Number - Scala Mathematical Library/com.phasmidsoftware.number/com.phasmidsoftware.number.algebra/com.phasmidsoftware.number.algebra.eager/Succ

Succ

com.phasmidsoftware.number.algebra.eager.Succ

case class Succ(pred: Nat) extends Nat

Represents the successor of a natural number in Peano arithmetic.

The Succ class is a case class that extends the Nat trait and signifies the successor of another natural number.

Value parameters

pred: The predecessor of this natural number, which is also a Nat.

Attributes

Graph
Supertypes: trait Serializable

trait Product

trait Equals

trait Nat

trait N

trait Z

trait Q

trait R

trait Eager

trait DyadicOps

trait Approximate

trait Valuable

trait TypeSafe

trait Normalizable[Valuable]

trait Exactitude

trait Unitary

trait Zeroable

trait Numeric

trait Renderable

class Object

trait Matchable

class Any
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Members list

Value members

Concrete methods

Adds the specified natural number to this natural number.

This method leverages the natIsSemiring.plus implementation, which defines addition for natural numbers recursively using Peano arithmetic.

Value parameters

that: the natural number to be added to this instance

Attributes

Returns: a new natural number representing the sum of this instance and the specified natural number

Compares this Succ instance for equality with another object.

This method determines whether the current Succ instance represents the same natural number as another object, based on their predecessors. Only instances of type Succ are eligible for comparison.

Value parameters

obj: the object to compare to this instance

Attributes

Returns: true if the specified object is a Succ instance and represents the same natural number as this instance; false otherwise
Definition Classes: Equals -> Any

Determines if the current number is equal to one.

This method establishes whether the numerical value of the current instance represents the first natural number (unity) based on its predecessor.

Attributes

Returns: true if the current number is one, false otherwise
Definition Classes: Unitary

Determines if the current number is equal to zero.

Attributes

Returns: true if the number is zero, false otherwise

Determines the sign of the Structure value represented by this instance. Returns an integer indicating whether the value is positive, negative, or zero.

Attributes

Returns: 1 if the value is positive, -1 if the value is negative, and 0 if the value is zero

Inherited methods

Adds the current Eager instance to another Eager instance using the DyadicOperator mechanism. The addition operation is implemented by delegating to the addEagers function for specific behavior, ensuring proper handling of various subtypes of Eager.

Value parameters

y: the Eager instance to be added to this Eager instance

Attributes

Returns: a Try[Eager] containing the result of the addition if successful, or a failure if the operation fails
Inherited from:: Eager

Computes an approximate representation of the current value.

This method utilizes the approximation mechanism to derive the most likely value in the form of a Real. Should the approximation fail, an AlgebraException will be raised to indicate the error.

Attributes

Returns: the approximate value as a Real if successful; throws an AlgebraException otherwise.
Inherited from:: Approximate

Attempts to compute an approximate representation of the current value.

This method provides an optional approximation of the value represented by the implementing class. The approximation may account for uncertainties or computational limitations. By default, this method does not force computation of the approximation unless explicitly requested.

Value parameters

force: a boolean flag indicating whether to force computation of the approximation. If true, the method will attempt to generate an approximation even if such computation is resource-intensive or not strictly necessary.

Attributes

Returns: an Option containing the approximate value as a Real if available, or None if no approximation can be computed.
Inherited from:: Nat

Attempts to compute an approximate complex representation of the current value.

This method provides an optional approximation in the form of an Eager type. By default, it does not perform the computation unless explicitly requested through the force flag. The method may return None if no approximation can be computed or if the operation fails.

Value parameters

force: a boolean flag indicating whether to force computation of the approximation. If true, the method will attempt to perform a complex approximation even if it is resource-intensive or otherwise unwarranted.

Attributes

Returns: an Option containing the approximate value as an Eager if successful, or None if no approximation is available.
Inherited from:: Approximate

Returns the category of this value in the Valuable type hierarchy.

Attributes

Returns: a string indicating the high-level category (e.g., "Expression", "Structure", "Nat", "Complex")
Inherited from:: TypeSafe

Compares two instances of Eager and determines their relative ordering. This method is not yet implemented and will raise an com.phasmidsoftware.number.algebra.util.AlgebraException if called.

Value parameters

x: the first Eager instance to compare
y: the second Eager instance to compare

Attributes

Returns: a Try[Int] that contains the comparison result: - 0 if x and y are equal, - a negative result if x is less than y, - and a positive result if x is greater than y. As the method is unimplemented, it will always return a failure with an AlgebraException.
Inherited from:: Eager

Returns a descriptive string combining category and type name. Useful for debugging to understand both the hierarchy level and concrete type.

Attributes

Returns: a string in the format "Category.TypeName" (e.g., "Structure.WholeNumber")
Inherited from:: TypeSafe

Performs division of the current Eager instance by another Eager instance. This operation is implemented using the DyadicOperator mechanism, delegating the actual division logic to the divideEagers function.

Value parameters

y: the Eager instance to divide the current instance by

Attributes

Returns: a Try[Eager] containing the result of the division if successful, or a failure if the operation cannot be performed
Inherited from:: Eager

Compares this Eager instance with another Eager instance for equality. This method is unimplemented and currently returns a failure with an AlgebraException.

Value parameters

that: the Eager instance to compare against

Attributes

Returns: a Try[Boolean] indicating whether the two instances are equal. As the method is unimplemented, it always returns a failure containing an AlgebraException.
Definition Classes: Nat -> Eager -> DyadicOps
Inherited from:: Nat

Attempts to convert the current object to an instance of Eager using an approximation method. If the conversion fails, it recovers by throwing an AlgebraException with a descriptive error message.

Attributes

Returns: An instance of Eager if the approximation is successful.
Inherited from:: Eager

Performs a fuzzy comparison between two Eager instances. The comparison is based on a specified tolerance and determines their relative ordering. If the comparison cannot be performed, an AlgebraException is returned as a failure.

Value parameters

p: the tolerance (as a Double) to be used for the comparison
x: the first Eager instance to be compared
y: the second Eager instance to be compared

Attributes

Returns: a Try[Int] representing the result of the comparison: - A negative integer if x is less than y - Zero if x is approximately equal to y within the tolerance p - A positive integer if x is greater than y - A Failure(AlgebraException) if the comparison cannot be performed
Inherited from:: Eager

Performs a fuzzy equality comparison between the current Eager instance and another Eager instance. The comparison is based on a specified tolerance level. This method is unimplemented and currently returns a failure containing an AlgebraException.

Value parameters

confidence: the tolerance level (as a Double) to be used for the fuzzy equality comparison
that: the Eager instance to compare against this instance

Attributes

Returns: a Try[Boolean] indicating whether the two instances are fuzzy equal. As the method is unimplemented, it always returns a failure containing an AlgebraException.
Inherited from:: Eager

If this Valuable is exact, it returns the exact value as a Double. Otherwise, it returns None. NOTE: do NOT implement this method to return a Double for a fuzzy Real--only for exact numbers.

Attributes

Returns: Some(x) where x is a Double if this is exact, else None.
Inherited from:: Eager

Attempts to obtain a Factor representation in a specific Context.

A Factor could represent entities like PureNumber, Radian, etc., that provide numerical or dimensional meaning to a value. This method evaluates the current instance within the given Context to determine if a valid factor can be generated.

Value parameters

context: the evaluation context in which to determine the factor. The Context specifies the criteria under which the factorization is valid.

Attributes

Returns: an Option[Factor] containing the factor if it can be determined, or None if no suitable factor exists within the provided Context.
Inherited from:: Nat

Retrieves an optional name associated with this instance.

Attributes

Returns: an Option[String] containing the name if present, otherwise None
Inherited from:: Nat

Multiplies the current Eager instance with another Eager instance. The multiplication operation is carried out using the DyadicOperator mechanism, which delegates to the multiplyEagers function for specific behavior. This ensures proper handling of various subtypes of Eager.

Value parameters

y: the Eager instance to multiply with this Eager instance

Attributes

Returns: a Try[Eager] containing the result of the multiplication if successful, or a failure if the operation cannot be performed
Inherited from:: Eager

Obtains the product of this Valuable instance and another Valuable instance. The behavior of the method is determined by whether the instances are of type Lazy or Eager. If the provided instances do not conform to the expected types, an AlgebraException is thrown. CONSIDER supporting sum also.

CONSIDER using lazify

Value parameters

other: the other Valuable instance to compute the product with

Attributes

Returns: a Valuable instance representing the product of this and the other instance
Note: throws AlgebraException if the computation involves unsupported Valuable types
Inherited from:: Valuable

An iterator over the names of all the elements of this product.

Attributes

Inherited from:: Product

An iterator over all the elements of this product.

Attributes

Returns: in the default implementation, an Iterator[Any]
Inherited from:: Product

Renders and returns a string representation of the object. By default, this is the same as render but it can be overridden in subclasses.

Attributes

Returns: a string representing the object
Inherited from:: Valuable

Subtracts the given Eager instance y from the current Eager instance. This operation is performed using the DyadicOperator mechanism, which delegates to the subtractEagers function to handle the specific subtraction behavior.

Value parameters

y: the Eager instance to be subtracted from this Eager instance

Attributes

Returns: a Try[Eager] containing the result of the subtraction if successful, or a failure if the operation fails
Inherited from:: Eager

Returns a simple string representation of the runtime type. Useful for debugging and logging.

Attributes

Returns: the simple class name (e.g., "WholeNumber", "RationalNumber")
Inherited from:: TypeSafe

Concrete fields

Converts this natural number into an integer.

We should CONSIDER making this either a BigInt or an Option[Long] or perhaps a SafeLong.

Attributes

Returns: the integer value corresponding to this natural number

Inherited fields

Converts the current instance to a Double representation. CONSIDER changing to maybeDouble returning Option[Double].

Attributes

Returns: the Double value corresponding to the current instance
Inherited from:: Nat

Casts this Valuable instance into a Structure type if it already is a Structure. If the instance is not a Structure, an AlgebraException is thrown. CONSIDER returning Option[Structure] instead.

Attributes

Returns: the current instance as a Structure
Note: Throws com.phasmidsoftware.number.algebra.util.AlgebraException if the instance is not of type Structure
Inherited from:: Valuable

Attempts to cast this instance to a Number. If the instance is of type Number, it is wrapped in an Option and returned. Otherwise, returns None.

Attributes

Returns: an Option containing the instance as a Number if applicable, or None if not.
Inherited from:: Valuable

Increments this natural number by one.

Attributes

Returns: a new natural number representing the successor of the current instance.
Inherited from:: Nat

Determines whether this Valuable is exact, i.e., has no approximation.

CONSIDER it may be possible that there are non-approximatable entities that are not exact either.

The method returns true if there is no approximate representation available (i.e., approximation is None), indicating that the entity is exact. Otherwise, it returns false.

Attributes

Returns: a Boolean indicating whether the entity is exact (true) or has an approximation (false).
Inherited from:: Nat

Converts the current Lazy instance into an Eager instance by forcing the resolution or evaluation of its underlying value.

The materialize method ensures that the computation of the value represented by this Lazy instance is completed and encapsulated within an appropriate Eager representation. This is particularly useful in scenarios where deferred computation needs to be explicitly resolved prior to further processing.

Attributes

Returns: the materialized Eager instance representing the resolved value
Inherited from:: Eager

Constructs an optional instance of Q for this Nat. The Q instance is derived from the rational representation of the Nat itself.

Attributes

Returns: an Option[Q] that contains the Q instance built from the rational value of the current Nat, or None if the representation cannot be determined.
Inherited from:: Nat

Computes a potential representation of this Nat instance as Z.

Attributes

Returns: an Option[Z] containing a corresponding instance of Z if available; otherwise, None.
Inherited from:: Nat

Normalizes this Nat instance to its simplest equivalent form. This operation does not modify the original instance but may return an adjusted Valuable representation that is equivalent to the original value but simpler.

For instance, the normalization process might reduce complex expressions or structures to their minimal form where possible. In this specific implementation, it directly returns the current instance.

Attributes

Returns: the simplest Valuable representation of this Nat instance, which in this case is this.
Inherited from:: Nat

Method to render this Renderable for presentation to the user.

Attributes

Returns: a String
Inherited from:: Nat

Converts the approximate representation of this number into a Double.

This method attempts to approximate the value of this number by invoking the approximation method with force = true. If the approximation exists, it is converted to a Double. If no approximation can be obtained, an AlgebraException is thrown to indicate a logic error.

Attributes

Returns: the approximate value as a Double.
Note: Throws an com.phasmidsoftware.number.algebra.util.AlgebraException if no approximation can be obtained.
Inherited from:: Approximate

Converts this instance of Q to its corresponding rational representation.

Attributes

Returns: a Rational instance representing the current value
Inherited from:: Nat

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