Global

Members

# (readonly) ErrorCode :number

Enum for all error codes.

Type:
Properties
Name Type Description
INT_BIGGER_THAN_MAX_ULL number

Error Code throwed because a big integer is bigget than the maximum unsigned integer value
DOUBLE_OVERFLOW number

Error Code throwed because a Integer value is too big to fit on a 64 bits float
LONG_LONG_OVERFLOW number

Error Code throwed because a Integer value is too big to fit on a 64 bits integer
DIVISION_BY_ZERO number

Error Code throwed because a division by zero occured
ARG_IS_INVALID number

Error Code throwed because an argument is invalid
MATRIX_INVALID_ADDITION number

Error Code throwed because a reduction encounter a invalid matrix addition
MATRIX_INVALID_MULTIPLICATION number

Error Code throwed because a reduction encounter a invalid matrix multiplication
NUMBER_HAVE_NO_MODULAR_INVERSE number

Error Code throwed because a number have no modular inverse
POLY_HAVE_NON_INTEGER_DEGREE number

Error Code throwed by methods that expects polynomial with integer degrees
POLY_HAVE_NON_CONSTANT_COEFFICIENT number

Error Code throwed by methods that expects polynomial expressions with constant coefficients
ARG_IS_NOT_SYM_EXPR number

Error Code throwed by methods that do not receive a symbol expr when expected
ARG_IS_NOT_POW_EXPR number

Error Code throwed by methods that do not receive a power expr when expected
ARG_IS_NOT_INT_EXPR number

Error Code throwed by methods that do not receive a integer expr when expected
ARG_IS_NOT_FRA_EXPR number

Error Code throwed by methods that do not receive a fraction expr when expected
ARG_IS_NOT_ADD_EXPR number

Error Code throwed by methods that do not receive a add expr when expected
ARG_IS_NOT_SUB_EXPR number

Error Code throwed by methods that do not receive a sub expr when expected
ARG_IS_NOT_ROOT_EXPR number

Error Code throwed by methods that do not receive a root expr when expected
ARG_IS_NOT_POLY_EXPR number

Error Code throwed by methods that do not receive a poly expr when expected
ARG_IS_NOT_LIST_EXPR number

Error Code throwed by methods that do not receive a list when expected
ARG_IS_NOT_UNIVARIATE_POLY number

Error Code throwed by methods that do not accept multivariate polynomials
ARG_IS_IMAGINARY number

Error Code throwed by methods that do not accept imaginary inputs
Source:

# Kind

Enumeration of all kinds possible for expressions.

Source:

Methods

# abs(scope, a) → {Expr}

Creates a abs call expression inside a scope, the expression is not evaluated, only the abstract tree of the expressions is created during the execution of this method.

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The operand.
Source:
Returns:

The call to abs function expression.

Type
Expr
Example 
let scope = scopeCreate();

let x = number(scope, 4);

// call abs
let z = abs(scope, x);
let t = toString(z); // abs(4)

scopeDestroy(scope);

# add(scope, a, b) → {Expr}

Creates an addition expression inside a scope, the expression is not evaluated, only the abstract tree of the expressions is created during the execution of this method.

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The first operand.
b Expr

The second operand.
Source:
Returns:

The addition expression.

Type
Expr
Example 
let scope = scopeCreate();

let x = number(scope, 2.5);
let y = symbol(scope, 'y');

// call add
let z = add(scope, x, y);
let t = toString(z); // 5/2 + y

scopeDestroy(scope);

# arccos(scope, x) → {Expr}

Return a call to the arccos function.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

The arccos argument.
Source:
Returns:

A call expression to the arccos function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = arccos(scope, x);

console.log(toString(z)); // arccos(x)

scopeDestroy(scope);

# arccosh(scope, x) → {Expr}

Return a call to the arccosh function.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

The arccosh argument.
Source:
Returns:

A call expression to the arccosh function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = arccosh(scope, x);

console.log(toString(z)); // arccosh(x)

scopeDestroy(scope);

# arccot(scope, x) → {Expr}

Return a call to the arccot function.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

The arccot argument.
Source:
Returns:

A call expression to the arccot function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = arccot(scope, x);

console.log(toString(z)); // arccot(x)

scopeDestroy(scope);

# arccsc(scope, x) → {Expr}

Return a call to the arccsc function.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

The arccsc argument.
Source:
Returns:

A call expression to the arccsc function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = arccsc(scope, x);

console.log(toString(z)); // arccsc(x)

scopeDestroy(scope);

# arcsec(scope, x) → {Expr}

Return a call to the arcsec function.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

The arcsec argument.
Source:
Returns:

A call expression to the arcsec function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = arcsec(scope, x);

console.log(toString(z)); // arcsec(x)

scopeDestroy(scope);

# arcsin(scope, x) → {Expr}

Return a call to the arcsin function.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

The arcsin argument.
Source:
Returns:

A call expression to the arcsin function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = arcsin(scope, x);

console.log(toString(z)); // arcsin(x)

scopeDestroy(scope);

# arctan(scope, x) → {Expr}

Return a call to the arctan function.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

The arctan argument.
Source:
Returns:

A call expression to the arctan function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = arctan(scope, x);

console.log(toString(z)); // arctan(x)

scopeDestroy(scope);

# arctanh(scope, x) → {Expr}

Return a call to the arctanh function.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

The arctanh argument.
Source:
Returns:

A call expression to the arctanh function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = arctanh(scope, x);

console.log(toString(z)); // arctanh(x)

scopeDestroy(scope);

# cos(scope, x) → {Expr}

Return a call to the cos function.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

The cos argument.
Source:
Returns:

A call expression to the cos function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = cos(scope, x);

console.log(toString(z)); // cos(x)

scopeDestroy(scope);

# cosh(scope, x) → {Expr}

Return a call to the cosh function.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

The cosh argument.
Source:
Returns:

A call expression to the cosh function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = cosh(scope, x);

console.log(toString(z)); // cosh(x)

scopeDestroy(scope);

# cot(scope, x) → {Expr}

Return a call to the cot function.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

The cot argument.
Source:
Returns:

A call expression to the cot function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = cot(scope, x);

console.log(toString(z)); // cot(x)

scopeDestroy(scope);

# coth(scope, x) → {Expr}

Return a call to the coth function.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

The coth argument.
Source:
Returns:

A call expression to the coth function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = coth(scope, x);

console.log(toString(z)); // coth(x)

scopeDestroy(scope);

# csc(scope, x) → {Expr}

Return a call to the csc function.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

The csc argument.
Source:
Returns:

A call expression to the csc function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = csc(scope, x);

console.log(toString(z)); // csc(x)

scopeDestroy(scope);

# csch(scope, x) → {Expr}

Return a call to the csch function.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

The csch argument.
Source:
Returns:

A call expression to the csch function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = csch(scope, x);

console.log(toString(z)); // csch(x)

scopeDestroy(scope);

# denominator(scope, a) → {Expr}

Return a new expression equal to the denominator of an expression.

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The expression.
Source:
Returns:

The denominator expresion.

Type
Expr
Example 
let scope = scopeCreate();

let x = number(scope, 1);
let y = number(scope, 2);
let z = div(scope, x, y);

let w = denominator(scope, z);
console.log(toString(w)); // 1

scopeDestroy(scope);

# derivative(scope, u, x) → {Expr}

Compute the derivative of an expression by a given symbol.

Parameters:
Name Type Description
scope Scope

The scope object.
u Expr

A polynomial expression.
x Expr

A symbol expression.
Source:
Returns:

The derivative of u by x.

Type
Expr

# errorArg(The) → {number}

Get the error argument, this argument is an number where its meaning is dependent on the context and errro code throwed.

Parameters:
Name Type Description
The GaussError

error object.
Source:
Returns:

The error argument.

Type
number

# errorCode(The) → {ErrorCode}

Get the error code of an error object.

Parameters:
Name Type Description
The GaussError

error object.
Source:
Returns:

The error code of the error object.

Type
ErrorCode

# evalSymbol(scope, a, x, v) → {Expr}

Return a new expression where the symbol 'x' on 'a' is replaced by 'v' and the resulting expression is reduced.

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The expression object.
x Expr

The symbol to be replaced.
v Expr

The expression that will replace x.
Source:
Returns:

A expression object.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let y = symbol(scope, 'y');
let z = add(scope, x, y);

console.log(toString(z)); // x + y

let k = evalSymbol(scope, z, x, y);

console.log(toString(k)); // 2*y

scopeDestroy(scope);

# exp(scope, a) → {Expr}

Return a call to the exp function.

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The argument for the exp expression.
Source:
Returns:

A call expression to the exp function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = exp(scope, x);

console.log(toString(z)); // exp(x)

scopeDestroy(scope);

# expand(scope, a) → {Expr}

Return a expanded and reduced expression.

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The expression.
Source:
Returns:

The expanded expression.

Type
Expr
Example 
let scope = scopeCreate();

let z = mul(scope,
	add(scope,
		number(scope, 2),
		symbol(scope, 'x'),
	),
	add(scope,
		symbol(scope, 'x'),
		number(scope 3)
	)
);

console.log(toString(z)); // (2 + x) * (x + 3)

let w = expand(scope, z);

console.log(toString(w)); // x^2 + 5x + 6

scopeDestroy(scope);

# freeSymbols(scope, u) → {Expr}

Return a set with the free symbols of an expression.

Parameters:
Name Type Description
scope Scope

The scope object.
u Expr

The expression object.
Source:
Returns:

A set of symbols.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let y = symbol(scope, 'y');
let z = number(scope, 2);

let w = add(scope, x, add(y, z));

let k = freeSymbols(scope, 2);

console.log(toString(k)); // {x, y}

scopeDestroy(scope);

# getOperand(scope, a, i) → {Expr}

Get the i'th operand of an expression.

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The expression object.
i number

The index of the operand.
Source:
Returns:

The i'th operand expression.

Type
Expr
Example 
let scope = scopeCreate();

let x = number(scope, 1);
let y = number(scope, 2);
let z = number(scope, 3);

let a = add(scope, x, y);
let b = add(scope, a, z);

toString(b); // (1 + 2) + 3
toString(getOperand(scope, b, 0)); // 1 + 2
toString(getOperand(scope, b, 1)); // 3

scopeDestroy(scope);

# is(a, k) → {Bool}

Return if an expression is of a given set of kinds.

Parameters:
Name Type Description
a Expr

The expression.
k Kind

The kind value.
Source:
Returns:

true if the expression is of at least one of the given kinds, false otherwise.

Type
Bool
Example 
let scope = scopeCreate();

let x = number(scope, 1);
d *
console.log(is(x, Kind.INT)); // true
console.log(is(x, Kind.DIV)); // false
console.log(is(x, Kind.INT | Kind.DIV)); // true

scopeDestroy(scope);

# isEqual(a, b) → {Bool}

Computes if two expressions are equal.

Parameters:
Name Type Description
a Expr

The first operand.
b Expr

The second operand.
Source:
Returns:

The result of the comparison.

Type
Bool
Example 
let scope = scopeCreate();

let x = number(scope, 1);
let y = number(scope, 1);
let z = number(scope, 3);

console.log(isEqual(x, y)); // true
console.log(isEqual(x, z)); // false

scopeDestroy(scope);

# kindOf(a) → {Kind}

Return the kind of the expression.

Parameters:
Name Type Description
a Expr

The expression.
Source:
Returns:

The Kind of the expresion.

Type
Kind
Example 
let scope = scopeCreate();

let x = number(scope, 1);
let y = symbol(scope,'x');
let z = div(scope, x, y);

console.log(kindOf(x) == Kind.INT); // true
console.log(kindOf(y) == Kind.SYM); // true
console.log(kindOf(z) == Kind.DIV); // true

scopeDestroy(scope);

# ln(scope, a) → {Expr}

Return a call to the ln function.

G * @example let scope = scopeCreate();

let x = symbol(scope, 'x'); let z = ln(scope, x);

console.log(toString(z)); // ln(x)

scopeDestroy(scope);

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The power for the ln expression.
Source:
Returns:

A call expression to the ln function.

Type
Expr

# log(scope, a, b) → {Expr}

Return a call to the log function.

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The power for the log expression.
b Expr

The base for the log expression.
Source:
Returns:

A call expression to the log function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let y = symbol(scope, 'y');
let z = log(scope, x, y);

console.log(toString(z)); // log(x, y)

scopeDestroy(scope);

# matrixDeterminant(scope, M) → {Expr}

Compute the determinant of a matrix expression.

Parameters:
Name Type Description
scope Scope

The scope object.
M Expr

The matrix expression.
Source:
Returns:

The determinant of the matrix expression.

Type
Expr

# matrixGet(scope, M, row, column) → {Expr}

Return a copy of an element inside a matrix.

Parameters:
Name Type Description
scope Scope

The scope object.
M Expr

The matrix expression.
row number

The rows of element inside the matrix.
column number

The column of the element inside the matrix.
Source:
Returns:

A matrix expression.

Type
Expr
Example 
let scope = scopeCreate();

let z = matrixIdentity(scope, 2, 2);

console.log(toString(matrixGet(scope, z, 0, 0))); // 1
console.log(toString(matrixGet(scope, z, 0, 1))); // 0

scopeDestroy(scope);

# matrixIndentity(scope, rows, columns) → {Expr}

Return a identity matrix.

Parameters:
Name Type Description
scope Scope

The scope object.
rows number

The number of rows of the matrix.
columns number

The number of columns of the matrix.
Source:
Returns:

A matrix expression.

Type
Expr
Example 
let scope = scopeCreate();

let z = matrixIdentity(scope, 2, 2);

console.log(toString(z)); // [[1,0],[0,1]]

scopeDestroy(scope);

# matrixInverse(scope, M) → {Expr}

Compute the inverse of a matrix expression.

Parameters:
Name Type Description
scope Scope

The scope object.
M Expr

The matrix expression.
Source:
Returns:

A matrix expression corresponding to the inverse of M.

Type
Expr

# matrixSet(M, row, column, a)

Set an element inside a matrix.

Parameters:
Name Type Description
M Expr

The matrix expression.
row number

The rows of element inside the matrix.
column number

The column of the element inside the matrix.
a number

The number to be placed on the matrix.
Source:
Example 
let scope = scopeCreate();

let z = matrixIdentity(scope, 2, 2);

console.log(toString(z)); // [[1,0],[0,1]]
matrixSet(z, 0, 0, 2);
console.log(toString(z)); // [[2,0],[0,1]]

scopeDestroy(scope);

# matrixSVD(scope, M) → {Expr}

Compute the singular value decomposition of a matrix expression.

Parameters:
Name Type Description
scope Scope

The scope object.
M Expr

The matrix expression.
Source:
Returns:

A list expression with three matrices representing the singular value decomposition of M.

Type
Expr

# matrixTranspose(scope, M) → {Expr}

Compute the transpose of a matrix expression.

Parameters:
Name Type Description
scope Scope

The scope object.
M Expr

The matrix expression.
Source:
Returns:

The determinant of the matrix expression.

Type
Expr

# matrixZeros(scope, rows, columns) → {Expr}

Return a matrix filled with zeros.

Parameters:
Name Type Description
scope Scope

The scope object.
rows number

The number of rows of the matrix.
columns number

The number of columns of the matrix.
Source:
Returns:

A matrix expression.

Type
Expr
Example 
let scope = scopeCreate();

let z = matrixZeros(scope, 2, 2);

console.log(toString(z)); // [[0,0],[0,0]]

scopeDestroy(scope);

# mul(scope, a, b) → {Expr}

Creates a multiplication expression inside a scope, the expression is not evaluated, only the abstract tree of the expressions is created during the execution of this method.

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The first operand.
b Expr

The second operand.
Source:
Returns:

The multiplication expression.

Type
Expr
Example 
let scope = scopeCreate();

let x = number(scope, 2.5);
let y = symbol(scope, 'y');

// call mul
let z = mul(scope, x, y);
let t = toString(z); // 5/2 * y

scopeDestroy(scope);

# number(scope, v) → {Expr}

Creates an expression of numeric type. This expression is stored internally as a fraction or a big integer to avoid precision problems with floating point values.

Parameters:
Name Type Description
scope Scope

scope The scope object.
v number

A number value.
Source:
Returns:

The numeric expression.

Type
Expr

# numerator(scope, a) → {Expr}

Return a new expression equal to the numerator of an expression.

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The expression.
Source:
Returns:

The numerator expresion.

Type
Expr
Example 
let scope = scopeCreate();

let x = number(scope, 1);
let y = number(scope, 2);
let z = div(scope, x, y);

let w = numerator(scope, z);
console.log(toString(w)); // 1

scopeDestroy(scope);

# polynomiaDivisionFiniteField(scope, u, v, p) → {Expr}

Compute the Division of two polynomial expressions on a finite field of length p.

Parameters:
Name Type Description
scope Scope

The scope object.
u Expr

A polynomial expression.
v Expr

A polynomial expression.
p number

A integer number.
Source:
Returns:

The division of u by v on Z_{p}, the the expression is returned as an addition of quotient and remainder.

Type
Expr

# polynomialCoefficient(scope, p, x, x) → {Expr}

Get the coefficient of a polynomial on a given symbol and degree.

Parameters:
Name Type Description
scope Scope

The scope object.
p Expr

The polynomial expression.
x Expr

The symbol in p.
x Expr

The symbol in p.
Source:
Returns:

The coefficient expression.

Type
Expr

# polynomialDegree(scope, p, x) → {Expr}

Get the degree of a polynomial on a given symbol.

Parameters:
Name Type Description
scope Scope

The scope object.
p Expr

The polynomial expression.
x Expr

The symbol in p.
Source:
Returns:

The degree expression.

Type
Expr

# polynomialDivision(scope, u, v) → {Expr}

Compute division between two polynomials and return a expression of form 'quotient + remainder'

Parameters:
Name Type Description
scope Scope

The scope object.
u Expr

A polynomial expression.
v Expr

A polynomial expression.
Source:
Returns:

A addition expression where the first operand is the quotient and the second is the remainder of the division.

Type
Expr

# polynomialFactors(scope, p) → {Expr}

Compute irreducible factorization of a multivariate polynomial.

Parameters:
Name Type Description
scope Scope

The scope object.
p Expr

The polynomial expression.
Source:
Returns:

The factorized form of a polynomial expression.

Type
Expr

# polynomialGCD(scope, u, v) → {Expr}

Compute greatest commom divisor between two polynomials.

Parameters:
Name Type Description
scope Scope

The scope object.
u Expr

A polynomial expression.
v Expr

A polynomial expression.
Source:
Returns:

The gcd expression.

Type
Expr

# polynomialLCM(scope, u, v) → {Expr}

Compute least commom multiple between two polynomials.

Parameters:
Name Type Description
scope Scope

The scope object.
u Expr

A polynomial expression.
v Expr

A polynomial expression.
Source:
Returns:

The lcm expression.

Type
Expr

# polynomialLeadingCoefficient(scope, p, x) → {Expr}

Get the leading coefficient of a polynomial on a given symbol.

Parameters:
Name Type Description
scope Scope

The scope object.
p Expr

The polynomial expression.
x Expr

The symbol in p.
Source:
Returns:

The leading coeffient expression.

Type
Expr

# polynomialProjectFiniteField(scope, u, p) → {Expr}

Compute the projection of a polynomial expression on a finite field of length p.

Parameters:
Name Type Description
scope Scope

The scope object.
u Expr

A polynomial expression.
p number

A integer number.
Source:
Returns:

The projection of u on Z_{p}.

Type
Expr

# polynomialResultant(scope, u, v) → {Expr}

Compute the resultant between two polynomial expressions.

Parameters:
Name Type Description
scope Scope

The scope object.
u Expr

A polynomial expression.
v Expr

A polynomial expression.
Source:
Returns:

The resultant between u and v.

Type
Expr

# polynomialRoots(scope, p) → {Expr}

Compute all the real and imaginary roots of an univariate polynomial with real coefficients.

Parameters:
Name Type Description
scope Scope

The scope object.
p Expr

The polynomial expression.
Source:
Returns:

A list with all the roots withing a reasonable precision.

Type
Expr

# powBase(scope, a) → {Expr}

Return a new expression equal to the degree of a pow expression.

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The pow expression.
Source:
Returns:

The base expresion.

Type
Expr
Example 
let scope = scopeCreate();

let x = number(scope, 1);
let y = number(scope, 2);
let z = pow(scope, x, y);

let w = powBase(scope, z);
console.log(toString(w)); // 1

scopeDestroy(scope);

# powDegree(scope, a) → {Expr}

Return a new expression equal to the degree of a pow expression.

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The pow expression.
Source:
Returns:

The degree expresion.

Type
Expr
Example 
let scope = scopeCreate();

let x = number(scope, 1);
let y = number(scope, 2);
let z = pow(scope, x, y);

let w = powDegree(scope, z);
console.log(toString(w)); // 2

scopeDestroy(scope);

# prime(scope, i) → {Expr}

Compute the i'th prime number.

Parameters:
Name Type Description
scope Scope

The scope object.
i number

The index of the prime number.
Source:
Returns:

The prime number.

Type
Expr

# primeFactors(scope, a) → {Expr}

Compute the prime factorization of a integer expression.

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The integer expression.
Source:
Returns:

The product of all prime factors of a. The first number returned is 1 or -1, meaning the sign of a.

Type
Expr

# reduce(scope, a) → {Expr}

Return a reduced expression without expanding.

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The expression.
Source:
Returns:

The reduced expresion.

Type
Expr
Example 
let scope = scopeCreate();

let z = add(scope,
	add(scope,
		number(scope, 1),
		symbol(scope, 'x'),
	),
	add(scope,
		symbol(scope, 'x'),
		number(scope 3)
	)
);

console.log(toString(z)); // (1 + x) + (x + 3)

let w = reduce(scope, z);

console.log(toString(w)); // 2*x + 4

scopeDestroy(scope);

# replace(scope, a, x, v) → {Expr}

Return a new expression where the symbol 'x' on 'a' is replaced by 'v'.

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The expression object.
x Expr

The symbol to be replaced.
v Expr

The expression that will replace x.
Source:
Returns:

A expression object.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let y = symbol(scope, 'y');
let z = add(scope, x, y);

console.log(toString(z)); // x + y

let k = replace(scope, z, x, y);

console.log(toString(k)); // y + y

scopeDestroy(scope);

# root(scope, a, b) → {Expr}

Creates a root call expression inside a scope, the expression is not evaluated, only the abstract tree of the expressions is created during the execution of this method.

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The radicand.
b Expr

The index.
Source:
Returns:

The root expression.

Type
Expr
Example 
let scope = scopeCreate();

let x = number(scope, 4);
let y = number(scope, 2);

// call root
let z = root(scope, x, y);
let t = toString(z); // root(4, 2)

scopeDestroy(scope);

# rootIndex(scope, a) → {Expr}

Return a new expression equal to the index of a root expression.

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The root expression.
Source:
Returns:

The index expresion.

Type
Expr
Example 
let scope = scopeCreate();

let x = number(scope, 1);
let y = number(scope, 2);
let z = root(scope, x, y);

let w = rootIndex(scope, z);
console.log(toString(w)); // 2

scopeDestroy(scope);

# rootRadicand(scope, a) → {Expr}

Return a new expression equal to the radicand of a root expression.

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The root expression.
Source:
Returns:

The radicand expresion.

Type
Expr
Example 
let scope = scopeCreate();

let x = number(scope, 1);
let y = number(scope, 2);
let z = root(scope, x, y);

let w = rootRadicand(scope, z);
console.log(toString(w)); // 1

scopeDestroy(scope);

# scopeAssign(scope, key, a)

Assign one expression to a string key inside a scope, so the expression can be retrieved by querying it using the key.

Parameters:
Name Type Description
scope Scope

The scope object.
key Expr

The string key.
a Expr

A expression object.
Source:

# scopeCreate() → {Scope}

Creates a scope, scopes are needed for creating and assigning expresions.

Source:
Returns:

A scope object that can be used to create and assign expressions.

Type
Scope

# scopeDestroy(scope)

Destroy a scope and deallocate all resources reserved by it and the expressions that it holds. This function is neccessary to avoid leaks when using this library.

Parameters:
Name Type Description
scope Scope

The scope object to be destroyed.
Source:

# scopeGet(scope, key) → {Expr}

Return the expression from the scope using the string key.

Parameters:
Name Type Description
scope Scope

The scope object.
key Expr

The key string.
Source:
Returns:

The expresion object assigned to the key.

Type
Expr

# sec(scope, x) → {Expr}

Return a call to the sec function.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

The sec argument.
Source:
Returns:

A call expression to the sec function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = sec(scope, x);

console.log(toString(z)); // sec(x)

scopeDestroy(scope);

# sech(scope, x) → {Expr}

Return a call to the sech function.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

The sech argument.
Source:
Returns:

A call expression to the sech function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = sech(scope, x);

console.log(toString(z)); // sech(x)

scopeDestroy(scope);

# setOperand(a, i, b)

Set the i'th operand of an expression.

Parameters:
Name Type Description
a Expr

The expression object.
i number

The index of the operand.
b Expr

The new operand.
Source:
Example 
let scope = scopeCreate();

let x = number(scope, 1);
let y = number(scope, 2);
let z = number(scope, 3);

let a = add(scope, x, y);
let b = add(scope, a, z);

console.log(toString(b)); // (1 + 2) + 3
setOperand(b, 0, x);
console.log(toString(b)); // 1 + 3

scopeDestroy(scope);

# sin(scope, x) → {Expr}

Return a call to the sin function.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

The sin argument.
Source:
Returns:

A call expression to the sin function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = sin(scope, x);

console.log(toString(z)); // sin(x)

scopeDestroy(scope);

# sinh(scope, x) → {Expr}

Return a call to the sinh function.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

The sinh argument.
Source:
Returns:

A call expression to the sinh function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = sinh(scope, x);

console.log(toString(z)); // sinh(x)

scopeDestroy(scope);

# solveLinearSystem(scope, M, b) → {Expr}

Compute the solution of a linear system.

Parameters:
Name Type Description
scope Scope

The scope object.
M Expr

The matrix with the equation coefficients.
b Expr

The matrix with the equation values.
Source:
Returns:

The matrix expression with the solutions.

Type
Expr

# sqrt(scope, a) → {Expr}

Creates a square root call expression inside a scope, the expression is not evaluated, only the abstract tree of the expressions is created during the execution of this method.

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The radicand.
Source:
Returns:

The root expression.

Type
Expr
Example 
let scope = scopeCreate();

let x = number(scope, 4);

// call sqrt
let z = sqrt(scope, x);
let t = toString(z); // root(4, 2)

scopeDestroy(scope);

# sub(scope, a, b) → {Expr}

Creates a subtraction expression inside a scope, the expression is not evaluated, only the abstract tree of the expressions is created during the execution of this method.

Parameters:
Name Type Description
scope Scope

The scope object.
a Expr

The first operand.
b Expr

The second operand.
Source:
Returns:

The subtraction expression.

Type
Expr
Example 
let scope = scopeCreate();

let x = number(scope, 2.5);
let y = symbol(scope, 'y');

// call sub
let z = sub(scope, x, y);
let t = toString(z); // 5/2 - y

scopeDestroy(scope);

# symbol(scope, x) → {Expr}

Creates an expression of symbol type.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

A string value.
Source:
Returns:

The symbol expression.

Type
Expr

# tan(scope, x) → {Expr}

Return a call to the tan function.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

The tan argument.
Source:
Returns:

A call expression to the tan function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = tan(scope, x);

console.log(toString(z)); // tan(x)

scopeDestroy(scope);

# tanh(scope, x) → {Expr}

Return a call to the tanh function.

Parameters:
Name Type Description
scope Scope

The scope object.
x Expr

The tanh argument.
Source:
Returns:

A call expression to the tanh function.

Type
Expr
Example 
let scope = scopeCreate();

let x = symbol(scope, 'x');
let z = tanh(scope, x);

console.log(toString(z)); // tanh(x)

scopeDestroy(scope);

# toLatex(a) → {String}

Compute a latex representation of a expression.

Parameters:
Name Type Description
a Expr

The expression.
Source:
Returns:

The latex representation of the expression.

Type
String

# toString(a) → {String}

Compute a string representation of a expression.

Parameters:
Name Type Description
a Expr

The expression.
Source:
Returns:

The string representation of the expression.

Type
String