SS.Symbolics 1.7.0
Exact symbolic values, transforms, calculus, solving, optimization, and compiled numerical-function evaluation
Language compatibility: >=1.0.0 <2.0.0
Runtime compatibility: >=1.0.0 <2.0.0
No package dependencies declared.
Public API
Symbolics.addExpression
export function addExpression(Expression left, Expression right) -> ExpressionParameters: left: Expression, right: Expression
export function addMultivariatePolynomial(MultivariatePolynomial left, MultivariatePolynomial right) -> MultivariatePolynomialParameters: left: MultivariatePolynomial, right: MultivariatePolynomial
Symbolics.addPolynomial
export function addPolynomial(Polynomial left, Polynomial right) -> PolynomialParameters: left: Polynomial, right: Polynomial
Symbolics.addRational
export function addRational(Rational left, Rational right) -> RationalParameters: left: Rational, right: Rational
Symbolics.addRationalFunction
export function addRationalFunction(RationalFunction left, RationalFunction right) -> RationalFunctionParameters: left: RationalFunction, right: RationalFunction
Symbolics.antiderivative
export function antiderivative(Expression value, Symbol variable, int maxNodes) -> AntiderivativeResultParameters: value: Expression, variable: Symbol, maxNodes: int
export record AntiderivativeResult(public Expression expression, public bool evaluated, public string diagnostic)Parameters: expression: Expression, evaluated: bool, diagnostic: string
Symbolics.apartRationalFunction
export function apartRationalFunction(RationalFunction value) -> PartialFractionDecompositionParameters: value: RationalFunction
Symbolics.cancel
export function cancel(Expression value, Symbol variable) -> ExpressionParameters: value: Expression, variable: Symbol
Symbolics.coefficient
export function coefficient(Expression value, Symbol variable, int degree) -> RationalParameters: value: Expression, variable: Symbol, degree: int
Symbolics.collect
export function collect(Expression value, Symbol variable) -> ExpressionParameters: value: Expression, variable: Symbol
Symbolics.complexSymbol
export function complexSymbol(string name) -> SymbolParameters: name: string
Symbolics.constantPolynomial
export function constantPolynomial(Symbol variable, Rational value) -> PolynomialParameters: variable: Symbol, value: Rational
Symbolics.cosExpression
export function cosExpression(Expression value) -> ExpressionParameters: value: Expression
Symbolics.coshExpression
export function coshExpression(Expression value) -> ExpressionParameters: value: Expression
Symbolics.declaration
export function declaration(Symbol value) -> stringParameters: value: Symbol
export function definiteIntegralPolynomial(Polynomial value, Rational lower, Rational upper) -> RationalParameters: value: Polynomial, lower: Rational, upper: Rational
export function derivativeMultivariatePolynomial(MultivariatePolynomial value, Symbol variable) -> MultivariatePolynomialParameters: value: MultivariatePolynomial, variable: Symbol
Symbolics.derivativePolynomial
export function derivativePolynomial(Polynomial value) -> PolynomialParameters: value: Polynomial
Symbolics.differentiate
export function differentiate(Expression value, Symbol variable, int maxNodes) -> ExpressionParameters: value: Expression, variable: Symbol, maxNodes: int
Symbolics.differentiateOrder
export function differentiateOrder(Expression value, Symbol variable, int order, int maxNodes) -> ExpressionParameters: value: Expression, variable: Symbol, order: int, maxNodes: int
Symbolics.divideExpression
export function divideExpression(Expression left, Expression right) -> ExpressionParameters: left: Expression, right: Expression
Symbolics.dividePolynomial
export function dividePolynomial(Polynomial dividend, Polynomial divisor) -> PolynomialDivisionParameters: dividend: Polynomial, divisor: Polynomial
Symbolics.divideRational
export function divideRational(Rational left, Rational right) -> RationalParameters: left: Rational, right: Rational
Symbolics.divideRationalFunction
export function divideRationalFunction(RationalFunction left, RationalFunction right) -> RationalFunctionParameters: left: RationalFunction, right: RationalFunction
Symbolics.equalPolynomial
export function equalPolynomial(Polynomial left, Polynomial right) -> boolParameters: left: Polynomial, right: Polynomial
Symbolics.equalRational
export function equalRational(Rational left, Rational right) -> boolParameters: left: Rational, right: Rational
Symbolics.equalRationalFunction
export function equalRationalFunction(RationalFunction left, RationalFunction right) -> boolParameters: left: RationalFunction, right: RationalFunction
export record EquationSolution(public string kind, public Rational[] roots, public Polynomial residual, public string diagnostic)Parameters: kind: string, roots: Rational[], residual: Polynomial, diagnostic: string
Symbolics.evaluateExact
export function evaluateExact(Expression value) -> RationalParameters: value: Expression
export function evaluateMultivariatePolynomial(MultivariatePolynomial value, Rational[] arguments) -> RationalParameters: value: MultivariatePolynomial, arguments: Rational[]
Symbolics.evaluateNumericalBatch
export function evaluateNumericalBatch(NumericalFunction functionValue, double[] rowMajorArguments, int rows) -> double[]Parameters: functionValue: NumericalFunction, rowMajorArguments: double[], rows: int
export function evaluateNumericalFunction(NumericalFunction functionValue, double[] arguments) -> doubleParameters: functionValue: NumericalFunction, arguments: double[]
Symbolics.evaluatePolynomial
export function evaluatePolynomial(Polynomial value, Rational argument) -> RationalParameters: value: Polynomial, argument: Rational
export function evaluateRationalFunction(RationalFunction value, Rational argument) -> RationalParameters: value: RationalFunction, argument: Rational
Symbolics.exactExpression
export function exactExpression(Rational value) -> ExpressionParameters: value: Rational
Symbolics.exactInteger
export function exactInteger(long value) -> RationalParameters: value: long
Symbolics.exactSquareRoot
export function exactSquareRoot(Rational value) -> ExactSquareRootParameters: value: Rational
export record ExactSquareRoot(public bool exact, public Rational value)Parameters: exact: bool, value: Rational
Symbolics.expand
export function expand(Expression value, Symbol variable) -> ExpressionParameters: value: Expression, variable: Symbol
Symbolics.expandElementary
export function expandElementary(Expression value, int maxNodes) -> ExpressionParameters: value: Expression, maxNodes: int
Symbolics.expExpression
export function expExpression(Expression value) -> ExpressionParameters: value: Expression
Symbolics.Expression
export record Expression(public int[] kinds, public long[] numerators, public long[] denominators, public string[] names, public string[] domains, public bool[] positives, public bool[] nonZeros, public int[] leftChildren, public int[] rightChildren, public int root)Parameters: kinds: int[], numerators: long[], denominators: long[], names: string[], domains: string[], positives: bool[], nonZeros: bool[], leftChildren: int[], rightChildren: int[], root: int
export record ExpressionMatrix(public int rows, public int columns, public Expression[] values)Parameters: rows: int, columns: int, values: Expression[]
Symbolics.expressionNodeCount
export function expressionNodeCount(Expression value) -> intParameters: value: Expression
Symbolics.expressionRootKind
export function expressionRootKind(Expression value) -> intParameters: value: Expression
export function expressionToMultivariatePolynomial(Expression value, Symbol[] variables) -> MultivariatePolynomialParameters: value: Expression, variables: Symbol[]
Symbolics.expressionToPolynomial
export function expressionToPolynomial(Expression value, Symbol variable) -> PolynomialParameters: value: Expression, variable: Symbol
export function expressionToRationalFunction(Expression value, Symbol variable) -> RationalFunctionParameters: value: Expression, variable: Symbol
Symbolics.factorPolynomial
export function factorPolynomial(Polynomial value) -> PolynomialFactorizationParameters: value: Polynomial
Symbolics.gcdPolynomial
export function gcdPolynomial(Polynomial left, Polynomial right) -> PolynomialParameters: left: Polynomial, right: Polynomial
Symbolics.gradient
export function gradient(Expression value, Symbol[] variables, int maxNodes) -> Expression[]Parameters: value: Expression, variables: Symbol[], maxNodes: int
Symbolics.hessian
export function hessian(Expression value, Symbol[] variables, int maxNodes) -> ExpressionMatrixParameters: value: Expression, variables: Symbol[], maxNodes: int
Symbolics.integerSymbol
export function integerSymbol(string name) -> SymbolParameters: name: string
Symbolics.integratePolynomial
export function integratePolynomial(Polynomial value) -> PolynomialParameters: value: Polynomial
export record LinearSystemSolution(public string kind, public Rational[] values, public int rank, public string diagnostic)Parameters: kind: string, values: Rational[], rank: int, diagnostic: string
Symbolics.logExpression
export function logExpression(Expression value) -> ExpressionParameters: value: Expression
export function maximizePolynomialOnInterval(Polynomial value, Rational lower, Rational upper) -> PolynomialOptimumParameters: value: Polynomial, lower: Rational, upper: Rational
export function minimizeConvexQuadratic(Polynomial value) -> PolynomialOptimumParameters: value: Polynomial
export function minimizePolynomialOnInterval(Polynomial value, Rational lower, Rational upper) -> PolynomialOptimumParameters: value: Polynomial, lower: Rational, upper: Rational
Symbolics.monomial
export function monomial(int[] exponents, Rational coefficient) -> MonomialParameters: exponents: int[], coefficient: Rational
Symbolics.Monomial
export record Monomial(public int[] exponents, public Rational coefficient)Parameters: exponents: int[], coefficient: Rational
Symbolics.multiplyExpression
export function multiplyExpression(Expression left, Expression right) -> ExpressionParameters: left: Expression, right: Expression
export function multiplyMultivariatePolynomial(MultivariatePolynomial left, MultivariatePolynomial right) -> MultivariatePolynomialParameters: left: MultivariatePolynomial, right: MultivariatePolynomial
Symbolics.multiplyPolynomial
export function multiplyPolynomial(Polynomial left, Polynomial right) -> PolynomialParameters: left: Polynomial, right: Polynomial
Symbolics.multiplyRational
export function multiplyRational(Rational left, Rational right) -> RationalParameters: left: Rational, right: Rational
export function multiplyRationalFunction(RationalFunction left, RationalFunction right) -> RationalFunctionParameters: left: RationalFunction, right: RationalFunction
Symbolics.multivariatePolynomial
export function multivariatePolynomial(Symbol[] variables, Monomial[] terms) -> MultivariatePolynomialParameters: variables: Symbol[], terms: Monomial[]
export record MultivariatePolynomial(public Symbol[] variables, public Monomial[] terms)Parameters: variables: Symbol[], terms: Monomial[]
Symbolics.negateRational
export function negateRational(Rational value) -> RationalParameters: value: Rational
Symbolics.nonZeroSymbol
export function nonZeroSymbol(string name) -> SymbolParameters: name: string
Symbolics.numericalFunction
export function numericalFunction(Expression expression, Symbol[] variables) -> NumericalFunctionParameters: expression: Expression, variables: Symbol[]
export record NumericalFunction(public Expression expression, public Symbol[] variables)Parameters: expression: Expression, variables: Symbol[]
export record PartialFractionDecomposition(public Polynomial polynomialPart, public Rational[] residues, public Rational[] poles, public RationalFunction remaining)Parameters: polynomialPart: Polynomial, residues: Rational[], poles: Rational[], remaining: RationalFunction
Symbolics.polynomial
export function polynomial(Symbol variable, Rational[] coefficients) -> PolynomialParameters: variable: Symbol, coefficients: Rational[]
Symbolics.Polynomial
export record Polynomial(public Symbol variable, public Rational[] coefficients)Parameters: variable: Symbol, coefficients: Rational[]
Symbolics.polynomialCoefficient
export function polynomialCoefficient(Polynomial value, int degree) -> RationalParameters: value: Polynomial, degree: int
Symbolics.polynomialDegree
export function polynomialDegree(Polynomial value) -> intParameters: value: Polynomial
export record PolynomialDivision(public Polynomial quotient, public Polynomial remainder)Parameters: quotient: Polynomial, remainder: Polynomial
export record PolynomialFactorization(public Rational scale, public Rational[] rationalRoots, public Polynomial remaining)Parameters: scale: Rational, rationalRoots: Rational[], remaining: Polynomial
export record PolynomialOptimum(public string kind, public Rational point, public Rational value, public bool proven, public string diagnostic)Parameters: kind: string, point: Rational, value: Rational, proven: bool, diagnostic: string
Symbolics.polynomialToExpression
export function polynomialToExpression(Polynomial value) -> ExpressionParameters: value: Polynomial
Symbolics.positiveSymbol
export function positiveSymbol(string name) -> SymbolParameters: name: string
Symbolics.powerRational
export function powerRational(Rational value, int exponent) -> RationalParameters: value: Rational, exponent: int
Symbolics.rational
export function rational(long numerator, long denominator) -> RationalParameters: numerator: long, denominator: long
Symbolics.Rational
export record Rational(public long numerator, public long denominator)Parameters: numerator: long, denominator: long
Symbolics.rationalFunction
export function rationalFunction(Polynomial numerator, Polynomial denominator) -> RationalFunctionParameters: numerator: Polynomial, denominator: Polynomial
export record RationalFunction(public Polynomial numerator, public Polynomial denominator, public Polynomial domainDenominator)Parameters: numerator: Polynomial, denominator: Polynomial, domainDenominator: Polynomial
export function rationalFunctionToExpression(RationalFunction value) -> ExpressionParameters: value: RationalFunction
Symbolics.rationalToDouble
export function rationalToDouble(Rational value) -> doubleParameters: value: Rational
Symbolics.realSymbol
export function realSymbol(string name) -> SymbolParameters: name: string
export function sameRationalFunctionDomain(RationalFunction left, RationalFunction right) -> boolParameters: left: RationalFunction, right: RationalFunction
Symbolics.sameSymbol
export function sameSymbol(Symbol left, Symbol right) -> boolParameters: left: Symbol, right: Symbol
Symbolics.scalePolynomial
export function scalePolynomial(Polynomial value, Rational scale) -> PolynomialParameters: value: Polynomial, scale: Rational
Symbolics.simplifyElementary
export function simplifyElementary(Expression value, int maxNodes) -> ExpressionParameters: value: Expression, maxNodes: int
Symbolics.sinExpression
export function sinExpression(Expression value) -> ExpressionParameters: value: Expression
Symbolics.sinhExpression
export function sinhExpression(Expression value) -> ExpressionParameters: value: Expression
export function solveExpressionEquation(Expression left, Expression right, Symbol variable) -> EquationSolutionParameters: left: Expression, right: Expression, variable: Symbol
Symbolics.solveLinearSystem
export function solveLinearSystem(Rational[] coefficients, int rows, int columns, Rational[] rightHandSide) -> LinearSystemSolutionParameters: coefficients: Rational[], rows: int, columns: int, rightHandSide: Rational[]
export function solvePolynomialEquation(Polynomial value) -> EquationSolutionParameters: value: Polynomial
export record StationaryPoint(public Rational point, public Rational value, public string kind)Parameters: point: Rational, value: Rational, kind: string
Symbolics.stationaryPoints
export function stationaryPoints(Polynomial value) -> StationaryPoint[]Parameters: value: Polynomial
Symbolics.subs
export function subs(Expression value, Symbol variable, Expression replacement) -> ExpressionParameters: value: Expression, variable: Symbol, replacement: Expression
Symbolics.substitute
export function substitute(Expression value, Symbol variable, Expression replacement) -> ExpressionParameters: value: Expression, variable: Symbol, replacement: Expression
Symbolics.substituteMany
export function substituteMany(Expression value, Symbol[] variables, Expression[] replacements) -> ExpressionParameters: value: Expression, variables: Symbol[], replacements: Expression[]
Symbolics.subtractExpression
export function subtractExpression(Expression left, Expression right) -> ExpressionParameters: left: Expression, right: Expression
Symbolics.subtractPolynomial
export function subtractPolynomial(Polynomial left, Polynomial right) -> PolynomialParameters: left: Polynomial, right: Polynomial
Symbolics.subtractRational
export function subtractRational(Rational left, Rational right) -> RationalParameters: left: Rational, right: Rational
export function subtractRationalFunction(RationalFunction left, RationalFunction right) -> RationalFunctionParameters: left: RationalFunction, right: RationalFunction
Symbolics.sym
export function sym(string name) -> SymbolParameters: name: string
Symbolics.symbol
export function symbol(string name) -> SymbolParameters: name: string
Symbolics.Symbol
export record Symbol(public string name, public string domain, public bool positive, public bool nonZero)Parameters: name: string, domain: string, positive: bool, nonZero: bool
Symbolics.symbolExpression
export function symbolExpression(Symbol value) -> ExpressionParameters: value: Symbol
Symbolics.symbolicJacobian
export function symbolicJacobian(Expression[] values, Symbol[] variables, int maxNodes) -> ExpressionMatrixParameters: values: Expression[], variables: Symbol[], maxNodes: int
Symbolics.symbolWithAssumptions
export function symbolWithAssumptions(string name, string domain, bool positive, bool nonZero) -> SymbolParameters: name: string, domain: string, positive: bool, nonZero: bool
Symbolics.syms
export function syms(string[] names) -> Symbol[]Parameters: names: string[]
Symbolics.tanExpression
export function tanExpression(Expression value) -> ExpressionParameters: value: Expression
Symbolics.tanhExpression
export function tanhExpression(Expression value) -> ExpressionParameters: value: Expression
Symbolics.together
export function together(Expression value, Symbol variable) -> ExpressionParameters: value: Expression, variable: Symbol
Symbolics.variablePolynomial
export function variablePolynomial(Symbol variable) -> PolynomialParameters: variable: Symbol
Documentation version
Language 1.0.0, compiler 1.0.0, runtime 1.0.0. This reference is generated from the official SS documentation so package and language details stay consistent with the release.