test returned true. Parameter path is a string containing a relative JSON Path. Returns an array with nodes for which test returned true

method forEach

forEach: (
    callback: (node: MathNode, path: string, parent: MathNode) => void
) => void;

[forEach description]

method map

map: (
    callback: (node: MathNode, path: string, parent: MathNode) => MathNode
) => MathNode;

Transform a node. Creates a new MathNode having it’s child's be the results of calling the provided callback function for each of the child's of the original node. The callback function is called as callback(child: MathNode, path: string, parent: MathNode) and must return a MathNode. Parameter path is a string containing a relative JSON Path.
See also transform, which is a recursive version of map.

method toHTML

toHTML: (options?: object) => string;

Get a HTML representation of the parsed expression.

method toString

toString: (options?: object) => string;

Get a string representation of the parsed expression. This is not exactly the same as the original input.

method toTex

toTex: (options?: object) => string;

Get a LaTeX representation of the expression.

method transform

transform: <TResult>(
    callback: (node: this, path: string, parent: MathNode) => TResult
) => TResult;

Recursively transform an expression tree via a transform function. Similar to Array.map, but recursively executed on all nodes in the expression tree. The callback function is a mapping function accepting a node, and returning a replacement for the node or the original node. Function callback is called as callback(node: MathNode, path: string, parent: MathNode) for every node in the tree, and must return a MathNode. Parameter path is a string containing a relative JSON Path.
For example, to replace all nodes of type SymbolMathNode having name ‘x’ with a ConstantMathNode with value 3:
var node = math.parse('x^2 + 5*x'); var transformed = node.transform(function (node, path, parent) { if (node.SymbolMathNode && node.name == 'x') { return new math.expression.node.ConstantMathNode(3); } else { return node; } }); transformed.toString(); // returns '(3 ^ 2) + (5 * 3)'

method traverse

traverse: (
    callback: (node: MathNode, path: string, parent: MathNode) => void
) => void;

traverse(callback)
Recursively traverse all nodes in a node tree. Executes given callback for this node and each of its child nodes. Similar to Array.forEach, except recursive. The callback function is a mapping function accepting a node, and returning a replacement for the node or the original node. Function callback is called as callback(node: MathNode, path: string, parent: MathNode) for every node in the tree. Parameter path is a string containing a relative JSON Path. Example:
var node = math.parse('3 * x + 2'); node.traverse(function (node, path, parent) { switch (node.type) { case 'OperatorMathNode': console.log(node.type, node.op); break; case 'ConstantMathNode': console.log(node.type, node.value); break; case 'SymbolMathNode': console.log(node.type, node.name); break; default: console.log(node.type); } }); // outputs: // OperatorMathNode + // OperatorMathNode * // ConstantMathNode 3 // SymbolMathNode x // ConstantMathNode 2

interface Matrix

interface Matrix<T = MathGeneric> {}

property type

type: string;

method clone

clone: () => Matrix<T>;

method create

create: (data: MathArray, datatype?: string) => void;

method datatype

datatype: () => string;

method density

density: () => number;

method diagonal

diagonal: (k?: number | BigNumber) => any[];

method forEach

forEach: (
    callback: (a: any, b: number[], c: Matrix) => void,
    skipZeros?: boolean
) => void;

method format

format: (
    options?: number | BigNumber | FormatOptions | ((value: any) => string)
) => string;

method get

get: (index: number[]) => any;

method map

map: (
    callback: (a: any, b: number[], c: Matrix) => any,
    skipZeros?: boolean
) => Matrix;

method resize

resize: (size: MathCollection, defaultValue?: number | string) => Matrix;

method set

set: (index: number[], value: any, defaultValue?: number | string) => Matrix;

method size

size: () => number[];

method storage

storage: () => string;

method subset

subset: (index: Index, replacement?: any, defaultValue?: any) => Matrix;

method swapRows

swapRows: (i: number, j: number) => Matrix<T>;

method toArray

toArray: () => MathArray<T>;

method toJSON

toJSON: () => any;

method toString

toString: () => string;

method valueOf

valueOf: () => MathArray<T>;

interface MatrixCtor

interface MatrixCtor {}

construct signature

new (): Matrix;

interface NodeCtor

interface NodeCtor {}

construct signature

new (): MathNode;

interface ObjectNode

interface ObjectNode<
    TProps extends Record<string, MathNode> = Record<string, MathNode>
> extends MathNode {}

property isObjectNode

isObjectNode: true;

property properties

properties: TProps;

property type

type: 'ObjectNode';

interface ObjectNodeCtor

interface ObjectNodeCtor {}

construct signature

new <TProps extends Record<string, MathNode> = Record<string, MathNode>>(
    properties: TProps
): ObjectNode<TProps>;

interface ObjectWrappingMap

interface ObjectWrappingMap<T extends string | number | symbol, U> {}

property wrappedObject

wrappedObject: Record<T, U>;

interface OperatorNode

interface OperatorNode<
    TOp extends OperatorNodeMap[TFn] = never,
    TFn extends OperatorNodeFn = never,
    TArgs extends MathNode[] = MathNode[]
> extends MathNode {}

property args

args: [...TArgs];

property fn

fn: TFn;

property implicit

implicit: boolean;

property isOperatorNode

isOperatorNode: true;

property op

op: TOp;

property type

type: 'OperatorNode';

method isBinary

isBinary: () => boolean;

method isUnary

isUnary: () => boolean;

interface OperatorNodeCtor

interface OperatorNodeCtor extends MathNode {}

construct signature

new <
    TOp extends OperatorNodeMap[TFn],
    TFn extends OperatorNodeFn,
    TArgs extends MathNode[]
>(
    op: TOp,
    fn: TFn,
    args: [...TArgs],
    implicit?: boolean
): OperatorNode<TOp, TFn, TArgs>;

interface ParenthesisNode

interface ParenthesisNode<TContent extends MathNode = MathNode> extends MathNode {}

property content

content: TContent;

property isParenthesisNode

isParenthesisNode: true;

property type

type: 'ParenthesisNode';

interface ParenthesisNodeCtor

interface ParenthesisNodeCtor {}

construct signature

new <TContent extends MathNode>(content: TContent): ParenthesisNode<TContent>;

interface ParseFunction

interface ParseFunction {}

Parse an expression. Returns a node tree, which can be evaluated by invoking node.evaluate().
Note the evaluating arbitrary expressions may involve security risks, see [https://mathjs.org/docs/expressions/security.html](https://mathjs.org/docs/expressions/security.html) for more information.
Syntax:
math.parse(expr) math.parse(expr, options) math.parse([expr1, expr2, expr3, ...]) math.parse([expr1, expr2, expr3, ...], options)
Example:
const node1 = math.parse('sqrt(3^2 + 4^2)') node1.compile().evaluate() // 5
let scope = {a:3, b:4} const node2 = math.parse('a * b') // 12 const code2 = node2.compile() code2.evaluate(scope) // 12 scope.a = 5 code2.evaluate(scope) // 20
const nodes = math.parse(['a = 3', 'b = 4', 'a * b']) nodes[2].compile().evaluate() // 12
See also:
evaluate, compile

method isAlpha

isAlpha: (c: string, cPrev: string, cNext: string) => boolean;

Checks whether the current character c is a valid alpha character:
- A latin letter (upper or lower case) Ascii: a-z, A-Z - An underscore Ascii: _ - A dollar sign Ascii: $ - A latin letter with accents Unicode: \u00C0 - \u02AF - A greek letter Unicode: \u0370 - \u03FF - A mathematical alphanumeric symbol Unicode: \u{1D400} - \u{1D7FF} excluding invalid code points
The previous and next characters are needed to determine whether this character is part of a unicode surrogate pair.
Parameter c
Current character in the expression
Parameter cPrev
Previous character
Parameter cNext
Next character

method isDecimalMark

isDecimalMark: (c: string, cNext: string) => boolean;

Test whether the character c is a decimal mark (dot). This is the case when it's not the start of a delimiter '.*', './', or '.^'
Parameter c
Parameter cNext

method isDigit

isDigit: (c: string) => boolean;

checks if the given char c is a digit
Parameter c
a string with one character

method isDigitDot

isDigitDot: (c: string) => boolean;

checks if the given char c is a digit or dot
Parameter c
a string with one character

method isHexDigit

isHexDigit: (c: string) => boolean;

checks if the given char c is a hex digit
Parameter c
a string with one character

method isValidLatinOrGreek

isValidLatinOrGreek: (c: string) => boolean;

Test whether a character is a valid latin, greek, or letter-like character
Parameter c

method isValidMathSymbol

isValidMathSymbol: (high: string, low: string) => boolean;

Test whether two given 16 bit characters form a surrogate pair of a unicode math symbol.
https://unicode-table.com/en/ https://www.wikiwand.com/en/Mathematical_operators_and_symbols_in_Unicode
Note: In ES6 will be unicode aware: https://stackoverflow.com/questions/280712/javascript-unicode-regexes https://mathiasbynens.be/notes/es6-unicode-regex
Parameter high
Parameter low

method isWhitespace

isWhitespace: (c: string, nestingLevel: number) => boolean;

Check whether given character c is a white space character: space, tab, or enter
Parameter c
Parameter nestingLevel

call signature

(expr: MathExpression, options?: ParseOptions): MathNode;

Parse an expression. Returns a node tree, which can be evaluated by invoking node.evaluate();
Parameter expr
Expression to be parsed
Parameter options
Available options
Returns
A node

call signature

(exprs: MathExpression[], options?: ParseOptions): MathNode[];

Parse an expression. Returns a node tree, which can be evaluated by invoking node.evaluate();
Parameter exprs
Expressions to be parsed
Parameter options
Available options
Returns
An array of nodes

interface ParseOptions

interface ParseOptions {}

Available options for parse

property nodes

nodes?: Record<string, MathNode>;

a set of custom nodes

interface Parser

interface Parser {}

property clear

clear: () => void;

Completely clear the parser’s scope.

property remove

remove: (name: string) => void;

Remove a variable or function from the parser’s scope.
Parameter name
The name of the variable or function to be removed

property set

set: (name: string, value: any) => void;

Set a variable or function in the parser’s scope.
Parameter name
The name of the variable or function to be set
Parameter value
The value of the variable or function to be set

method evaluate

evaluate: (expr: string | string[]) => any;

Evaluate an expression. Returns the result of the expression.
Parameter expr
The expression to evaluate

method get

get: (name: string) => any;

Retrieve a variable or function from the parser’s scope.
Parameter name
The name of the variable or function to be retrieved

method getAll

getAll: () => { [key: string]: any };

Retrieve an object with all defined variables in the parser’s scope.
Returns
An object with all defined variables

method getAllAsMap

getAllAsMap: () => Map<string, any>;

Retrieve a map with all defined variables in the parser’s scope.

interface PartitionedMap

interface PartitionedMap<T, U> {}

property a

a: Map<T, U>;

property b

b: Map<T, U>;

interface PolarCoordinates

interface PolarCoordinates {}

property phi

phi: number;

property r

r: number;

interface QRDecomposition

interface QRDecomposition {}

property Q

Q: MathCollection;

property R

R: MathCollection;

interface RangeNode

interface RangeNode<
    TStart extends MathNode = MathNode,
    TEnd extends MathNode = MathNode,
    TStep extends MathNode = MathNode
> extends MathNode {}

property end

end: TEnd;

property isRangeNode

isRangeNode: true;

property start

start: TStart;

property step

step: TStep | null;

property type

type: 'RangeNode';

interface RangeNodeCtor

interface RangeNodeCtor {}

construct signature

new <
    TStart extends MathNode = MathNode,
    TEnd extends MathNode = MathNode,
    TStep extends MathNode = MathNode
>(
    start: TStart,
    end: TEnd,
    step?: TStep
): RangeNode<TStart, TEnd, TStep>;

interface RelationalNode

interface RelationalNode<TParams extends MathNode[] = MathNode[]> extends MathNode {}

property conditionals

conditionals: string[];

property isRelationalNode

isRelationalNode: true;

property params

params: [...TParams];

property type

type: 'RelationalNode';

interface RelationalNodeCtor

interface RelationalNodeCtor {}

construct signature

new <TParams extends MathNode[] = MathNode[]>(
    conditionals: string[],
    params: [...TParams]
): RelationalNode<TParams>;

interface ResultSet

interface ResultSet {}

property entries

entries: unknown[];

method toJSON

toJSON: () => MathJSON;

method toString

toString: () => string;

method valueOf

valueOf: () => unknown[];

interface SchurDecomposition

interface SchurDecomposition {}

property T

T: MathCollection;

property U

U: MathCollection;

interface Simplify

interface Simplify {}

property rules

rules: SimplifyRule[];

call signature

(expr: MathNode | string): MathNode;

call signature

(
    expr: MathNode | string,
    rules: SimplifyRule[],
    scope?: MathScope,
    options?: SimplifyOptions
): MathNode;

call signature

(expr: MathNode | string, scope: MathScope, options?: SimplifyOptions): MathNode;

interface SimplifyOptions

interface SimplifyOptions {}

property consoleDebug

consoleDebug?: boolean;

A boolean which is false by default.

property context

context?: SimplifyContext;

gives properties of each operator, which determine what simplifications are allowed. Properties are commutative, associative, total (whether the operation is defined for all arguments), and trivial (whether the operation applied to a single argument leaves that argument unchanged).

property exactFractions

exactFractions?: boolean;

A boolean which is true by default.

property fractionsLimit

fractionsLimit?: number;

When exactFractions is true, a fraction will be returned only when both numerator and denominator are smaller than fractionsLimit. Default value is 10000.

interface SLUDecomposition

interface SLUDecomposition extends LUDecomposition {}

property q

q: number[];

interface SymbolNode

interface SymbolNode extends MathNode {}

property isSymbolNode

isSymbolNode: true;

property name

name: string;

property type

type: 'SymbolNode';

interface SymbolNodeCtor

interface SymbolNodeCtor {}

property onUndefinedSymbol

onUndefinedSymbol: (name: string) => any;

construct signature

new (name: string): SymbolNode;

interface Unit

interface Unit {}

property dimensions

dimensions: number[];

property fixPrefix

fixPrefix: boolean;

property skipAutomaticSimplification

skipAutomaticSimplification: true;

property units

units: UnitComponent[];

property value

value: number;

method abs

abs: (unit: Unit) => Unit;

method clone

clone: () => Unit;

method divide

divide: (unit: Unit) => Unit | number;

method equalBase

equalBase: (unit: Unit) => boolean;

method equals

equals: (unit: Unit) => boolean;

method format

format: (options: FormatOptions) => string;

method formatUnits

formatUnits: () => string;

method hasBase

hasBase: (base: BaseUnit | string | undefined) => boolean;

method multiply

multiply: (unit: Unit) => Unit;

method pow

pow: (unit: Unit) => Unit;

method simplify

simplify: () => Unit;

method splitUnit

splitUnit: (parts: ReadonlyArray<string | Unit>) => Unit[];

method to

to: (unit: string | Unit) => Unit;

method toBest

toBest: { (): Unit; (units?: string[] | Unit[], options?: object): Unit };

method toJSON

toJSON: () => MathJSON;

method toNumber

toNumber: (unit?: string) => number;

method toNumeric

toNumeric: (unit?: string) => number | Fraction | BigNumber;

method toSI

toSI: () => Unit;

method toString

toString: () => string;

method valueOf

valueOf: () => string;

interface UnitComponent

interface UnitComponent {}

property power

power: number;

property prefix

prefix: string;

property unit

unit: {
    name: string;
    base: BaseUnit;
    prefixes: Record<string, UnitPrefix>;
    value: number;
    offset: number;
    dimensions: number[];
};

interface UnitCtor

interface UnitCtor extends UnitStatic {}

construct signature

new (
    value: number | BigNumber | Fraction | Complex | boolean,
    name: string
): Unit;

interface UnitDefinition

interface UnitDefinition {}

property aliases

aliases?: string[];

property baseName

baseName?: string;

property definition

definition?: string | Unit;

property offset

offset?: number;

property prefixes

prefixes?: string;

interface UnitPrefix

interface UnitPrefix {}

property name

name: string;

property scientific

scientific: boolean;

property value

value: number;

interface UnitStatic

interface UnitStatic {}

property BASE_DIMENSIONS

BASE_DIMENSIONS: string[];

property BASE_UNITS

BASE_UNITS: Record<string, BaseUnit>;

property PREFIXES

PREFIXES: Record<string, UnitPrefix>;

property UNIT_SYSTEMS

UNIT_SYSTEMS: Record<
    UnitSystemName,
    Record<string, { unit: Unit; prefix: UnitPrefix }>
>;

property UNITS

UNITS: Record<string, Unit>;

method createUnit

createUnit: (
    obj: Record<string, string | Unit | UnitDefinition>,
    options?: { override: boolean }
) => Unit;

method createUnitSingle

createUnitSingle: (
    name: string,
    definition: string | Unit | UnitDefinition
) => Unit;

method fromJSON

fromJSON: (json: MathJSON) => Unit;

method getUnitSystem

getUnitSystem: () => UnitSystemName;

method isValidAlpha

isValidAlpha: (c: string) => boolean;

method isValuelessUnit

isValuelessUnit: (name: string) => boolean;

method parse

parse: (str: string) => Unit;

method setUnitSystem

setUnitSystem: (name: UnitSystemName) => void;

Type Aliases

type FactoryDependencies

type FactoryDependencies = void;

Deprecated
since v12.0.0. Use MathJsFactory instead and import dependency maps directly from the library

type FactoryFunction

type FactoryFunction<T> = (scope: MathScope) => T;

type MathArray

type MathArray<T = MathGeneric> = T[] | Array<MathArray<T>>;

type MathCollection

type MathCollection<T = MathGeneric> = MathArray<T> | Matrix<T>;

type MathExpression

type MathExpression = string | string[] | MathCollection;

type MathGeneric

type MathGeneric<T extends MathScalarType = MathNumericType> = T;

type MathJsFunctionName

type MathJsFunctionName = keyof MathJsInstance;

type MathJsStatic

type MathJsStatic = MathJsInstance;

Deprecated
since v12.0.0. The interface MathJsStatic has been renamed to MathJsInstance

type MathNodeCommon

type MathNodeCommon = MathNode;

Deprecated
since version 11.3. Prefer MathNode instead

type MathNumericType

type MathNumericType = number | BigNumber | bigint | Fraction | Complex;

type MathScalarType

type MathScalarType = MathNumericType | Unit;

type MathScope

type MathScope<TValue = any> = Record<string, TValue> | MapLike<string, TValue>;

type MathType

type MathType = MathScalarType | MathCollection;

type MatrixFromFunctionCallback

type MatrixFromFunctionCallback<T extends MathScalarType> = (index: number[]) => T;

type MatrixStorageFormat

type MatrixStorageFormat = 'dense' | 'sparse';

type NoLiteralType

type NoLiteralType<T> = T extends number
    ? number
    : T extends string
    ? string
    : T extends boolean
    ? boolean
    : T;

type OperatorNodeFn

type OperatorNodeFn = keyof OperatorNodeMap;

type OperatorNodeMap

type OperatorNodeMap = {
    xor: 'xor';
    and: 'and';
    or: 'or';
    bitOr: '|';
    bitXor: '^|';
    bitAnd: '&';
    equal: '==';
    unequal: '!=';
    smaller: '<';
    larger: '>';
    smallerEq: '<=';
    largerEq: '>=';
    leftShift: '<<';
    rightArithShift: '>>';
    rightLogShift: '>>>';
    to: 'to';
    add: '+';
    subtract: '-';
    multiply: '*';
    divide: '/';
    dotMultiply: '.*';
    dotDivide: './';
    mod: 'mod';
    unaryPlus: '+';
    unaryMinus: '-';
    bitNot: '~';
    not: 'not';
    pow: '^';
    dotPow: '.^';
    factorial: '!';
};

type OperatorNodeOp

type OperatorNodeOp = OperatorNodeMap[keyof OperatorNodeMap];

type SimplifyContext

type SimplifyContext = Partial<
    Record<
        OperatorNodeFn,
        {
            trivial: boolean;
            total: boolean;
            commutative: boolean;
            associative: boolean;
        }
    >
>;

type SimplifyRule

type SimplifyRule =
    | {
          l: string;
          r: string;
          repeat?: boolean;
          assuming?: SimplifyContext;
          imposeContext?: SimplifyContext;
      }
    | {
          s: string;
          repeat?: boolean;
          assuming?: SimplifyContext;
          imposeContext?: SimplifyContext;
      }
    | string
    | ((node: MathNode) => MathNode);

type UnitSystemName

type UnitSystemName = 'si' | 'cgs' | 'us' | 'auto';

Package Files (1)

types/index.d.ts

Dependencies (9)

Peer Dependencies (0)

No peer dependencies.

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mathjs

Install

Overview

Index

Interfaces

Type Aliases

Interfaces

interface AccessorNode

property index

property isAccessorNode

property name

property object

property type

interface AccessorNodeCtor

interface ArrayNode

property isArrayNode

property items

property type

interface ArrayNodeCtor

interface AssignmentNode

property index

property isAssignmentNode

property name

property object

property type

property value

interface AssignmentNodeCtor

interface BaseUnit

property dimensions

property key

interface BigNumber

interface BlockNode

property blocks

property isBlockNode

property type

interface BlockNodeCtor

interface Complex

property im

property re

method clone

method compare

method equals

method format

method fromJSON

method fromPolar

method toJSON

method toPolar

method toString

interface ConditionalNode

property condition

property falseExpr

property isConditionalNode

property trueExpr

property type

interface ConditionalNodeCtor

interface ConfigOptions

property absTol

property epsilon

Deprecated

property matrix

property number

property numberFallback

property precision

property predictable

property randomSeed

property relTol

interface ConstantNode

property isConstantNode

property type

property value

interface ConstantNodeCtor

interface CreateUnitOptions

property aliases

property offset

property override

property prefixes

interface Distribution

method pickRandom

method random

method randomInt