Number - Scala Mathematical Library
1.10.6
API
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Number - Scala Mathematical Library/com.phasmidsoftware.number/com.phasmidsoftware.number.expression/com.phasmidsoftware.number.expression.expr/AtomicExpression

AtomicExpression

com.phasmidsoftware.number.expression.expr.AtomicExpression
See theAtomicExpression companion object
trait AtomicExpression extends Expression, Nameable

An Expression that is based on one simple constant value. The four subtypes of AtomicExpression are:

  • ValueExpression
  • Root
  • Transcendental
  • Noop

Attributes

Companion
object
Graph
Supertypes
trait Nameable
trait Expression
trait Approximate
trait Lazy
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
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
Show all

Members list

Value members

Abstract methods

def simplifyAtomic: em.AutoMatcher[Expression]

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

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 methods

def approximate: Real

Computes an approximate representation of the current value.

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
def approximationComplex(force: Boolean = ...): Option[Eager]

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

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
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 multiply(other: Lazy): Lazy

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.

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
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 protectedName: Boolean

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.

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 from:
Nameable
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
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 from:
Expression

Inherited and Abstract methods

def approximation(force: Boolean = ...): Option[Real]

Attempts to compute an approximate representation of the current value.

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:
Approximate
def evaluate(context: Context): Option[Eager]

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

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

Attributes

Returns

an optional Field.

Inherited from:
Expression
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 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 maybeName: Option[String]

Retrieves an optional name associated with the implementing class.

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:
Nameable
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

val depth: Int

Attributes

Returns
val isAtomic: Boolean

Indicates whether the expression is atomic.

Indicates whether the expression is atomic.

Attributes

Returns

true, as this expression is atomic and cannot be further simplified.

Inherited fields

lazy val approximation: Option[Real]

A lazily evaluated optional approximation of this Expression.

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
lazy val approximationComplex: Option[Eager]

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.

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
lazy val asCoreNumber: Option[Number]

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.

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
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
lazy val containsI: Boolean

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

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
lazy val debug: String

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.

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
lazy val evaluateAsIs: Option[Eager]

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.

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
lazy val fuzzy: Eager

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.

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
lazy val isEager: Boolean

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.

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
lazy val keepSymbolic: Boolean

Indicates whether symbolic names are preserved.

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
lazy val materialize: Eager

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.

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
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 from:
Lazy
lazy val simplify: Expression

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.

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
lazy val toDouble: Double

Converts the approximate representation of this number into a Double.

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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