Number - Scala Mathematical Library
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Number - Scala Mathematical Library/com.phasmidsoftware.number/com.phasmidsoftware.number.core/com.phasmidsoftware.number.core.numerical/Complex

Complex

com.phasmidsoftware.number.core.numerical.Complex
See theComplex companion object
trait Complex extends Multivariate

Trait which defines the behavior of a type of Field called a Complex. A Complex is a Field and also supports the various methods defined below.

Attributes

Companion
object
Graph
Supertypes
trait Multivariate
trait Field
trait Ordered[Field]
trait Comparable[Field]
trait Numerical
trait NumberLike
class Object
trait Matchable
class Any
Show all
Known subtypes
class BaseComplex
class ComplexPolar

Members list

Value members

Abstract methods

def argument: Number

Method to determine the argument (angle) of this Complex number.

Method to determine the argument (angle) of this Complex number.

Attributes

Returns

a Number (in radians).

def conjugate: Complex

Method to determine the conjugate of this Complex number.

Method to determine the conjugate of this Complex number.

Attributes

Returns

the conjugate of this Complex.

def doAdd(complex: Complex): Complex

Method to add this Complex to another Complex.

Method to add this Complex to another Complex.

Value parameters

complex

the other Complex.

Attributes

Returns

the sum of the Complexes.

def doMultiply(complex: Complex): Complex

Method to multiply this Complex by another Complex.

Method to multiply this Complex by another Complex.

Value parameters

complex

the other Complex.

Attributes

Returns

the product of the Complexes.

def modulus: Number

Method to determine the modulus of this Complex number.

Method to determine the modulus of this Complex number.

Attributes

Returns

the modulus of this Complex.

def numberProduct(n: Number): Complex

Method to scale this Complex by a Number.

Method to scale this Complex by a Number.

Value parameters

n

the Number.

Attributes

Returns

a Complex with the same argument as this but a different magnitude.

def rotate: Complex

Rotate this Complex number by pi/2 counter-clockwise (i.e. multiply by i).

Rotate this Complex number by pi/2 counter-clockwise (i.e. multiply by i).

Attributes

Returns

the value of this * i.

Concrete methods

def maybeFactor: Option[Factor]

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

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

TODO it's more complicated than this! CONSIDER having a Complex sub-type of Factor.

Attributes

Returns

an optional Factor.

Inherited methods

infix def *(x: Field): Field

Multiply this Field by the given Field and return the result.

Multiply this Field by the given Field and return the result.

Value parameters

x

the multiplicand, an instance of Field.

Attributes

Returns

the product of this Field and the given Field.

Inherited from:
Field
infix def +(x: Field): Field

Synonym for add.

Synonym for add.

Value parameters

x

the addend.

Attributes

Returns

the result.

Inherited from:
Field
infix def -(x: Field): Field

Synonym for subtract.

Synonym for subtract.

Value parameters

x

the subtrahend.

Attributes

Returns

this - x.

Inherited from:
Field
def <(that: Field): Boolean

Returns true if this is less than that

Returns true if this is less than that

Value parameters

that

the instance to compare against

Attributes

Inherited from:
Ordered
def <=(that: Field): Boolean

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

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

Attributes

Inherited from:
Ordered
def >(that: Field): Boolean

Returns true if this is greater than that.

Returns true if this is greater than that.

Value parameters

that

the instance to compare against

Attributes

Inherited from:
Ordered
def >=(that: Field): Boolean

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

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

Attributes

Inherited from:
Ordered
def approximation: Option[Real]

Computes an approximation of the field as a real number, if possible. This method attempts to map the underlying numerical representation to a real value.

Computes an approximation of the field as a real number, if possible. This method attempts to map the underlying numerical representation to a real value.

Attributes

Returns

an Option containing the Real representation of this field if it can be approximated, or None if the approximation is not possible.

Inherited from:
Field
def asJavaNumber: Option[Number]

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

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

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

  • If the NumberLike object is an ExactNumber and its factor is PureNumber, the result is converted using Value.asJavaNumber.
  • If the NumberLike object is a FuzzyNumber 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:
NumberLike
def compareTo(that: Field): Int

Result of comparing this with operand that.

Result of comparing this with operand that.

Value parameters

that

the instance to compare against

Attributes

Inherited from:
Ordered
def memberOf(set: NumberSet): Boolean

Method to determine if this NumberLike object is a member of the given set.

Method to determine if this NumberLike object is a member of the given set.

Value parameters

set

the candidate NumberSet.

Attributes

Returns

true if this is exact and belongs to set.

Inherited from:
NumberLike
def memberOf: Option[NumberSet]

Method to determine the NumberSet, if any, to which this NumberLike object belongs. NOTE that we don't yet support H, the quaternions.

Method to determine the NumberSet, if any, to which this NumberLike object belongs. NOTE that we don't yet support H, the quaternions.

Attributes

Returns

Some(numberSet) or None if it doesn't belong to any (for example, it is fuzzy).

Inherited from:
NumberLike
infix def power(p: Int): Field

Raise this Field to the power p.

Raise this Field to the power p.

Value parameters

p

an Int.

Attributes

Returns

this Field raised to power p.

Inherited from:
Field
def show: String

Method to show this NumberLike in a human-friendly manner. Subclasses may override for prettier output (vulgar fractions, dropped trailing zeros, etc.). The default falls back to render.

Method to show this NumberLike in a human-friendly manner. Subclasses may override for prettier output (vulgar fractions, dropped trailing zeros, etc.). The default falls back to render.

Attributes

Returns

a String

Inherited from:
NumberLike
infix def subtract(x: Field): Field

Subtract x from this Field and return the result.

Subtract x from this Field and return the result.

Value parameters

x

the subtrahend.

Attributes

Returns

the difference of this - x.

Inherited from:
Field
def toRational: Option[Rational]

Converts this Field instance to its equivalent rational representation if it is real-valued.

Converts this Field instance to its equivalent rational representation if it is real-valued.

Attributes

Returns

an Option containing the rational representation of this Field if it is real-valued; otherwise, None.

Inherited from:
Field

Inherited and Abstract methods

def abs: Numerical

Computes the absolute value of this Numerical instance. The result is a Numerical object representing a non-negative magnitude of this instance.

Computes the absolute value of this Numerical instance. The result is a Numerical object representing a non-negative magnitude of this instance.

Attributes

Returns

a Numerical object representing the absolute value of this instance.

Inherited from:
Numerical
infix def add(x: Field): Field

Add x to this Field and return the result. See Number.plus for more detail.

Add x to this Field and return the result. See Number.plus for more detail.

Value parameters

x

the addend.

Attributes

Returns

the sum.

Inherited from:
Field
def asComplex: Complex

Method to return this Field as a Complex. If this is a Real number x, return ComplexPolar(x) otherwise, return this.

Method to return this Field as a Complex. If this is a Real number x, return ComplexPolar(x) otherwise, return this.

Attributes

Returns

a Complex.

Inherited from:
Numerical
def asNumber: Option[Number]

Method to represent this NumberLike object as an optional Number. The result will be defined if: (1) we do not lose precision and (2) this object is not complex.

Method to represent this NumberLike object as an optional Number. The result will be defined if: (1) we do not lose precision and (2) this object is not complex.

NOTE: to force this as a Number, use convertToNumber in the companion Object.

CONSIDER redefining this as Option[Field] or Option[Real].

Attributes

Returns

a Some(x) if this is a Number; otherwise return None.

Inherited from:
NumberLike
def asReal: Option[Real]

Method to return this Field as a Real, if possible. If this is a Real number x, return Some(x) otherwise, return None.

Method to return this Field as a Real, if possible. If this is a Real number x, return Some(x) otherwise, return None.

Attributes

Returns

an Option[Real].

Inherited from:
Numerical
def atan(y: Real): Field

Calculates the arctangent (inverse tangent) of the given Real number.

Calculates the arctangent (inverse tangent) of the given Real number.

Value parameters

y

the Real number whose arctangent is to be calculated.

Attributes

Returns

the arctangent of the specified Real number, represented as a Field.

Inherited from:
Field
def compare(that: Field): Int

Result of comparing this with operand that.

Result of comparing this with operand that.

Implement this method to determine how instances of A will be sorted.

Returns x where:

  • x &lt; 0 when this &lt; that

  • x == 0 when this == that

  • x > 0 when this > that

Value parameters

that

the instance to compare against

Attributes

Returns

an integer whose sign indicates the ordering relation between this and that

Inherited from:
Ordered
def cos: Field

Computes the trigonometric cosine of this Field.

Computes the trigonometric cosine of this Field.

Attributes

Returns

the cosine of this Field.

Inherited from:
Field
def cosh: Field

Attributes

Inherited from:
Field
infix def divide(x: Field): Field

Divide this Field by x and return the result.

Divide this Field by x and return the result.

Value parameters

x

the divisor.

Attributes

Returns

the quotient.

Inherited from:
Field
def exp: Field

Computes the exponential of this Field.

Computes the exponential of this Field.

Attributes

Returns

a Field representing the exponential of this instance.

Inherited from:
Field
def invert: Field

Yields the inverse of this Field. This Number is first normalized so that its factor is PureNumber, since we cannot directly invert Numbers with other factors. TODO note that this method does not belong in Numerical: it belongs in Field.

Yields the inverse of this Field. This Number is first normalized so that its factor is PureNumber, since we cannot directly invert Numbers with other factors. TODO note that this method does not belong in Numerical: it belongs in Field.

Attributes

Inherited from:
Numerical
def isExact: Boolean

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.

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.

Inherited from:
NumberLike
def isImaginary: Boolean

Method to determine if this Field is imaginary-valued (i.e., the point lies on the imaginary axis).

Method to determine if this Field is imaginary-valued (i.e., the point lies on the imaginary axis).

Attributes

Returns

true if this is imaginary.

Inherited from:
Field
def isInfinite: Boolean

Method to determine if this Field has infinite magnitude.

Method to determine if this Field has infinite magnitude.

Attributes

Returns

true if the magnitude of this Field is infinite.

Inherited from:
Numerical
def isProbablyZero(confidence: Double = ...): Boolean

Determines whether the magnitude of this Numerical instance is probably zero based on a given probability threshold.

Determines whether the magnitude of this Numerical instance is probably zero based on a given probability threshold.

Value parameters

confidence

the probability threshold (default is oneSigma). A higher value increases the confidence needed to determine that the magnitude is zero.

Attributes

Returns

true if the magnitude is considered to be probably zero based on the probability threshold, false otherwise.

Inherited from:
Numerical
def isReal: Boolean

Method to determine if this Field is real-valued (i.e., the point lies on the real axis).

Method to determine if this Field is real-valued (i.e., the point lies on the real axis).

Attributes

Returns

true if not imaginary.

Inherited from:
Field
def isSame(x: Numerical, confidence: Double = ...): Boolean

Method to determine if this Numerical is equivalent to another Numerical object (x).

Method to determine if this Numerical is equivalent to another Numerical object (x).

Value parameters

x

the other Numerical.

Attributes

Returns

true if they are most probably the same, otherwise false.

Inherited from:
Numerical
def isUnity: Boolean

Method to determine if this Field has unity magnitude. Unity is the multiplicative identity.

Method to determine if this Field has unity magnitude. Unity is the multiplicative identity.

Attributes

Returns

true if the magnitude of this Field is one.

Inherited from:
Numerical
def isZero: Boolean

Method to determine if this Field has zero magnitude. Zero is the additive identity.

Method to determine if this Field has zero magnitude. Zero is the additive identity.

Attributes

Returns

true if the magnitude of this Field is zero.

Inherited from:
Numerical
def ln: Field

Computes the natural logarithm (log base e) of this Field. CONSIDER renaming this as "ln" but note that the Java library calls this operation "log."

Computes the natural logarithm (log base e) of this Field. CONSIDER renaming this as "ln" but note that the Java library calls this operation "log."

Attributes

Returns

a new Field representing the result of the logarithmic computation.

Inherited from:
Field
infix def multiply(x: Field): Field

Multiply this Field by x and return the result.

Multiply this Field by x and return the result.

  • @param x the multiplicand.
  • @return the product.

Attributes

Inherited from:
Field
def normalize: Field

Method to "normalize" a field.

Method to "normalize" a field.

Attributes

Returns

a Field which is in canonical form.

Inherited from:
Numerical
infix def power(p: Field): Field

Raise this Field to the power p.

Raise this Field to the power p.

Value parameters

p

a Field.

Attributes

Returns

this Field raised to power p.

Inherited from:
Field
infix def power(p: Number): Field

Raises this Field to the power of the specified number.

Raises this Field to the power of the specified number.

Value parameters

p

the exponent, provided as a Number.

Attributes

Returns

the result of raising this Field to the power p.

Inherited from:
Field
def render: String

Method to render this NumberLike in a presentable manner.

Method to render this NumberLike in a presentable manner.

Attributes

Returns

a String

Inherited from:
NumberLike
def signum: Int

Determine the "sign" of this field. For a real-valued quantity (Real or Number), we try to determine if it is to the right, left or at the origin. For a complex number, we get the signum of the real part.

Determine the "sign" of this field. For a real-valued quantity (Real or Number), we try to determine if it is to the right, left or at the origin. For a complex number, we get the signum of the real part.

Attributes

Returns

+1 if to the right of the origin, -1 if to the left, 0 if at the origin.

Inherited from:
Numerical
def sin: Field

Computes the sine of this Field.

Computes the sine of this Field.

Attributes

Returns

the sine of this Field, as an instance of Field.

Inherited from:
Field
def sinh: Field

Attributes

Inherited from:
Field
def square: Field

Squares this Field instance by multiplying it with itself.

Squares this Field instance by multiplying it with itself.

Attributes

Returns

the result of squaring this Field.

Inherited from:
Field
def tan: Field

Computes the tangent of this Field.

Computes the tangent of this Field.

Attributes

Returns

the tangent of this Field as a new Field.

Inherited from:
Field
def tanh: Field

Attributes

Inherited from:
Field
def unary_-: Field

Change the sign of this Field.

Change the sign of this Field.

Attributes

Inherited from:
Numerical

Concrete fields

lazy val isComplex: Boolean

Attributes

Returns

true.

Inherited fields

lazy val isAlgebraic: Boolean

Attributes

Returns

true.

Inherited from:
Multivariate
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