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

ExactNumber

com.phasmidsoftware.number.algebra.eager.ExactNumber

trait ExactNumber extends Number, Exact, Q, Scalable[ExactNumber], CanPower[Eager]

Represents a number that can be expressed and operated on with exactitude.

Subtypes of ExactNumber include WholeNumber and RationalNumber. Although some instances of Real are exact, the type in general cannot be assumed to represent an exact value.

Attributes

Graph
Supertypes: trait CanPower[Eager]

trait Scalable[ExactNumber]

trait Q

trait R

trait Exact

trait Number

trait Ordered[Scalar]

trait Comparable[Scalar]

trait Scalar

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
Show all
Known subtypes: class RationalNumber

class WholeNumber

Members list

Value members

Concrete methods

Determines if the current instance of RationalNumber is represented exactly.

Attributes

Returns: true as the instance is always exact.

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

Attempts to retrieve an optional integer representation of the current exact number. The value is returned as an Option[Int] if the underlying rational number is a whole number and fits within the range of a 32-bit signed integer. Otherwise, None is returned.

Attributes

Returns: an optional integer representation of the number.

Raises the current ExactNumber to the power of the given ExactNumber. The operation leverages the underlying rational representations of both numbers and computes the result exactly if possible.

Value parameters

that: the exponent as an ExactNumber to which the current number is raised

Attributes

Returns: an Option[ExactNumber] containing the resulting value if the power operation can be computed exactly, or None if it cannot

Scales the current WholeNumber by a given Rational multiplier and returns the result wrapped as an Option[Structure]. CONSIDER renaming as *

Value parameters

scale: the Rational multiplier to scale the current WholeNumber

Attributes

Returns: an Option[Structure] representing the scaled result

Converts this ExactNumber into a RationalNumber representation.

Attributes

Returns: A RationalNumber instance representing the current value.

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

Multiplies the current number with another number using the defined multiplicative group.

Value parameters

other: The number to be multiplied with the current number.

Attributes

Returns: The result of the multiplication as a number.
Inherited from:: Number

Adds this Number instance to another Number instance and returns the result.

CONSIDER: there is an alternative way of adding Numbers and that is to summon an commutative addend. Which should we be using? This method allows for appropriate conversions whereas the other method does not.

The addition is performed based on the types of the two Number instances:

If both are WholeNumber, their values are added directly.
If one is a RationalNumber and the other is an ExactNumber, the ExactNumber is converted to match the type of the RationalNumber before addition.
If one is a Real, an attempt is made to convert the other number to match the type of the Real before addition.
For unsupported or invalid type combinations, an AlgebraException is thrown.

Value parameters

other: the Number instance to add to this instance

Attributes

Returns: a Number instance representing the sum of this instance and the provided other instance
Note: Throws an com.phasmidsoftware.number.algebra.util.AlgebraException if the addition cannot be performed due to unsupported or invalid type combinations
Inherited from:: Number

Subtracts another Number from this Number instance and returns the result.

The subtraction is performed based on the types of the two Number instances:

If both are WholeNumber, their values are subtracted directly.
If one is a RationalNumber and the other is an ExactNumber, the ExactNumber is converted to match the type of the RationalNumber before subtraction.
If one is a Real, an attempt is made to convert the other number to match the type of the Real before subtraction.
For unsupported or invalid type combinations, an AlgebraException is thrown.

Value parameters

other: the Number instance to subtract from this instance

Attributes

Returns: a Number instance representing the difference of this instance and the provided other instance
Note: Throws an com.phasmidsoftware.number.algebra.util.AlgebraException if the subtraction cannot be performed due to unsupported or invalid type combinations
Inherited from:: Number

Divides this Number by another Number.

The division is performed based on the type of the input Number:

If the input is an ExactNumber, it computes the reciprocal of the input, converts it to a RationalNumber, multiplies it with this Number, and normalizes the result.
For unsupported types, an AlgebraException is thrown.

Value parameters

other: the Number by which this Number is to be divided

Attributes

Returns: the result of division as a Number
Throws: com.phasmidsoftware.number.algebra.util.AlgebraException
if the division is unsupported for the provided other type
Inherited from:: Number

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 given number to the current instance and returns the result.

Value parameters

other: the number to be added to the current instance

Attributes

Returns: a Try containing the result of the addition if successful, or a failure if an exception occurs
Inherited from:: Number

Adds the specified Scalar instance to this Scalar and returns the result. The addition operation is performed for compatible scalar types. If the types are incompatible or the operation fails, a Failure is returned.

Value parameters

y: the Scalar instance to add to this instance

Attributes

Returns: a Try[Scalar] containing the resulting Scalar if the addition is successful, or a Failure if the operation cannot be performed
Inherited from:: Scalar

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 the current Number instance with another Number instance.

This method performs a comparison of two Number instances. If both numbers are exact, it uses exact comparison. If one or both numbers are not exact, it attempts to approximate and compare. Note that in some cases, this method may throw an exception if an invalid approximation logic is encountered.

Value parameters

that: the Number instance to compare the current instance against

Attributes

Returns: an integer value: - a negative value if this Number is lower than that - zero if this Number is equal to that - a positive value if this Number is greater than that
Note: Throws an com.phasmidsoftware.number.algebra.util.AlgebraException if the comparison cannot be performed due to invalid approximation logic
Inherited from:: Number

Compares this Number instance with a Scalar instance.

This method matches the type of the input Scalar and performs a comparison based on its type. If the input is a Number, it delegates to the compare(Number) method. If the input is a Radians, it first attempts to convert the Radians into a comparable value and then performs the comparison.

Value parameters

that: the Scalar instance to compare the current instance against.

Attributes

Returns: an integer value: - a negative value if the current instance is less than that. - zero if the current instance is equal to that. - a positive value if the current instance is greater than that.
Note: Throws an com.phasmidsoftware.number.algebra.util.AlgebraException if the conversion to a comparable value is not possible
Inherited from:: Number

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.
Definition Classes: Scalar -> Eager -> DyadicOps
Inherited from:: Scalar

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 number by the given number.

Value parameters

other: The number to divide the current number by.

Attributes

Returns: A Try[Number] containing the result of the division if successful, or a failure if an exception occurs (e.g., division by zero).
Inherited from:: Number

Divides this Scalar instance by another Scalar instance of type B. The result of the division is wrapped in a Try to safely handle potential failures.

Value parameters

y: The Scalar instance to divide by. Must be a subtype of Scalar.

Attributes

Returns: A Try containing the result of the division as a Scalar, or a failure if the division cannot be performed.
Inherited from:: Scalar

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

Determines if this instance is equivalent to another Eager instance.

Compares two instances, this and that, for equivalence. If both instances are of type Number, it checks for exact equality when both are exact. If one or both are not exact, it attempts an approximate comparison using their approximation values. For types other than Number, it delegates to the super implementation.

Value parameters

that: the Eager instance to compare with this instance

Attributes

Returns: a Try[Boolean] indicating: - Success(true) if the instances are equivalent - Success(false) if the instances are not equivalent - Failure if an error occurs during the comparison process
Definition Classes: Number -> Eager -> DyadicOps
Inherited from:: Number

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

Performs a fuzzy equivalence comparison between this Number instance and another Eager instance.

This method evaluates whether two instances are approximately equal within a given tolerance p. If both instances are of type Number, it converts them to Real for the comparison. If either of the approximations fails, or the comparison is not applicable, it delegates to the super implementation.

Value parameters

confidence: the tolerance level for the fuzzy equality comparison. A higher value increases the permissible difference.
that: the Eager instance to compare this Number instance against.

Attributes

Returns: a Try[Boolean] indicating whether the two instances are approximately equal (true) or not (false). Returns Failure if the comparison cannot be performed or encounters an error.
Definition Classes: Number -> Structure -> Eager -> DyadicOps
Inherited from:: Number

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:: Eager

Attempts to obtain a Factor representation in a specific Context.

A Factor could represent entities like PureNumber, Radian, etc., that provide numerical or dimensional meaning to a value. This method evaluates the current instance within the given Context to determine if a valid factor can be generated.

Value parameters

context: the evaluation context in which to determine the factor. The Context specifies the criteria under which the factorization is valid.

Attributes

Returns: an Option[Factor] containing the factor if it can be determined, or None if no suitable factor exists within the provided Context.
Inherited from:: Number

Multiplies this number by the given number and returns the result wrapped in a Try.

Value parameters

other: the number to multiply with this number

Attributes

Returns: a Try containing the product of this number and the given number, or a Failure if an error occurs during multiplication
Inherited from:: Number

Multiplies this Scalar instance by another Scalar of type B. The operation uses a dyadic operator to compute the product of the two scalars. The result is wrapped in a Try to handle any potential failures during the operation.

Value parameters

y: the Scalar instance to multiply with this instance. Must be a subtype of Scalar.

Attributes

Returns: a Try[Scalar] representing the product of the multiplication, or a failure if the operation is not possible.
Inherited from:: Scalar

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

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
Inherited from:: Scalar

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

Scales the current scalar instance by a factor derived from the specified integer.

Value parameters

x: the integer factor by which to scale the scalar

Attributes

Returns: a new Scalar instance representing the scaled value
Inherited from:: Scalar

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 number from the current number and returns the result.

Value parameters

other: the number to be subtracted from the current number

Attributes

Returns: a Try containing the result of the subtraction as a Number, or a failure if an error occurs
Inherited from:: Number

Subtracts the given scalar from this scalar and returns the result wrapped in a Try. The operation is performed using the dyadic operator logic powered by DyadicOperator, with the subtraction behavior provided by subtractScalars.

Value parameters

y: The scalar value to subtract, which must be a subtype of Scalar.

Attributes

Returns: A Try[Scalar] containing the result of the subtraction if successful, or a failure if the operation cannot be completed (e.g., type mismatch or invalid operation).
Inherited from:: Scalar

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

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

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.

The result is not guaranteed to be normalized.

Value parameters

factor: the rational number representing the scale factor

Attributes

Returns: the scaled instance of type T
Inherited from:: Scalable

Compares this Scalar with another Scalar for exact equivalence. This method checks if both instances can be compared exactly.

CONSIDER moving this up into Structure and having that be a Structure

Value parameters

that: the Scalar instance to compare against

Attributes

Returns: an Option[Int] value: - Some(-1) if this Scalar is less than that - Some(0) if this Scalar is equal to that - Some(1) if this Scalar is greater than that - None if the exact comparison is not possible
Inherited from:: Scalar

Converts the given Structure object to an optional instance of the same type.

TODO refactor this method to use a type class instance of CanConvert[T, Structure] instead of ClassTag.

Value parameters

t: the input object of type T which is a subtype of Structure.

Attributes

Returns: an Option containing a transformed instance of type T if the conversion is successful, or None otherwise.
Inherited from:: Structure

Retrieves an optional name associated with this instance.

Attributes

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

Returns an optional instance of Q from this R value.

Attributes

Returns: an optional instance of Q representing this specified R value
Inherited from:: R

Retrieves an optional instance of Z if it exists.

Attributes

Returns: an Option[Z] that contains a Z instance if it's available, or None if not.
Inherited from:: Q

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

Attributes

Returns: the simplest representation of this value that is a subtype of Number.
Inherited from:: Number

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

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

Converts this instance of Q to its corresponding rational representation.

Attributes

Returns: a Rational instance representing the current value
Inherited from:: Q

Concrete fields

Converts this WholeNumber instance to its Double representation.

Attributes

Returns: the Double value obtained by converting this WholeNumber to a Rational and then to a Double.

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

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.
Inherited from:: Exact

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

A scale factor applied to this Number.

The scaleFactor represents a multiplier that influences computations or adjustments involving this number. It is commonly used to scaleFactor or manipulate the magnitude of the number in various arithmetic or operational contexts.

Attributes

Inherited from:: Number

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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