Polynomial

public class Polynomial : Expression

Special type of Expression to represent polynomials

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  • List of coefficients

    Declaration

    Swift

    public var coefs: [BigDouble] { get set }
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  • Creates a polynomial based on the coefficients

    Declaration

    Swift

    public convenience init(_ coefficients: BigDouble...) throws
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  • Creates a polynomial based on the coefficients

    Declaration

    Swift

    public init(_ coefficients: [BigDouble]) throws
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  • Evaluates the current polynomial at the given point

    Let f be a polynomial function. Evaluate returns the number given by f(x)

    Declaration

    Swift

    public func evaluate(at x: BigNumber) -> BigNumber

    Parameters

    x

    The input value for the polynomial function
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  • Equal operator

    Returns true only if all the coefficient exactly match.

    Declaration

    Swift

    public static func == (lhs: Polynomial, rhs: Polynomial) -> Bool

    Parameters

    lhs

    Left hand side
    rhs

    Right hand side
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  • Produces a string represenation of the polynomial

    Declaration

    Swift

    public override var description: String { get }
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  • Add polynomials to each other non-destructively.

    Declaration

    Swift

    public static func + (lhs: Polynomial, rhs: Polynomial) -> Polynomial

    Parameters

    lhs

    Left hand side
    rhs

    Right hand side
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  • Substract polynomials to each other non-destructively.

    Declaration

    Swift

    public static func - (lhs: Polynomial, rhs: Polynomial) -> Polynomial

    Parameters

    lhs

    Left hand side
    rhs

    Right hand side
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  • Negates this polynomial.

    Does so non-destructively

    Declaration

    Swift

    public var negated: Polynomial { get }
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  • Computes the derivative of this polynomial

    Declaration

    Swift

    public var derivative: Polynomial { get }
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  • Divides the polynomial by the leading coefficient so that we would have a monic polynomial

    Declaration

    Swift

    public var normalized: Polynomial { get }
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  • Returns the Cauchy Polynomial from this polynomial

    Declaration

    Swift

    public var cauchyPoly: Polynomial { get }
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  • Divides this polynomial by given linear (1 degree) polynomial (Non destructive)

    Declaration

    Swift

    public func linearDivision(x_coef: BigDouble, x_const: BigDouble) -> Polynomial

    Parameters

    x_coefs

    coefficient of the (x-)term
    x_const

    constant term
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  • Multiplies through this polynomial by the given constant

    Declaration

    Swift

    public static func * (lhs: Polynomial, rhs: BigDouble) -> Polynomial

    Parameters

    lhs

    Left hand side
    rhs

    Right hand side
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  • Finds roots of the polynomial

    Not always inclusive. Sometimes, for the same polynomials, results are different as it relies on guesses.

    Note to dev team: performance is not ideal and could be improved by relying on native numbers when possible.

    Declaration

    Swift

    public var roots: [BigDouble] { get }
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