Number - Scala Mathematical Library
1.10.6
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Number - Scala Mathematical Library/com.phasmidsoftware.number/com.phasmidsoftware.number.core/com.phasmidsoftware.number.core.inner/Radian

Radian

com.phasmidsoftware.number.core.inner.Radian
case object Radian extends Scalar

This factor is primarily used for rotation by an angle.

A number x with factor Radian (theoretically) evaluates to e raised to the power ix. So, you could think of it as essentially a shorthand for writing both cosine and sine. NOTE however that, unlike, with the factor NatLog, we currently do not treat Radian values in quite this way in the code.

CONSIDER implementing the Radian factor conversions in a manner similar to that of NatLog. This would entail conversion from a single number to a pair of Doubles when going from Radian to PureNumber. We could do that using a Complex number but I'd rather do it as a 2-tuple of Doubles. Perhaps the whole idea of our Complex implementation is misguided (although it does allow us to represent complex numbers in Polar form since, in that case, the real part is a PureNumber number, and the imaginary part is coded in with factor Radian).

The range of these values is 0 thru 2, which represents the radian values of 0 thru 2pi.

Attributes

Graph
Supertypes
trait Singleton
trait Product
trait Mirror
trait Serializable
trait Product
trait Equals
trait Scalar
trait Factor
class Object
trait Matchable
class Any
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Self type
Radian.type

Members list

Type members

Inherited types

type MirroredElemLabels = EmptyTuple

The names of the product elements.

The names of the product elements.

Attributes

Inherited from:
Singleton
type MirroredElemTypes = EmptyTuple

Attributes

Inherited from:
Singleton
type MirroredMonoType = this.type

The mirrored *-type.

The mirrored *-type.

Attributes

Inherited from:
Singleton
type MirroredType = this.type

Attributes

Inherited from:
Singleton

Inherited and Abstract types

type MirroredLabel <: String

The name of the type.

The name of the type.

Attributes

Inherited from:
Mirror

Value members

Concrete methods

override def canRaise(f: Factor, exponent: Field): Boolean

Determines whether this factor can be raised by the given factor f.

Determines whether this factor can be raised by the given factor f.

Value parameters

f

the factor to be checked for compatibility with raising to a power.

Attributes

Returns

true if the factors can be powered; false otherwise.

Definition Classes
def doRaiseByPureNumber(x: Value, y: Value): Option[ProtoNumber]

Raises the value x to the power of the value y.

Raises the value x to the power of the value y.

Value parameters

x

the base value to be raised

y

the exponent value (from a PureNumber)

Attributes

Returns

an optional result of type ProtoNumber, representing the computed value if the operation is valid, or None otherwise

def invert(x: Value): Option[ProtoNumber]

Inverts the given value by raising it to the power of -1, using a pure number factor.

Inverts the given value by raising it to the power of -1, using a pure number factor.

Value parameters

x

the value to be inverted

Attributes

Returns

None.

def isExact: Boolean

Determines whether the current Radian instance represents an exact value.

Determines whether the current Radian instance represents an exact value.

Attributes

Returns

true if the instance is considered exact, false otherwise.

def modulate(value: Value): Value

Modulates the provided value using a monadic transformation defined by a specific range and circularity settings.

Modulates the provided value using a monadic transformation defined by a specific range and circularity settings.

TODO there are other places in the code where we use the MonadicOperationModulate more directly. We should get those place to use this method.

Value parameters

value

the input value to be modulated.

Attributes

Returns

the modulated value if the transformation is successful, or the original value if the operation fails.

def multiply(x: Value, y: Value, f: Factor): Option[ProtoNumber]

Multiplies x with y provided that f is a PureNumber.

Multiplies x with y provided that f is a PureNumber.

Value parameters

f

the factor associated with y

x

the first value

y

the multiplicand

Attributes

Returns

an optional tuple containing the resultant value and its factor

def render(x: String): String

Renders a string by appending the mathematical symbol for pi (π).

Renders a string by appending the mathematical symbol for pi (π).

Value parameters

x

the input string to which the mathematical symbol for pi will be appended

Attributes

Returns

a new string consisting of the input string followed by the symbol for pi

override def toString: String

Returns the string representation of the Radian factor.

Returns the string representation of the Radian factor.

Attributes

Returns

a string representation of the mathematical constant π.

Definition Classes
Any

Inherited methods

def add(x: Value, y: Value, f: Factor, negative: Boolean): Option[ProtoNumber]

Adds two values together, applying the specified factor, to compute a resultant value and factor.

Adds two values together, applying the specified factor, to compute a resultant value and factor.

TODO handle the negative cases properly

Value parameters

f

the factor associated with the operation

negative

NOTE ignored.

x

the first value to be added

y

the second value (addend) to be added

Attributes

Returns

an optional tuple containing the resultant value, its factor, and optional fuzziness, or None if the operation cannot be performed under the given factor

Inherited from:
Scalar
def canAdd(f: Factor): Boolean

Determines whether the current factor can be augmented by the given factor. CONSIDER do we need this method now that we have add(x, y, this)?

Determines whether the current factor can be augmented by the given factor. CONSIDER do we need this method now that we have add(x, y, this)?

Value parameters

f

the factor to be checked for compatibility with addition.

Attributes

Returns

true if the factors can be added; false otherwise.

Inherited from:
Factor
def canMultiply(f: Factor): Boolean

Determines whether the current factor can be multiplied by the given factor.

Determines whether the current factor can be multiplied by the given factor.

Value parameters

f

the factor to be checked for compatibility with multiplication.

Attributes

Returns

true if the factors can be multiplied; false otherwise.

Inherited from:
Scalar
def canShow(value: Value): Boolean

Determines whether given value with this Factor can be rendered exactly.

Determines whether given value with this Factor can be rendered exactly.

Attributes

Returns

true (value is ignored).

Inherited from:
Scalar
def clean(po: Option[ProtoNumber]): Option[ProtoNumber]

Cleans a given optional ProtoNumber by potentially simplifying its root quantities based on specific conditions and returning the modified result.

Cleans a given optional ProtoNumber by potentially simplifying its root quantities based on specific conditions and returning the modified result.

Value parameters

po

an optional ProtoNumber that may be simplified

Attributes

Returns

an optional ProtoNumber, simplified if applicable, or None if input is None

Inherited from:
Factor
def convert(v: Value, f: Factor): Option[Value]

Convert a value x from this factor to f if possible, using simple scaling. Result is defined only if f is a Scalar.

Convert a value x from this factor to f if possible, using simple scaling. Result is defined only if f is a Scalar.

Value parameters

f

the factor of the result.

v

the value to be converted.

Attributes

Returns

a Try of Value which, given factor f, represents the same quantity as x given this.

Inherited from:
Scalar
def fromProduct(p: Product): MirroredMonoType

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

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

Attributes

Inherited from:
Singleton
def isA(context: CoreContext): Boolean

Determines if the current factor satisfies certain conditions within the given context.

Determines if the current factor satisfies certain conditions within the given context.

Value parameters

context

the context in which the factor is evaluated.

Attributes

Returns

a Boolean indicating whether the factor satisfies the specified conditions in the given context.

Inherited from:
Scalar
def negate(x: Value): Option[ProtoNumber]

This doesn't seem to be invoked and looks wrong anyway.

This doesn't seem to be invoked and looks wrong anyway.

Value parameters

x

the value to negate

Attributes

Returns

an optional ProtoNumber representing the negated value, or None if the operation is not valid

Inherited from:
Scalar
def productElementNames: Iterator[String]

An iterator over the names of all the elements of this product.

An iterator over the names of all the elements of this product.

Attributes

Inherited from:
Product
def productIterator: Iterator[Any]

An iterator over all the elements of this product.

An iterator over all the elements of this product.

Attributes

Returns

in the default implementation, an Iterator[Any]

Inherited from:
Product
def raise(x: Value, y: Value, f: Factor): Option[ProtoNumber]

Raises x to the power of y and compute an appropriate factor for the result. NOTE: for now, we only allow raising to a power of a PureNumber. TODO: enable powers of Radian factor.

Raises x to the power of y and compute an appropriate factor for the result. NOTE: for now, we only allow raising to a power of a PureNumber. TODO: enable powers of Radian factor.

Value parameters

f

the factor associated with y

x

the first value

y

the power

Attributes

Returns

an optional tuple containing the resultant value and its factor

Inherited from:
Factor
def render(x: Value): String

Method to render a Value in the context of this Factor.

Method to render a Value in the context of this Factor.

Value parameters

x

the Value.

Attributes

Returns

a String.

Inherited from:
Factor

Concrete fields

val value: Double

Represents the mathematical constant π (pi), approximately equal to 3.14159. This value is commonly used in trigonometric, geometric, and other mathematical computations.

Represents the mathematical constant π (pi), approximately equal to 3.14159. This value is commonly used in trigonometric, geometric, and other mathematical computations.

Attributes

Inherited fields

lazy val isAdditive: Boolean

Determines if the current factor operates additively.

Determines if the current factor operates additively.

Attributes

Returns

true if the factor is additive; false otherwise.

Inherited from:
Scalar
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