Number - Scala Mathematical Library/com.phasmidsoftware.number/com.phasmidsoftware.number.algebra/com.phasmidsoftware.number.algebra.eager/InversePower

InversePower

com.phasmidsoftware.number.algebra.eager.InversePower

See theInversePower companion object

case class InversePower extends Transformed, Scalable[InversePower], CanPower[Number]

Represents an eager mathematical root, parameterized with an integral root degree and a base number.

NOTE do not invoke the constructor directory: all construction should go via the apply method(s) which will normalize as appropriate.

TODO there are problems with multiplication (class cast exception, for example). Therefore, we should remove the CanMultiplyAndDivide mixin.

CONSIDER making this an (abstract?) class and having subclasses for square root and cube root.

Value parameters

n: the degree of the root, specified as an integer
number: the base Number value on which the root operation is defined

Attributes

Companion: object
Graph
Supertypes: trait Serializable

trait Product

trait Equals

trait CanPower[Number]

trait Scalable[InversePower]

trait Transformed

trait Functional

trait Ordered[Functional]

trait Comparable[Functional]

trait MaybeFuzzy

trait Structure

trait Negatable[Structure]

trait WithFuzziness

trait Eager

trait DyadicOps

trait Approximate

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

Scales the current instance by the given factor.

This method applies a scaling operation on the instance using the provided rational factor and returns the resulting scaled instance.

Value parameters

factor: the rational number representing the scale factor

Attributes

Returns: the scaled instance of type T

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.

Compares this InversePower instance with another Functional instance.

Value parameters

that: The Functional instance to compare against.

Attributes

Returns: An integer where: - a negative value indicates this instance is less than that, - zero indicates this instance is equal to that, - a positive value indicates this instance is greater than that.

Compares the current Root instance with another Number to determine their exact order.

If the provided Number is a Root, this method compares their underlying radian values. If the provided Number is not a Root, the comparison cannot be performed, and None is returned.

Value parameters

that: the Number instance to compare with the current Root instance

Attributes

Returns: an Option[Int], where Some(-1) indicates that the current Root is less than the provided Root, Some(0) indicates that both roots are equal, Some(1) indicates that the current Root is greater, and None is returned if the comparison cannot be made

Converts the current number to a representation of the specified type T, if possible.

This method attempts to convert the number to a type T that has implicit evidence of Ordering. If the conversion is successful, it returns an Option containing the resulting typed value. If the conversion is not valid or not possible for the given type T, it returns None.

Attributes

Returns: an Option containing the converted value of type T if successful, or None if the conversion is not possible.

Scales the current instance using the provided Number.

The method performs a scaling operation by applying the given Number to the current instance, producing an optional result of type T. If the scaling operation cannot be defined for the given Number, it returns None.

Value parameters

that: the Number used to scale the current instance

Attributes

Returns: an Option[T] containing the result of the scaling operation if successful, or None if the operation cannot be performed

Checks for equality between the current instance of Eager and another Eager instance.

This method determines equality by comparing the structure of the two instances:

If both instances are of type InversePower, their associated parameters (n and x) are compared. If their n values match, the equality of their x values is evaluated recursively using their own eqv method.
For other cases, the method defers to the eqv implementation of the superclass.

Value parameters

that: the Eager instance to compare with the current instance

Attributes

Returns: a Try[Boolean] where: - Success(true) indicates the two instances are equal. - Success(false) indicates the two instances are not equal. - A failed Try may be returned if an error occurs during comparison.
Definition Classes: Eager -> DyadicOps

Retrieves an optional fuzziness value associated with this instance.

The fuzziness value, if present, provides information about the level of uncertainty or imprecision, modeled as a Fuzziness[Double].

Attributes

Returns: an Option containing the Fuzziness[Double] value if defined, or None if no fuzziness is specified.

Compares this instance with another Eager instance using a specified precision. The comparison involves converting both instances to Real and performing a fuzzy equivalence check with the specified precision.

Value parameters

confidence: The precision parameter used in the fuzzy equivalence comparison.
that: The Eager instance to be compared against.

Attributes

Returns: A Try[Boolean] indicating the result of the fuzzy equivalence check. Success with true if the instances are equivalent within the given precision, false if they are not equivalent, or a failure if a comparison cannot be performed.
Definition Classes: Structure -> Eager -> DyadicOps

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.

Determines whether this object represents unity.

Attributes

Returns: true if the object represents unity, false otherwise

Determines if the current number is equal to zero.

Attributes

Returns: true if the number is zero, false otherwise

Computes the potential factor associated with this instance.

Attributes

Returns: an Option containing a Factor if available, otherwise None

Returns a new instance of Structure that is the negation of the current instance. CONSIDER sorting out the use of CanNegate so that we can extend that for Structure.

Attributes

Returns: a Structure representing the negation of this instance
Note: Throws an com.phasmidsoftware.number.algebra.util.AlgebraException if the negation operation is not defined for the current instance

Represents the multiplicative identity element of the structure.

The one value serves as the neutral element for the multiplication operation, meaning that for any instance t of type T, the equation one * t = t * one = t holds true.

Attributes

Computes the result of raising an instance of type T to the power specified by the given ExactNumber.

This method performs the power operation and returns the result wrapped in an Option[T]. If the operation is invalid or cannot be performed, None is returned.

Value parameters

that: the ExactNumber exponent to which the instance is raised

Attributes

Returns: an Option[T] containing the result of the power operation if valid, or None if the operation could not be performed

Determines the sign of the scalar 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

Converts this Number into its corresponding Rational representation, if possible.

Attributes

Returns: an Option[Rational] containing the Rational representation of this Number if it can be converted, or None if the conversion is not possible.

Defines a transformation that transforms a Structure instance into a corresponding Scalar value.

The transformation defines how a Structure is interpreted or converted in the context of Scalar.

Attributes

Returns: a transformation that maps a Structure object to a Scalar result

Inherited methods

Multiplies the current instance by the specified integer factor.

Value parameters

factor: the integer value to multiply with the current instance

Attributes

Returns: a new instance of type T representing the result of the multiplication
Inherited from:: Scalable

Returns true if this is less than that

Value parameters

that: the instance to compare against

Attributes

Inherited from:: Ordered

Returns true if this is less than or equal to that.

Attributes

Inherited from:: Ordered

Returns true if this is greater than that.

Value parameters

that: the instance to compare against

Attributes

Inherited from:: Ordered

Returns true if this is greater than or equal to that.

Attributes

Inherited from:: Ordered

Adds the specified Structure instance to the current instance, producing a new Structure.

Value parameters

y: The Structure instance to be added.

Attributes

Returns: A Try wrapping the resulting Structure instance, or a failure if the operation cannot be completed.
Inherited from:: Structure

Adds the current Eager instance to another Eager instance using the DyadicOperator mechanism. The addition operation is implemented by delegating to the addEagers function for specific behavior, ensuring proper handling of various subtypes of Eager.

Value parameters

y: the Eager instance to be added to this Eager instance

Attributes

Returns: a Try[Eager] containing the result of the addition if successful, or a failure if the operation fails
Inherited from:: Eager

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

Attempts to approximate the current instance to a Real value. If the instance is already of type Real, it is simply returned, wrapped inside Some. Otherwise, depending on the value of force, it either attempts a conversion to a default Real (if force is true), or returns None.

NOTE that this method tries to keep exact quantities exact.

Value parameters

force: a boolean flag indicating whether to force the conversion to a default Real value when the current instance is not of type Real

Attributes

Returns: an Option[Real] containing the approximated value if successful, or None if approximation fails
Inherited from:: Structure

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

Converts this Structure object into an optional java.lang.Number provided that the conversion can be performed without loss of precision.

The method determines whether the current Structure object can be represented as a java.lang.Number by leveraging the asNumber method and further evaluating certain conditions:

If the Structure object is an ExactNumber and its factor is PureNumber, the result is converted using Value.asJavaNumber.
If the Structure object is a Real with a wiggle value below a specified tolerance, the result is also converted using Value.asJavaNumber.
In all other cases, None is returned.

Attributes

Returns: an optional java.lang.Number representation of this object. The result is Some(java.lang.Number) if the conversion is successful under the stated conditions; otherwise, None.
Inherited from:: Structure

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

Compares two instances of Eager and determines their relative ordering. This method is not yet implemented and will raise an com.phasmidsoftware.number.algebra.util.AlgebraException if called.

Value parameters

x: the first Eager instance to compare
y: the second Eager instance to compare

Attributes

Returns: a Try[Int] that contains the comparison result: - 0 if x and y are equal, - a negative result if x is less than y, - and a positive result if x is greater than y. As the method is unimplemented, it will always return a failure with an AlgebraException.
Inherited from:: Eager

Result of comparing this with operand that.

Value parameters

that: the instance to compare against

Attributes

Inherited from:: Ordered

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

Divides the current Structure instance by another Structure instance. The operation is performed using the DyadicOperator defined for Structure. The result is wrapped in a Try to handle potential failures during the operation.

Value parameters

y: the Structure instance to divide the current instance by

Attributes

Returns: a Try[Structure] containing the result of the division if successful, or a failure if the operation cannot be performed
Inherited from:: Structure

Performs division of the current Eager instance by another Eager instance. This operation is implemented using the DyadicOperator mechanism, delegating the actual division logic to the divideEagers function.

Value parameters

y: the Eager instance to divide the current instance by

Attributes

Returns: a Try[Eager] containing the result of the division if successful, or a failure if the operation cannot be performed
Inherited from:: Eager

Attempts to convert the current object to an instance of Eager using an approximation method. If the conversion fails, it recovers by throwing an AlgebraException with a descriptive error message.

Attributes

Returns: An instance of Eager if the approximation is successful.
Inherited from:: Eager

Performs a fuzzy comparison between two Eager instances. The comparison is based on a specified tolerance and determines their relative ordering. If the comparison cannot be performed, an AlgebraException is returned as a failure.

Value parameters

p: the tolerance (as a Double) to be used for the comparison
x: the first Eager instance to be compared
y: the second Eager instance to be compared

Attributes

Returns: a Try[Int] representing the result of the comparison: - A negative integer if x is less than y - Zero if x is approximately equal to y within the tolerance p - A positive integer if x is greater than y - A Failure(AlgebraException) if the comparison cannot be performed
Inherited from:: Eager

Multiplies the current Structure instance by the specified Structure operand. The result of the operation is wrapped in a Try, allowing for safe handling of failures.

Value parameters

y: the Structure operand with which the current instance is multiplied

Attributes

Returns: a Try[Structure] containing the result of the multiplication if successful, or a failure if the operation is not valid or cannot be performed
Inherited from:: Structure

Multiplies the current Eager instance with another Eager instance. The multiplication operation is carried out using the DyadicOperator mechanism, which delegates to the multiplyEagers function for specific behavior. This ensures proper handling of various subtypes of Eager.

Value parameters

y: the Eager instance to multiply with this Eager instance

Attributes

Returns: a Try[Eager] containing the result of the multiplication if successful, or a failure if the operation cannot be performed
Inherited from:: Eager

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

Subtracts the given Structure instance (y) from the current instance. The operation is performed using a dyadic operator that ensures type safety and handles any failures during the subtraction via a Try.

Value parameters

y: the Structure instance to be subtracted from the current instance

Attributes

Returns: a Try[Structure] containing the result of the subtraction if successful, or a failure if the subtraction operation cannot be performed
Inherited from:: Structure

Subtracts the given Eager instance y from the current Eager instance. This operation is performed using the DyadicOperator mechanism, which delegates to the subtractEagers function to handle the specific subtraction behavior.

Value parameters

y: the Eager instance to be subtracted from this Eager instance

Attributes

Returns: a Try[Eager] containing the result of the subtraction if successful, or a failure if the operation fails
Inherited from:: Eager

Converts the current instance of Functional into a Real representation.

The conversion is achieved by applying the scaleFunction to the value derived from the number method, and optionally utilizing maybeFuzz if available. This process encapsulates the numerical transformation, resulting in the Real type.

Attributes

Returns: a Real object representing the scaled and transformed value of the current instance.
Inherited from:: Functional

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

Concrete fields

Attempts to interpret this InversePower as a complex value.

This method evaluates the structure of the expression and returns an optional Complex value if the expression can be interpreted as such. The possible cases are:

If the expression is an inverse power of 2 with a positive number, it converts the number to a real complex.
If the expression represents an imaginary number, it converts the number to a real complex and applies a rotation to represent the imaginary component.
For all other cases, it returns None.

Attributes

Returns: An Option[Complex] representing the interpreted complex value, or None if the expression cannot be interpreted as a complex.

Represents the derivative function associated with this Functional instance. That's to say d(f(number)) by d(number) where f is this Functional. For a Structure, the derivative should be positive, however, it is possible that it is not positive for certain types of Functional.

The derivativeFunction provides a mathematical operation that computes the derivative with respect to a given input value. It is typically used to evaluate rates of change or sensitivity in the context of numerical transformations.

Attributes

Returns: A function that accepts a Double value and returns the computed derivative as a Double.

Retrieves an optional name associated with this instance.

Attributes

Returns: an Option[String] containing the name if present, otherwise None

Normalizes this Valuable to its simplest equivalent form. This may change the type (e.g., RationalNumber → WholeNumber, Complex(5,0) → WholeNumber(5)).

For Expression types, this will attempt to simplify and materialize if the result is exact. For Eager types, this will reduce to the simplest type representation.

Attributes

Returns: the simplest Valuable representation of this value

Renders this Root instance as a string representation of base in terms of π.

The method formats the radius equivalent to π, omitting the numeric coefficient if it is 1.

Attributes

Returns: a string representation of the Root in terms of π

This yields the scale function for this Functional.

Attributes

Returns: a function to transform the nominal value into the actual value as it would appear in a PureNumber context.

Inherited fields

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

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:: Eager

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:: Functional

Retrieves an optional fuzziness value for a given number.

Attributes

Returns: An Option containing the fuzziness representation of the number, or None if not available.
Inherited from:: Functional

Retrieves the nominal (non-fuzzy) value associated with the entity.

This value represents the precise or primary measurement or parameter of the entity, without considering any associated fuzziness or uncertainty.

Attributes

Returns: The nominal value as a Double.
Inherited from:: Functional

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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