Number - Scala Mathematical Library/com.phasmidsoftware.number/com.phasmidsoftware.number.expression/com.phasmidsoftware.number.expression.expr/ETranscendental

ETranscendental

com.phasmidsoftware.number.expression.expr.ETranscendental

case object ETranscendental extends AbstractTranscendental

Case object representing the transcendental constant e.

Extends the AbstractTranscendental class, providing implementations specific to the mathematical constant e (Euler's number), known for its importance in the Valuable of mathematics, particularly in calculus and exponential growth behavior.

The name parameter is set to "xD835DF00", which represents a unique identifier for this transcendental, and its expression is given by the constant E.

The E object inherits all methods and properties from AbstractTranscendental, allowing it to be treated as an atomic and exact mathematical expression with various evaluative and comparison capabilities. It also ensures consistency in rendering and context-based operations.

Attributes

Deprecated: [Since version 0.1.0] use E instead.
Graph
Supertypes: trait Singleton

trait Product

trait Mirror

trait Serializable

trait Product

trait Equals

class AbstractTranscendental

trait Transcendental

trait AtomicExpression

trait Nameable

trait Expression

trait Approximate

trait Lazy

trait Valuable

trait TypeSafe

trait Normalizable[Valuable]

trait Exactitude

trait Unitary

trait Zeroable

trait Numeric

trait Renderable

class Object

trait Matchable

class Any
Show all
Self type: ETranscendental.type

Members list

Type members

Inherited types

The names of the product elements.

Attributes

Inherited from:: Singleton

Attributes

Inherited from:: Singleton

The mirrored *-type.

Attributes

Inherited from:: Singleton

Attributes

Inherited from:: Singleton

Inherited and Abstract types

The name of the type.

Attributes

Inherited from:: Mirror

Value members

Inherited methods

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

Provides an approximation of this number, if applicable.

This method attempts to compute an approximate representation of the number in the form of a Real, which encapsulates uncertainty or imprecision in its value. If no meaningful approximation is possible for the number, it returns None.

Attributes

Returns: an Option[Real] containing the approximate representation of this Number, or None if no approximation is available.
Inherited from:: AbstractTranscendental

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

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

Determines if the provided object is equal to the current instance. The comparison considers the object's type and specific attributes.

Value parameters

other: the object to be compared with the current instance

Attributes

Returns: true if the provided object is an instance of AbstractTranscendental, can be equal to the current instance, and has the same expression value; false otherwise
Definition Classes: AbstractTranscendental -> Any
Inherited from:: AbstractTranscendental

Action to evaluate this Expression as a Valuable, if possible. NOTE: no simplification or factor-based conversion occurs here.

Attributes

Returns: an optional Valuable.
Inherited from:: AbstractTranscendental

Creates a new instance of type T with elements taken from product p.

Attributes

Inherited from:: Singleton

Applies a given ExpressionMonoFunction to create a new instance of Transcendental.

Value parameters

f: the ExpressionMonoFunction to be applied, representing a lazy monadic operation.

Attributes

Returns: a new Transcendental instance that encapsulates the applied function and updated expression.
Inherited from:: AbstractTranscendental

Computes the hash code for this instance of AbstractTranscendental.

Attributes

Returns: an integer representing the hash code of the expression Eager.
Definition Classes: AbstractTranscendental -> Any
Inherited from:: AbstractTranscendental

Method to determine what Factor, if there is such, this Structure object is based on. Unlike context, a None result is not permissive.

Attributes

Returns: an optional Factor.
Inherited from:: AbstractTranscendental

Multiplies this Expression with another Lazy instance. If the other instance is of type Expression, a product operation is performed, and the result is simplified. If the other instance is not of type Expression, an ExpressionException is thrown.

Value parameters

other: the Lazy instance to multiply with this Expression

Attributes

Returns: a new Lazy instance representing the product of this Expression and the supplied Lazy instance
Throws: ExpressionException
if the provided other is not of type Expression
Inherited from:: Expression

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

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

Transforms an instance of the Eager type into a Lazy instance, allowing for deferred computation or evaluation. NOTE that this method ignores this.

Value parameters

x: an instance of Eager that is to be converted into a Lazy representation

Attributes

Returns: a Lazy instance representing the deferred computation or evaluation of the input
Inherited from:: Expression

Inherited fields

A lazily evaluated optional approximation of this Expression.

This field holds the result of simplifying the Expression with the approximation flag set to true. If the approximation is possible, it will store the approximated Real value; otherwise, it will remain None.

This approximation is computed based on the context of the simplify method, which determines how the expression should be approximated.

Attributes

Inherited from:: Expression

Represents the optional approximate evaluation of a complex Expression. The property retrieves the result of invoking the approximationComplex method on the simplify field, passing true as an argument to indicate that the result should be computed for complex approximations.

This lazy value ensures that the computation is deferred until accessed, and only computed once for performance optimization.

Attributes

Returns: An Option of type Eager, containing the approximate complex representation of this Expression, if available. Otherwise, None.
Inherited from:: Expression

Method to determine if the materialized value of this Expression is defined and corresponds to a Number. If this expression is exact, then evaluate as is and convert the result to a Number. Otherwise, we simply materialize this expression and convert the result to a Number.

Attributes

Returns: a Some(x) if this materializes as a Number; otherwise None.
Inherited from:: Expression

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

Determines if the current Expression or any of its sub-expressions contains the constant I.

For Expression instances:

If the Expression is exactly the constant I, returns true.
If the Expression is a composite of other expressions (CompositeExpression), recursively searches through the terms to check if any of them contains the constant I.
For all other cases, returns false.

Attributes

Returns: true if the constant I is present in the Expression or its components, false otherwise.
Inherited from:: Expression

Method to use when debugging to know exactly what an Expression is in tree form. This is needed because toString and other renderers all use some sort of syntactic sugar to make things look nice for us humans.

Creates a string representation of this Expression for debugging purposes. Depending on the type of this Expression, the output format varies:

For atomic Product instances (arity 0), the productPrefix is returned.
For non-atomic Product instances, the productPrefix is combined with the debug representation of contained sub-expressions (if they are Expressions) or their toString representation otherwise.
For all other cases, the default toString implementation is used.

Attributes

Returns: a String representation useful for debugging.
Inherited from:: Expression

Attributes

Returns

Inherited from:

AtomicExpression

Evaluates this Expression in the context of AnyContext without simplification or factor-based conversion. This allows obtaining a direct evaluation of the Expression as a Eager, if possible. NOTE: no simplification or factor-based conversion occurs here.

Attributes

Returns: either a Some[Eager] containing the value if evaluation is successful, or None otherwise.
Inherited from:: Expression

Attributes

Inherited from:: AbstractTranscendental

Computes the fuzzy (approximate) value of this Expression. If the current Expression can be matched to a simpler form via matchSimpler, its fuzzy value is derived from the simplified expression. Otherwise, the fuzzy result is delegated to the superclass implementation.

Attributes

Returns: an eager.Real representing the approximate value of this Expression
Inherited from:: Expression

Indicates whether the expression is atomic.

Attributes

Returns: true, as this expression is atomic and cannot be further simplified.
Inherited from:: AtomicExpression

Method to determine if this Expression can be evaluated as is. If so, then materialize will not lose any precision because no approximation will be required. NOTE that, it is conceivable that simplifying this Expression first might result in an eager value even though this method would return false.

Attributes

Returns: true if evaluateAsIs is defined.
Inherited from:: Expression

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:: AbstractTranscendental

Determines whether this object represents unity.

Attributes

Returns: true if the object represents unity, false otherwise
Inherited from:: AbstractTranscendental

Determines if the current number is equal to zero.

Attributes

Returns: true if the number is zero, false otherwise
Inherited from:: AbstractTranscendental

Indicates whether symbolic names are preserved.

This method determines if symbolic representation should be retained when working with names in entities implementing the Nameable trait.

Attributes

Returns: true if symbolic names are kept, otherwise false
Inherited from:: Nameable

Materializes this Expression into an Eager object by simplifying it, evaluating as-is, optionally approximating it, and recovering with a defined exception in case of failure.

This method should be the final step when dealing with an Expression. Do not materialize early because that defeats the entire purpose of lazy evaluation.

The method first simplifies the expression, attempts to evaluate it directly, and then tries an approximation if necessary. Ultimately, it ensures the resulting materialized object is an instance of Eager.

The Eager result will be normalized if appropriate.

Attributes

Returns: an Eager representation of this Expression achieved through evaluation and/or approximation.
Inherited from:: Expression

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:: AbstractTranscendental

Retrieves an optional name associated with the implementing class.

The method returns an Option wrapping a String. If a name is available, it will be contained within the Option as Some(name). If no name is present, the method will return None.

Attributes

Returns: an Option[String] representing the optional name
Inherited from:: AbstractTranscendental

Attributes

Inherited from:: AbstractTranscendental

Normalizes the current Lazy instance to its simplest Valuable equivalent. The method first attempts to simplify the instance using the simplify method. If the simplified result is exact, the method materializes it and normalizes the resulting value. Otherwise, the simplified value is returned as is.

Attributes

Returns: the simplest Valuable representation of this value after normalization
Inherited from:: Lazy

This ensures that all Transcendental instances are protected from evaluation during simplification. Such transcendentals as the Euler-Mascheroni constant are kept as is during simplification.

Attributes

Inherited from:: AbstractTranscendental

Method to render this Structure in a presentable manner.

Attributes

Returns: a String
Inherited from:: AbstractTranscendental

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 from:: AbstractTranscendental

Simplifies the current Expression instance. If a simpler representation of the Expression can be determined, it returns that representation. Otherwise, it returns the current Expression unchanged. NOTE: be careful not to invoke recursively.

Attributes

Returns: the simplified Expression, or the current Expression if no simplification is possible
Inherited from:: Expression

Attempts to simplify an atomic expression, for example, we replace Literal(Eager.pi) with Pi.

Attributes

Returns: an em.AutoMatcher[Expression] representing the process of handling or matching the atomic expression.
Inherited from:: AbstractTranscendental

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

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