This object represents utility methods and predefined constants for working with continued fractions. It provides functionality to construct, transform, and manipulate ContinuedFraction instances.
Attributes
- Companion
- class
- Graph
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- Supertypes
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trait Producttrait Mirrorclass Objecttrait Matchableclass Any
- Self type
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ContinuedFraction.type
Members list
Type members
Inherited and Abstract types
The names of the product elements.
The names of the product elements.
Attributes
- Inherited from:
- Mirror
The name of the type.
The name of the type.
Attributes
- Inherited from:
- Mirror
Value members
Concrete methods
Construct a ContinuedFraction based on a LazyList of Pairs.
Construct a ContinuedFraction based on a LazyList of Pairs.
Value parameters
- infinite
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true if xs is infinite (defaults to true).
- markov
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the value of Markov constant (defaults to Hurwitz).
- ps
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a lazy list of Pairs.
Attributes
- Returns
-
a ContinuedFraction
Construct a ContinuedFraction based on a function.
Construct a ContinuedFraction based on a function.
CONSIDER changing the f to be Int => Pair.
Value parameters
- f
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a function which yields a
LazyListofPairs. - infinite
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true if xs is infinite (defaults to true).
- markov
-
the value of the
Markovconstant (defaults toHurwitz).
Attributes
- Returns
-
a
ContinuedFraction
Construct a ContinuedFraction based on an initial pair sequence and a transforming function.
Construct a ContinuedFraction based on an initial pair sequence and a transforming function.
Value parameters
- f
-
a function which repeatedly transforms the current sequence.
- sequence
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a sequence of Pairs which will be form the initial pattern.
Attributes
- Returns
-
a ContinuedFraction.
Construct a ContinuedFraction based on an initial pattern and a transforming function.
Construct a ContinuedFraction based on an initial pattern and a transforming function.
Value parameters
- f
-
a function which repeatedly transforms the current Pair value.
- start
-
a starting Pair value.
Attributes
- Returns
-
a ContinuedFraction
Construct a ContinuedFraction based on a function.
Construct a ContinuedFraction based on a function.
Value parameters
- sequence
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a sequence of Pairs which will be repeated.
Attributes
- Returns
-
a ContinuedFraction
Construct a ContinuedFraction based on a repeated pair.
Construct a ContinuedFraction based on a repeated pair.
Value parameters
- p
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a Pair which will be repeated continually to create the coefficients of a ContinueFraction.
Attributes
- Returns
-
a ContinuedFraction
Construct a simple ContinuedFraction based on a repeated constant. Basically, this creates the series for phi.
Construct a simple ContinuedFraction based on a repeated constant. Basically, this creates the series for phi.
Value parameters
- x
-
a Long value which will be repeated continually to create the simple ContinuedFraction.
Attributes
- Returns
-
a (simple) ContinuedFraction.
Construct a ContinuedFraction based on an initial pattern and a transforming function.
Construct a ContinuedFraction based on an initial pattern and a transforming function.
Value parameters
- f
-
a function which repeatedly transforms the current sequence.
- markov
-
the value of Markov constant (defaults to Hurwitz).
- sequence
-
a sequence of Pairs which will be form the initial pattern.
Attributes
- Returns
-
a ContinuedFraction
Construct a ContinuedFraction based on an initial pattern and a transforming function.
Construct a ContinuedFraction based on an initial pattern and a transforming function.
Value parameters
- f
-
a function which repeatedly transforms the current Pair value.
- markov
-
the value of Markov constant (defaults to Hurwitz).
- start
-
a starting Pair value.
Attributes
- Returns
-
a ContinuedFraction
Construct a ContinuedFraction based on a repeated sequence.
Construct a ContinuedFraction based on a repeated sequence.
Value parameters
- markov
-
the value of Markov constant (defaults to Hurwitz).
- sequence
-
a sequence of Pairs which will be repeated.
Attributes
- Returns
-
a ContinuedFraction
Concrete fields
ContinuedFaction representing e.
ContinuedFaction representing e.
Attributes
Represents the continued fraction for 4 divided by Pi, derived using the Leibniz series.
Represents the continued fraction for 4 divided by Pi, derived using the Leibniz series.
This is an infinite continued fraction built using the function fPiBy4Leibniz. The default Markov constant, Hurwitz, is used.
Attributes
The Markov constant for all irrational numbers. Many individual irrationals can use a smaller value for their Markov number. See https://en.wikipedia.org/wiki/Hurwitz%27s_theorem_(number_theory) See https://en.wikipedia.org/wiki/Markov_constant
The Markov constant for all irrational numbers. Many individual irrationals can use a smaller value for their Markov number. See https://en.wikipedia.org/wiki/Hurwitz%27s_theorem_(number_theory) See https://en.wikipedia.org/wiki/Markov_constant
Attributes
Represents the continued fraction representation of π (Pi) using a specific functional series, denoting an infinite continued fraction approximation of the mathematical constant π.
Represents the continued fraction representation of π (Pi) using a specific functional series, denoting an infinite continued fraction approximation of the mathematical constant π.
This value is built using the fPi function as its series function and specifies that the continued fraction is infinite. The Markov constant used in this instance is Hurwitz.
Attributes
ContinuedFaction representing pi.
ContinuedFaction representing pi.
Attributes
Represents an infinite continued fraction of Pi based on the fPiSomayaji function.
Represents an infinite continued fraction of Pi based on the fPiSomayaji function.
This specific continued fraction is constructed using the fPiSomayaji generator function, designating it to be infinite and associated with the Hurwitz Markov constant.
Attributes
This is the Leibniz formula for pi.
This is the Leibniz formula for pi.
Attributes
ContinuedFaction representing the golden ratio (phi).
ContinuedFaction representing the golden ratio (phi).
Attributes
ContinuedFaction representing the square root of 19.
ContinuedFaction representing the square root of 19.
Attributes
ContinuedFaction representing the square root of 2.
ContinuedFaction representing the square root of 2.
Attributes
ContinuedFaction representing the square root of 3.
ContinuedFaction representing the square root of 3.