RatTerm

public struct RatTerm : Equatable, CustomStringConvertible

RatTerm is an immutable representation of a term in a single-variable polynomial expression. The term has the form C*x^E where C is a rational number and E is an integer.

AbstractState: A RatTerm, t, can be notated by the pair (C . E), where C is the coefficient of t, and E is the exponent of t.

The zero RatTerm, (0 . 0), is the only RatTerm that may have a zero coefficient. For example, (0 . 7) is an invalid RatTerm and an attempt to construct such a RatTerm (through the constructor or arithmetic operations on existing RatTerms) will return the semantically equivalent RatTerm (0 . 0). For example, (1 . 7) + (-1 . 7) = (0 . 0).

(0 . 0), (1 . 0), (1 . 1), (1 . 3), (¾ . 17), (7/2 . -1), and (NaN . 74) are all valid RatTerms, corresponding to the polynomial terms 0, 1, x, x^3, ¾*x^17, 7/2*x^-1 and NaN*x^74, respectively.

  • Coefficient of this term.

    Declaration

    Swift

    public let coeff: RatNum

  • Exponent of this term.

    Declaration

    Swift

    public let exponent: Int
  • nan

    A constant holding a Not-a-Number (NaN) value of type RatTerm

    Declaration

    Swift

    public static let nan: RatTerm

  • A constant holding a zero value of type RatTerm

    Declaration

    Swift

    public static let zero: RatTerm

  • true if and only if self has NaN as a coefficient.

    Declaration

    Swift

    public var isNaN: Bool { get }

  • true if and only if self has zero as a coefficient.

    Declaration

    Swift

    public var isZero: Bool { get }

  • A String representation of the expression represented by this RatTerm:

    • There is no whitespace in the returned string.
    • If the term is itself zero, the returned string will just be 0.
    • If self.isNaN, then the returned string will be just NaN

    The string for a non-zero, non-NaN RatTerm is in the form C*x^E where C is a valid string representation of a RatNum and E is an integer. UNLESS:

    1. the exponent E is zero, in which case T takes the form C
    2. the exponent E is one, in which case T takes the form C*x
    3. the coefficient C is one, in which case T takes the form x^E or x (if E is one) or 1 (if E is zero).

    Valid example outputs include 3/2*x^2, -½, 0, and NaN.

    Declaration

    Swift

    public var description: String { get }

  • Returns the value of this RatTerm, evaluated at d.

    Declaration

    Swift

    public func eval(_ d: Double) -> Double

    Parameters

    d

    The value at which to evaluate this term.

    Return Value

    the value of this polynomial when evaluated at ‘d’. For example, 3*x^2 evaluated at 2 is 12. if (self.isNaN == true), return Double.NaN

  • Declaration

    Swift

    public prefix static func - (rhs: RatTerm) -> RatTerm

    Return Value

    a RatTerm equals to (-rhs). If rhs is NaN, then returns NaN.

  • Addition operation.

    Declaration

    Swift

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

    Parameters

    lhs

    The first operand.
    rhs

    The second operand.

    Return Value

    A RatTerm equals to (lhs + rhs), or: if either argument is NaN, then returns NaN, or: if (lhs.expt != rhs.expt) and neither argument is zero or NaN, then returns nil.

  • Subtraction operation.

    Declaration

    Swift

    public static func - (lhs: RatTerm, rhs: RatTerm) -> RatTerm?

    Parameters

    lhs

    The first operand.
    rhs

    The second operand.

    Return Value

    A RatTerm equals to (lhs - rhs), or: if either argument is NaN, then returns NaN, or: if (lhs.expt != rhs.expt) and neither argument is zero or NaN, then returns nil.

  • Multiplication operation.

    Declaration

    Swift

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

    Parameters

    lhs

    The first operand.
    rhs

    The second operand.

    Return Value

    A RatTerm equals to (lhs * rhs). If either argument is NaN, then returns NaN.

  • Division operation.

    Declaration

    Swift

    public static func / (lhs: RatTerm, rhs: RatTerm) -> RatTerm

    Parameters

    lhs

    The first operand.
    rhs

    The second operand.

    Return Value

    A RatTerm equals to (lhs / rhs). If either argument is NaN, then returns NaN.

  • Return the derivative of this RatTerm.

    Given a term, a*x^b, the derivative of the term is: (a*b)*x^(b-1) for b > 0 and 0 for b == 0 (Do not worry about the case when b < 0. The caller of this function, RatPoly, contains a rep. invariant stating that b is never less than 0.)

    Requires: If self is not NaN, then expt >= 0.

    Declaration

    Swift

    public func differentiate() -> RatTerm

    Return Value

    a RatTerm that, q, such that q = dy/dx, where self == y. In other words, q is the derivative of self. If self.isNaN, then return some q such that q.isNaN

  • Returns the antiderivative of this RatTerm.

    Given a term, a*x^b, (where b >= 0) the antiderivative of the term is: a/(b+1)*x^(b+1) (Do not worry about the case when b < 0. The caller of this function, RatPoly, contains a rep. invariant stating that b is never less than 0.)

    Requires: If self is not NaN, then expt >= 0.

    Declaration

    Swift

    public func antiDerivative() -> RatTerm

    Return Value

    a RatTerm, q, such that dq/dx = self where the constant of intergration is assumed to be 0. In other words, q is the antiderivative of self. If self.isNaN, then return some q such that q.isNaN

  • Builds a new RatTerm, given a descriptive String.

    Requires: ‘description’ is an instance of a string with no spaces that expresses a RatTerm in the form defined by the description property of RatTerm

    Valid inputs include 0, x, and -5/3*x^3, and NaN.

    Declaration

    Swift

    public init?(_ description: String)

    Parameters

    description

    A string of the format described in the @requires clause.

    Return Value

    a RatTerm t such that t.toString() = description

  • Standard equality operation.

    Declaration

    Swift

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

    Return Value

    true iff lhs and rhs represent the same RatTerm. Note that all NaN RatTerms are equal.