Euler
This factor allows the representation of quantities of the form e power ix.
NOTE: A number in factor Euler will evaluate as e raised to (i times that power). So, the value is the natural log of the evaluation.
We call this Euler because it is used in Euler's formula https://en.wikipedia.org/wiki/Euler's_formula. However, let the record state that Roger Cotes, an English mathematician, used this quantity before Euler https://en.wikipedia.org/wiki/Euler's_formula#History.
Thus the range of such values is subject to the same modulation as Radian.
Attributes
- Graph
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- Supertypes
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trait Singletontrait Producttrait Mirrortrait Serializabletrait Producttrait Equalstrait Logarithmictrait Factorclass Objecttrait Matchableclass AnyShow all
- Self type
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Euler.type
Members list
Type members
Inherited types
The names of the product elements.
The names of the product elements.
Attributes
- Inherited from:
- Singleton
Attributes
- Inherited from:
- Singleton
The mirrored *-type.
The mirrored *-type.
Attributes
- Inherited from:
- Singleton
Attributes
- Inherited from:
- Singleton
Inherited and Abstract types
The name of the type.
The name of the type.
Attributes
- Inherited from:
- Mirror
Value members
Concrete methods
Determines whether the current scalar can be exactly converted to a PureNumber.
Determines whether the current scalar can be exactly converted to a PureNumber.
Attributes
- Returns
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true if the scalar represents an exact value; false otherwise.
Returns a string representation of the object.
Returns a string representation of the object.
The default representation is platform dependent.
Attributes
- Returns
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a string representation of the object.
- Definition Classes
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Any
Inherited methods
Adds two values together and computes an appropriate factor for the result.
Adds two values together and computes an appropriate factor for the result.
Value parameters
- f
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the factor associated with y
- negative
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NOTE ignored.
- x
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the first value
- y
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the addend
Attributes
- Returns
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an optional tuple containing the resultant value and its factor
- Inherited from:
- Logarithmic
Converts a given value into a string representation of its corresponding power notation or root notation based on specific conditions.
Converts a given value into a string representation of its corresponding power notation or root notation based on specific conditions.
Value parameters
- v
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the value to be converted, which can represent an integer power or a rational root.
Attributes
- Returns
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a string representing the value in power notation, root notation, or a generic exponential format.
- Inherited from:
- Logarithmic
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
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the factor to be checked for compatibility with addition.
Attributes
- Returns
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true if the factors can be added; false otherwise.
- Inherited from:
- Factor
Determines whether the current factor can be multiplied by the given factor.
Determines whether the current factor can be multiplied by the given factor.
TODO implement me properly
Value parameters
- f
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the factor to be checked for compatibility with multiplication.
Attributes
- Returns
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true if the factors can be multiplied; false otherwise.
- Inherited from:
- Logarithmic
Determines whether this factor can be raised by the given factor f. CONSIDER do we need this method now that we have raise(x, y, this)?
Determines whether this factor can be raised by the given factor f. CONSIDER do we need this method now that we have raise(x, y, this)?
Value parameters
- f
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the factor to be checked for compatibility with raising to a power.
Attributes
- Returns
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true if the factors can be powered; false otherwise.
- Inherited from:
- Factor
Determines whether given value with this Factor can be rendered exactly.
Determines whether given value with this Factor can be rendered exactly.
Attributes
- Returns
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true if this
Factorcan be rendered exactly; false otherwise. - Inherited from:
- Logarithmic
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
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an optional ProtoNumber that may be simplified
Attributes
- Returns
-
an optional ProtoNumber, simplified if applicable, or
Noneif input isNone - Inherited from:
- Factor
Convert a value x from this factor to f if possible, using simple scaling. Result is defined only if f is Logarithmic.
Convert a value x from this factor to f if possible, using simple scaling. Result is defined only if f is Logarithmic.
Value parameters
- f
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the factor of the result.
- v
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the value to be converted.
Attributes
- Returns
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a Try of Value which, given factor f, represents the same quantity as x given this.
- Inherited from:
- Logarithmic
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
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the base value to be raised
- y
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the exponent value (from a PureNumber)
Attributes
- Returns
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an optional result of type
ProtoNumber, representing the computed value if the operation is valid, orNoneotherwise - Inherited from:
- Logarithmic
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
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
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the value to be inverted
Attributes
- Returns
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an optional result of type
ProtoNumber, representing the inverted value if the operation is valid, orNoneotherwise - Inherited from:
- Logarithmic
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
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the context in which the factor is evaluated.
Attributes
- Returns
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a Boolean indicating whether the factor satisfies the specified conditions in the given context.
- Inherited from:
- Logarithmic
Modulates a given value and returns the result.
Modulates a given value and returns the result.
Value parameters
- v
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the value to be modulated
Attributes
- Returns
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the original value
- Inherited from:
- Logarithmic
Multiplies two values together and computes an appropriate factor for the result. TODO implement for Log10
Multiplies two values together and computes an appropriate factor for the result. TODO implement for Log10
Value parameters
- f
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the factor associated with y
- x
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the first value
- y
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the multiplicand
Attributes
- Returns
-
an optional tuple containing the resultant value and its factor
- Inherited from:
- Logarithmic
Negates the given value and returns the result as an optional ProtoNumber.
Negates the given value and returns the result as an optional ProtoNumber.
Value parameters
- x
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the value to be negated
Attributes
- Returns
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an optional ProtoNumber representing the negated value, or None if the operation is invalid
- Inherited from:
- Logarithmic
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
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
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
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the factor associated with y
- x
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the first value
- y
-
the power
Attributes
- Returns
-
an optional tuple containing the resultant value and its factor
- Inherited from:
- Factor
Renders a string representation of the value based on the current base and the given input value. CONSIDER why do we have a second signature for render?
Renders a string representation of the value based on the current base and the given input value. CONSIDER why do we have a second signature for render?
Value parameters
- v
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the input value to be rendered, represented as a string
Attributes
- Returns
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a string combining the base and the input value in a specific exponential format
- Inherited from:
- Logarithmic
Renders a string representation of the given value based on specific conditions. If the value can be represented in power or root notation, it uses that representation; otherwise, it falls back to the string representation of the value.
Renders a string representation of the given value based on specific conditions. If the value can be represented in power or root notation, it uses that representation; otherwise, it falls back to the string representation of the value.
Value parameters
- x
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the value to be rendered into a string representation.
Attributes
- Returns
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a string representation of the value, using power or root notation when applicable.
- Definition Classes
- Inherited from:
- Logarithmic
Concrete fields
Represents the base symbol used for the NatLog factor.
Represents the base symbol used for the NatLog factor.
The symbol is defined as the mathematical constant ℯ to the power i. This constant is used to indicate the base of the imaginary natural logarithm and is sourced from the Factor object.
Attributes
Represents the default value for the Euler factor. Should not be used.
Represents the default value for the Euler factor. Should not be used.
Attributes
Inherited fields
Determines if the current factor operates additively.
Determines if the current factor operates additively.
Attributes
- Returns
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false.
- Inherited from:
- Logarithmic