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

BiFunction

com.phasmidsoftware.number.expression.expr.BiFunction

See theBiFunction companion object

case class BiFunction(a: Expression, b: Expression, f: ExpressionBiFunction) extends BinaryFunction

This class represents a dyadic function of the two given expressions.

Value parameters

a: the first expression being operated on.
b: the second expression being operated on.
f: the function to be applied to a and b.

Attributes

Companion: object
Graph
Supertypes: trait Serializable

trait Product

trait Equals

class BinaryFunction

trait Multiple

trait CompositeExpression

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
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Members list

Value members

Concrete methods

An equals method which considers two BiFunctions, which are non-identical but symmetric, to be equal.

Value parameters

obj: the other object.

Attributes

Returns: true if the values of these two expressions would be the same (without any evaluation).
Definition Classes: Equals -> Any

Determines whether to leave operands unchanged based on specific conditions.

Attributes

Returns: true if any of the operands match the conditions IsCoshSquared or IsSinhSquared, false otherwise.
Definition Classes: CompositeExpression

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:: BinaryFunction

Attempts to compute an approximation of a complex operation defined by f using the approximations of components a and b. The operation can be a sum, product, power, or other types defined by f.

Value parameters

force: A boolean flag indicating whether the approximation should forcibly be computed even if conditions might not favor it.

Attributes

Returns: An Option containing the computed Eager result if successful, or None if the approximation cannot be determined.
Definition Classes: BinaryFunction -> Approximate
Inherited from:: BinaryFunction

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

Action to simplify this Expression as a Field. NOTE that because we need to be able to evaluate this Expression exactly, we need to be sure that the Context passed in to f.evaluate is not None.

Attributes

Returns: the materialized Field.
Inherited from:: BinaryFunction

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:: BinaryFunction

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

Determines if all components within a given Expression are named.

TODO handle the specific cases at their proper level in the type hierarchy.

This method recursively checks whether each component of the provided Expression either has a name (in the case of a Nameable expression) or, if it is a composite expression (CompositeExpression), ensures that all of its terms also have names.

Attributes

Returns: true if all components of the expression are named, otherwise false.
Inherited from:: CompositeExpression

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

Concrete fields

Regular hashCode method.

Attributes

Returns: an Int depending on f, a, and b.

Simplifies a given BiFunction expression where trivial simplifications can be applied. This method identifies patterns in the expression that represent mathematical identities or redundancies and replaces them with their simplified form. Examples of such patterns include removing identities, handling zero and one in products or powers, and other basic algebraic simplifications.

The simplifications include:

Removing or simplifying identity elements (e.g., x * 1 = x, x + 0 = x).
Handling special cases like zeroes in products or powers.
Applying reductions for specific constants or algebraic terms.

If no simplification can be applied, the method encapsulates this as a "miss" result. Implementations of this method aim to provide lightweight simplification logic, with more complex cases deferred to other parts of the system.

Attributes

Returns: an em.AutoMatcher[Expression] instance encapsulating the simplified Expression if simplification was possible, or a "miss" if no trivial simplification could be applied.

Simplifies the components of a BiFunction expression by applying a matcher that reduces its constituent expressions (x and y), individually, to their simpler forms.

Attributes

Returns: An AutoMatcher for the Expression type that matches and simplifies BiFunction expressions.

Renders the CompositeExpression as a string representation of the expression itself, typically in a structured or human-readable mathematical format.

Attributes

Returns: a string representation of the CompositeExpression as an expression.

Simplifies a CompositeExpression represented as a BiFunction by applying various matchers to identify opportunities for simplification. Specifically:

Converts the BiFunction into an Aggregate for consistent simplification processing.
Attempts to simplify complementary terms within the BiFunction.
Applies additional simplification logic as defined by Expression.structuralMatcher and matchSimpler.

TODO try to shorten this method.

If the expression cannot be simplified, the result will indicate the failure.

Attributes

Returns: an em.AutoMatcher[Expression] that encapsulates the logic for simplifying the BiFunction. It provides either the simplified Expression or indicates that no simplification was possible.

Render this BiFunction for debugging purposes.

Attributes

Returns: a String showing a, f, and b in parentheses (or in braces if not exact).

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

Method to determine the depth of this Expression.

Attributes

Returns: the depth (an atomic expression has depth of 1).
Inherited from:: BinaryFunction

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 this expression is atomic.

Attributes

Returns: false as the default value, indicating the expression is not atomic.
Inherited from:: CompositeExpression

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:: BinaryFunction

Determines whether this object represents unity.

Attributes

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

Determines if the current number is equal to zero.

Attributes

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

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:: CompositeExpression

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

Provides a lazy string representation of the CompositeExpression, delegating the rendering logic to the renderAsExpression method.

This value is computed only once, upon its first access, and caches the result for subsequent accesses. It is intended to present the CompositeExpression in a structured or human-readable mathematical format by reusing the string output generated by renderAsExpression.

Attributes

Returns: the string representation of this CompositeExpression.
Inherited from:: CompositeExpression

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:: CompositeExpression

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

Simplifies the exact form of a CompositeExpression by identifying and transforming sub-expressions into their precise, simplified forms. This method focuses on exact mathematical simplifications that can be performed without introducing approximations.

TODO try to merge this method with Expression.simplifyByEvaluation.

Attributes

Returns: an em.AutoMatcher[Expression] that encapsulates the logic for simplifying exact expressions. The result contains the simplified Expression if successful, or indicates no simplification was possible.
Inherited from:: CompositeExpression

Provides the terms that comprise this CompositeExpression.

Attributes

Returns: a sequence of Expression objects representing the individual terms of this CompositeExpression.
Inherited from:: BinaryFunction

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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