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

Infinity

com.phasmidsoftware.number.expression.expr.Infinity

case object Infinity extends NamedConstant

Represents an infinite value in the Valuable of expressions.

The Infinity object is a special case of NamedConstant with a value of positive infinity. It is immutable and serves as a singleton instance to represent the mathematical concept of infinity in calculations or expressions. It overrides certain behaviors of ValueExpression to handle operations specific to infinity.

Attributes

Graph
Supertypes: trait Singleton

trait Product

trait Mirror

trait Serializable

trait Product

trait Equals

class NamedConstant

class ValueExpression

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: Infinity.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

Concrete methods

Applies the given ExpressionMonoFunction to the current context of the ValueExpression and attempts to produce an atomic result.

Value parameters

f: the ExpressionMonoFunction to be applied. This function determines how the evaluation will transform the current ValueExpression into a potential result.

Attributes

Returns: an Option containing an ValueExpression if the evaluation succeeds, or None if the evaluation fails.

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:: ValueExpression

Provides an approximation of the ValueExpression as an Eager, if applicable.

This method checks if the associated value is an instance of eager.Complex. If it is, the method directly returns it wrapped in an Option. Otherwise, it delegates to the approximation method to compute a possible approximation.

Value parameters

force: a Boolean flag indicating whether the approximation should be forced. If true, the method may attempt a broader range of approximations. Defaults to false.

Attributes

Returns: an Option[Eager] containing the approximation if one exists, or None if an approximation is not available or applicable.
Definition Classes: ValueExpression -> Approximate
Inherited from:: ValueExpression

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

Compares this ValueExpression with another object for equality. The comparison considers the value Valuable and whether the other object can be equal to this instance.

Value parameters

other: the object to compare for equality with this instance.

Attributes

Returns: true if the provided object is equal to this instance, false otherwise.
Definition Classes: ValueExpression -> Any
Inherited from:: ValueExpression

Evaluates the current Valuable expression within the given context and determines if the Valuable qualifies based on the context's rules.

NOTE: we now have Valuable values that may not have a unique factor (Algebraics). That's why we need to check first if value has a unique factor.

If the Valuable meets the qualifications specified by the context, the method returns an Option containing the Valuable. Otherwise, it returns None.

Value parameters

context: the context in which the Valuable is evaluated. It defines the qualification rules for determining whether the Valuable is valid.

Attributes

Returns: Some(Valuable) if the Valuable qualifies within the given context, otherwise None.
Inherited from:: ValueExpression

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

Attributes

Inherited from:: Singleton

Computes the hash code for this ValueExpression instance.

The hash code is derived from the hash code of the value Valuable, ensuring that the behavior adheres to the contract of the hashCode method, particularly in relation to the equals method.

Attributes

Returns: an integer hash code that represents this ValueExpression instance.
Definition Classes: ValueExpression -> Any
Inherited from:: ValueExpression

Method to determine if this Structure object is exact. For instance, Number.pi is exact, although if you converted it into a PureNumber, it would no longer be exact.

Attributes

Returns: true if this Structure object is exact in the context of No factor, else false.
Inherited from:: ValueExpression

Determines whether this object represents unity.

Attributes

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

Determines if the current number is equal to zero.

Attributes

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

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:: ValueExpression

Method to determine what Factor, if there is such, this Structure object is based on.

Attributes

Returns: an optional Factor.
Inherited from:: ValueExpression

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

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:: ValueExpression

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

Attributes

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

Returns a string representation of this constant. If the constant has a name, the name is returned enclosed in angular brackets. Otherwise, the string representation of the associated Valuable is used.

Attributes

Returns: A string representing this constant, using its name if available, or the value's string representation if the name is absent.
Definition Classes: NamedConstant -> ValueExpression -> Any
Inherited from:: NamedConstant

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

Concrete fields

Determines if the name is protected, for example, it represents a mathematical symbol for a transcendental value (e.g., pi), or a commonly used root such as √2.

This method indicates whether a name associated with an entity is considered protected. The protection status could influence how the name is accessed or utilized by external systems.

Attributes

Returns: true if the name is protected, otherwise false

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

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

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

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:: ValueExpression

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

Method to render this Structure in a presentable manner.

Attributes

Returns: a String
Inherited from:: ValueExpression

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

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

Attributes

Inherited from:: ValueExpression

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