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

NoScalar

com.phasmidsoftware.number.algebra.eager.NoScalar

case object NoScalar extends Scalar, Exact

NoScalar is a singleton object representing a special case of a Scalar that does not conform to standard scalar operations. It serves as a placeholder or non-standard entity in the scalar hierarchy, and most of its operations are unsupported or return default values.

This object extends both the Scalar and Exact traits, adhering to their respective contracts while providing specific overrides and limitations.

Attributes

Graph
Supertypes: trait Singleton

trait Product

trait Mirror

trait Serializable

trait Product

trait Equals

trait Exact

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
Self type: NoScalar.type

Members list

Type members

Inherited types

The names of the product elements.

Attributes

Inherited from:: Singleton

Attributes

Inherited from:: Singleton

The mirrored *-type.

Attributes

Inherited from:: Singleton

Attributes

Inherited from:: Singleton

Inherited and Abstract types

The name of the type.

Attributes

Inherited from:: Mirror

Value members

Concrete methods

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 -
Note: Throws an com.phasmidsoftware.number.algebra.util.AlgebraException if called

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

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.

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).

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

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.
Definition Classes: Eager -> Numeric

Attempts to yield a factor for the instance, if available.

A Factor is a representation of the underlying numerical domain, for example, PureNumber, Radian, etc.

Attributes

Returns: an Option[Factor] containing the factor representation of this object, or None if factorization is not applicable or unavailable.

Retrieves an optional name associated with this instance.

Attributes

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

Scales the current scalar instance by the specified rational factor.

Value parameters

r: the Rational factor by which to scale the scalar

Attributes

Returns: a new Scalar instance representing the scaled value
Note: Throws an com.phasmidsoftware.number.algebra.util.AlgebraException if called

Represents the scaleFactor of a scalar value as a Double. This value indicates the magnitude by which a scalar is scaled, and the conversion factor to yield a PureNumber.

Attributes

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
Note: Throws an com.phasmidsoftware.number.algebra.util.AlgebraException if called

Inherited methods

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 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

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 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

Compares this Eager instance with another Eager instance for equality. This method is unimplemented and currently returns a failure with an AlgebraException.

Value parameters

that: the Eager instance to compare against

Attributes

Returns: a Try[Boolean] indicating whether the two instances are equal. As the method is unimplemented, it always returns a failure containing an AlgebraException.
Inherited from:: Eager

Creates a new instance of type T with elements taken from product p.

Attributes

Inherited from:: Singleton

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 equality comparison between the current Structure instance and another Eager instance. The comparison is based on a specified tolerance level.

If both instances are of type Structure, this method attempts to convert them to Real and performs a fuzzy equality check with the specified tolerance. If the conversion or comparison fails, a failure with an appropriate AlgebraException is returned.

If either of the instances is not of type Structure, a failure with an AlgebraException is returned.

Value parameters

confidence: the tolerance level (as a Double) to be used for the fuzzy equality comparison.
that: the Eager instance to compare against the current instance.

Attributes

Returns: a Try[Boolean] indicating whether the two instances are fuzzy equal within the specified tolerance. Returns a Success(true) or Success(false) if the comparison completes successfully, or a Failure(AlgebraException) if an error occurs.
Definition Classes: Structure -> Eager -> DyadicOps
Inherited from:: Structure

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

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

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 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

Concrete fields

Normalizes this NoScalar instance to its simplest equivalent form.

This operation ensures that the NoScalar object is in its most reduced or canonical representation. If no changes are required to achieve normalization, the instance itself is returned.

Attributes

Returns: the normalized Valuable representation of this instance

Method to render this Valuable for presentation to the user.

Attributes

Returns: a String

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

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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