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

Algebraic

com.phasmidsoftware.number.algebra.eager.Algebraic

See theAlgebraic companion object

sealed trait Algebraic extends Solution, Unitary, Scalable[Algebraic]

Trait to model the behavior of a solution to an equation. All such solutions are exact. Typically, however, such solutions cannot be represented exactly as pure numbers. The four parameters of a Algebraic are: base, offset, coefficient, and factor. Solutions are subject to various operations such as addition, scaling, and number conversions. Extends the NumberLike trait, inheriting behavior common to number-like entities.

CONSIDER why is there so much dependence on the core module here? We shouldn't need that at all!

Attributes

Companion: object
Graph
Supertypes: trait Scalable[Algebraic]

trait Solution

trait Negatable[Solution]

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 LinearSolution

class QuadraticSolution

Members list

Value members

Abstract methods

Multiplies this Algebraic by another Algebraic and returns the result.

Value parameters

other: the other Algebraic to be multiplied with this

Attributes

Returns: a new Algebraic resulting from the multiplication

Adds a Rational value to the current solution and returns a new Algebraic as the result.

Value parameters

addend: the Rational value to be added to the current solution

Attributes

Returns: a new Algebraic instance representing the sum of the current solution and the given addend

Retrieves the base value of the solution.

Attributes

Returns: the base value of type Value

This is the coefficient of the offset (square root term) the solution of a quadratic equation.

Attributes

Returns: the coefficient.

Determines whether the solution is a pure number. A pure number is defined as one without any associated factors or offsets.

Attributes

Returns: true if the solution is a pure number, false otherwise

Retrieves the offset value of the solution.

Attributes

Returns: the offset value of type Value

Concrete methods

Performs a fuzzy equivalence comparison between the current solution and another solution. The comparison allows for a degree of tolerance specified by the parameter p.

Value parameters

confidence: the tolerance level for the fuzzy equivalence comparison; smaller values impose stricter equality conditions
that: the other solution to compare against, which must be of type Eager

Attributes

Returns: a Try[Boolean] indicating whether the two solutions are approximately equivalent within the specified tolerance, or an error if the comparison cannot be performed
Definition Classes: Eager -> DyadicOps

Method to determine if this NumberLike 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 NumberLike object is exact in the context of No factor, else false.

Determines the factor associated with this solution based on certain conditions. If the solution is a pure number, it returns Some(PureNumber). If the base value of the solution is zero, it returns Some(factor). Otherwise, it returns None.

CONSIDER invoke normalize and then apply maybeFactor to the result.

Attributes

Returns: an Option of type Factor, where Some may contain the factor depending on the conditions, or None if no factor is applicable

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

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 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

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

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

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

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

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

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

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 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

Adds another Solution instance to the current instance, combining their effects or values based on the implementation of the + operation in the Solution trait.

CONSIDER this should be defined in CanAdd[Solution] rather than Solution. Maybe we could achieve that by defining Can as a subtype of Eager, rather than of Structure.

Value parameters

other: the Solution instance to add to the current instance

Attributes

Returns: a new Solution instance representing the result of the addition
Inherited from:: Solution

Attempts to compute an approximate representation of the current value.

This method provides an optional approximation of the value represented by the implementing class. The approximation may account for uncertainties or computational limitations. By default, this method does not force computation of the approximation unless explicitly requested.

Value parameters

force: a boolean flag indicating whether to force computation of the approximation. If true, the method will attempt to generate an approximation even if such computation is resource-intensive or not strictly necessary.

Attributes

Returns: an Option containing the approximate value as a Real if available, or None if no approximation can be computed.
Inherited from:: Approximate

Computes and returns the conjugate of the current Solution instance.

The conjugate represents a value or transformation that is mathematically paired oppositely with the current instance based on the structure and properties of the Solution implementation.

Normally, the branch of the conjugate, added to the current branch should equal branches.

Attributes

Returns: a new Solution instance representing the conjugate of the current instance
Inherited from:: Solution

Determines whether this object represents unity.

Attributes

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

Determines if the current number is equal to zero.

Attributes

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

Retrieves an optional name associated with this instance.

Attributes

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

Returns a new instance of T 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:: Negatable

Normalizes the current instance of Eager. This operation ensures that the instance is in its standard or canonical form. Be very wary of changing the way normalization works! One place that we don't routinely normalize (maybe we should) is in the Eq and FuzzyEq comparisons.

Attributes

Returns: the normalized instance of Eager as Self
Inherited from:: Eager

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

Scales the current Solution instance by a given Rational factor. CONSIDER this could be merged with *.

The scaling operation adjusts the Solution based on the value of the provided Rational parameter, resulting in a new Solution instance that reflects the modification.

Value parameters

r: the Rational value by which to scale the current Solution

Attributes

Returns: a new Solution instance representing the result of the scaling operation
Inherited from:: Solution

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

If this Solution can be represented as a Structure, return it wrapped in Some, otherwise return None.

Attributes

Returns: an Option[Structure].
Inherited from:: Solution

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

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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