Number - Scala Mathematical Library
1.10.6
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Number - Scala Mathematical Library/com.phasmidsoftware.number/com.phasmidsoftware.number.algebra/com.phasmidsoftware.number.algebra.core/Lazy

Lazy

com.phasmidsoftware.number.algebra.core.Lazy
trait Lazy extends Valuable

The Lazy trait extends the Valuable interface and represents an abstraction for objects that are lazy in their evaluation or resolution. This trait provides methods for simplification, materialization, and normalization of the underlying value.

The key distinction of Lazy implementations is their support for deferred computation, whereby full resolution or evaluation may not be required unless explicitly invoked.

Attributes

Graph
Supertypes
trait Valuable
trait TypeSafe
trait Exactitude
trait Unitary
trait Zeroable
trait Numeric
trait Renderable
class Object
trait Matchable
class Any
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Known subtypes
trait Expression
class Noop
trait Root
class AbstractRoot
class LinearRoot
object L2
object LgE
class Literal
object E
object I
object Infinity
object Half
object MinusOne
object One
object Pi
object Two
object Zero
class Euler
trait Multiple
class Aggregate
class BiFunction
class UniFunction
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Members list

Value members

Abstract methods

def multiply(other: Lazy): Lazy

Multiplies this Lazy instance with another Lazy instance, producing a new Lazy result that represents the product of the two inputs.

Multiplies this Lazy instance with another Lazy instance, producing a new Lazy result that represents the product of the two inputs.

CONSIDER we should probably orivude an add method as well.

Value parameters

other

the Lazy instance to multiply with this instance

Attributes

Returns

a new Lazy instance representing the product of the two inputs

def simplify: Lazy

Simplifies the given expression or computation and returns a lazy evaluation result.

Simplifies the given expression or computation and returns a lazy evaluation result.

Attributes

Returns

a lazy evaluation result representing the simplified expression or computation

def unit(x: Eager): Lazy

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

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 methods

def category: String

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

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
def describe: String

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

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
def product(other: Valuable): Valuable

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.

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
def show: String

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

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
def typeName: String

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

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

Inherited and Abstract methods

def isExact: Boolean

Determines whether this object is exact, i.e., is not any kind of approximation.

Determines whether this object is exact, i.e., is not any kind of approximation.

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

The method returns true if the value is represented exactly in IEEE 754 format, or Two's complement or the exact value must be represented symbolically. Examples of the first type include the number one (represented here as either WholeNumber(1) or Succ(NatZero). Examples of the second type include 1.5 or the square root of two (represented here as InversePower(2,2)).

When we are forced to approximate a value, for example when we want to print the decimal value of 𝛗, the Golden Ratio, then we mark such a representation as approximate, i.e., this method returns false.

Attributes

Returns

a Boolean indicating whether the entity is exact (true) or is an approximation (false).

Inherited from:
Exactitude
def isUnity: Boolean

Determines whether this object represents unity.

Determines whether this object represents unity.

Attributes

Returns

true if the object represents unity, false otherwise

Inherited from:
Unitary
def isZero: Boolean

Determines if the current number is equal to zero.

Determines if the current number is equal to zero.

Attributes

Returns

true if the number is zero, false otherwise

Inherited from:
Zeroable
def materialize: Eager

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

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:
Valuable
def maybeDouble: Option[Double]

If this 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.

If this 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:
Numeric
def maybeFactor(context: Context): Option[Factor]

Attempts to retrieve a factor based on the provided context. This method evaluates whether there is an applicable factor within the given context.

Attempts to retrieve a factor based on the provided context. This method evaluates whether there is an applicable factor within the given context.

Value parameters

context

the context in which the factor is evaluated.

Attributes

Returns

an optional Factor if one qualifies under the provided context; otherwise, None.

Inherited from:
Valuable
def render: String

Method to render this Valuable for presentation to the user. NOTE to implementors: never ever invoke this.toString in your implementation lest you get a StackOverflow.

Method to render this Valuable for presentation to the user. NOTE to implementors: never ever invoke this.toString in your implementation lest you get a StackOverflow.

Attributes

Returns

a String

Inherited from:
Renderable
def signum: Int

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

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:
Zeroable

Concrete fields

lazy val normalize: Valuable

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.

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 fields

lazy val asMonotone: Structure

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.

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
lazy val asNumber: Option[Number]

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.

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
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