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

AbstractRoot

com.phasmidsoftware.number.expression.expr.AbstractRoot

sealed abstract class AbstractRoot(equ: Equation, branch: Int, maybeName: Option[String]) extends Root

Represents the root of an equation, associated with a specific branch.

This class models the concept of a mathematical root, where an equation is solved for a specific branch index, yielding a solution that adheres to the constraints defined in the Algebraic trait. It extends AtomicExpression to integrate with the broader mathematical expression framework.

Value parameters

branch: the branch index used to solve the equation
equ: the mathematical equation whose solution is represented by this root

Attributes

Graph
Supertypes: trait Root

trait Branched[Root]

trait AtomicExpression

trait Nameable

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
Show all
Known subtypes: class LinearRoot

class QuadraticRoot

Members list

Value members

Abstract methods

Computes and returns a Root associated with the given Equation and branch.

Value parameters

branch: an integer value representing the specific branch of the Equation.
equ: the Equation for which the Root is to be computed.

Attributes

Returns: the Root corresponding to the provided Equation and branch.

Concrete methods

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 AbstractRoot instance with another object for equality. The method checks if the other object is of a compatible type and whether all relevant Valuables of both objects are equal.

Value parameters

other: the object to compare for equality with this instance

Attributes

Returns: true if the given object is an instance of AbstractRoot, has canEqual compatibility with this instance, and if all relevant Valuables are equal; otherwise, false
Definition Classes: Any

Action to evaluate this Expression as a Valuable, if possible. NOTE: no simplification or factor-based conversion occurs here.

Evaluation only occurs if the solution is exact and it has a factor that qualifies in the given context.

Attributes

Returns: an optional Valuable.

Generates a hash code for the instance based on its equ and branch Valuables.

Attributes

Returns: an integer hash code value obtained by hashing the equ and branch Valuables.
Definition Classes: Any

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

Method to determine what Factor, if there is such, this Structure object is based on.

Attributes

Returns: an optional Factor.

Creates a new Expression that represents the negation of the current Expression. This operation is equivalent to multiplying the current Expression by -1.

Attributes

Returns: an Expression representing the negation of the current Expression.

Computes the power of the current Expression raised to the specified Rational exponent.

Value parameters

r: the Rational exponent to which the current Expression is to be raised. If the exponent is negative, the method computes the reciprocal of the positive power. If the exponent is zero, the result is the identity One. Otherwise, the computation involves recursive calls to this method.

Attributes

Returns: an Expression representing the result of raising the current Expression to the power of r.

Computes the reciprocal of the current Expression.

For a quadratic equation in the form Quadratic(p, q), the reciprocal is computed as: (this / Literal(-q)) + Literal(-p / q). Otherwise, the reciprocal is calculated as One / this.

Attributes

Returns: an Expression representing the reciprocal of the current Expression.

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

Attempts to simplify an atomic expression, for example, we replace Literal(Eager.pi) with Pi.

Attributes

Returns: an em.AutoMatcher[Expression] representing the process of handling or matching the atomic expression.

Computes the square root of this Root. For a Quadratic equation, this method calculates one of its roots based on the specified parameter. If the Expression is not quadratic, an ExpressionException is thrown.

Value parameters

plus: a boolean value that determines which square root (positive or negative root) to compute: if true, compute the positive root; if false, compute the negative root.

Attributes

Returns: an Expression representing the computed square root of the current Expression.
Note: Throws com.phasmidsoftware.number.expression.expr.ExpressionException if the square root computation is not supported for the current Expression.

Computes the square of the current Expression. If the current equation is quadratic, it computes the result of the operation: this * -p + q. If the current equation is linear, it computes the result of the operation: this * -r. Otherwise, it returns the square of this expression by performing this * this.

Attributes

Returns: the result of squaring the current Expression, evaluated according to the type of the equation.

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

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

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

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:: Root

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

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

Computes the square of the current Expression. This method raises the current Root to the power of 2, which is equivalent to squaring it.

Attributes

Returns: an Expression representing the square of the current Root.
Inherited from:: Root

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

Inherited and Abstract methods

Adds another Root to this Root, resulting in a new Root that represents the sum of the two roots. If the addition is not valid or cannot be performed, returns None.

Value parameters

other: the Root to be added to the current Root. This parameter represents another mathematical root to combine with the current Root.

Attributes

Returns: an Option[Root] containing the resulting Root if the addition is successful, or None if the addition is not valid.
Inherited from:: Root

Retrieves the branch at the specified index.

Value parameters

index: the index of the branch to retrieve, where the index starts from 0.

Attributes

Returns: the element of type T at the specified branch index. If the index is out of range, the behavior is implementation-specific.
Inherited from:: Branched

Returns the number of branches in this.

branches corresponds to the number of possible solutions to some equation.

Attributes

Returns: the number of branches as an integer.
Inherited from:: Branched

Retrieves the Equation associated with this Root.

Attributes

Returns: an Equation, which represents a mathematical relationship, typically defined by a monic polynomial and may have multiple branches of solutions.
Inherited from:: Root

Concrete fields

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 Field, if possible. NOTE: no simplification or factor-based conversion occurs here.

Attributes

Returns: an Option[Eager] containing the evaluated value if evaluation is successful, or None otherwise.

Represents an optional value for the current AbstractRoot instance, resulting from a numerical transformation of its associated solution if the solution is exact.

The value is computed by invoking the whenever method with a predicate that checks whether the associated solution is exact (solution.isExact). If the predicate is true, the asField method of the solution is accessed, and its value is converted to a real number and subsequently mapped to a Double. If the predicate is false

Attributes

This indicates whether this Root is protected from evaluation during simplification. Such roots as the golden ratio are kept as is during simplification. A Root instance is only protected if it also has a defined name.

Attributes

Method to render this Structure in a presentable manner.

Attributes

Returns: a String

Represents the solution of an equation for a specific branch in the context of a mathematical expression. The solution is computed by invoking the solve method of the equation with the provided branch index. The resulting solution is exact and adheres to the constraints described in the Algebraic trait.

Attributes

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

Attributes

Returns

Inherited from:

AtomicExpression

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 the expression is atomic.

Attributes

Returns: true, as this expression is atomic and cannot be further simplified.
Inherited from:: AtomicExpression

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

Indicates whether symbolic names are preserved.

This method determines if symbolic representation should be retained when working with names in entities implementing the Nameable trait.

Attributes

Returns: true if symbolic names are kept, otherwise false
Inherited from:: Nameable

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

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

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

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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