java.lang.Object
- org.mariuszgromada.math.mxparser.mathcollection.NumberTheory

public final class NumberTheory
extends java.lang.Object

NumberTheory - summation / products etc...

Version:: 6.1.0

Field Summary

Fields
Modifier and Type Field Description

static long DEFAULT_TO_FRACTION_INIT_SEARCH_SIZE

private static long TO_FRACTION_INIT_SEARCH_SIZE
Initial search size 1 ...

Constructor Summary

Constructors
Constructor Description

NumberTheory()

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method	Description
`static double`	`argmax(double... numbers)`	Arg-Max function.
`static double`	`argmin(double... numbers)`	Arg-Min function.
`static java.lang.String`	`convDecimal2OthBase(double decimalNumber, int numeralSystemBase)`	Decimal number to other numeral system conversion with base between 1 and 36.
`static java.lang.String`	`convDecimal2OthBase(double decimalNumber, int numeralSystemBase, int format)`	Decimal number to other numeral system conversion with base between 1 and 36.
`static double`	`convOthBase2Decimal(double[] baseAndDigits)`	Other base to decimal conversion.
`static double`	`convOthBase2Decimal(double numeralSystemBase, double... digits)`	Other base to decimal conversion.
`static double`	`convOthBase2Decimal(int[] baseAndDigits)`	Other base to decimal conversion.
`static double`	`convOthBase2Decimal(int numeralSystemBase, int... digits)`	Other base to decimal conversion.
`static double`	`convOthBase2Decimal(java.lang.String numberLiteral)`	Other base (base between 1 and 36) number literal conversion to decimal number.
`static double`	`convOthBase2Decimal(java.lang.String numberLiteral, int numeralSystemBase)`	Other base (base between 1 and 36) number literal conversion to decimal number.
`static double`	`digitAtPosition(double number, double position)`	Digit at position - numeral system with base 10
`static double`	`digitAtPosition(double number, double position, double numeralSystemBase)`	Digit at position - numeral system with given base
`static int`	`digitAtPosition(long number, int position)`	Digit at position - numeral system with base 10
`static int`	`digitAtPosition(long number, int position, int numeralSystemBase)`	Digit at position - numeral system with given base
`static char`	`digitChar(int digitIndex)`	Character representing digit for numeral systems with base between 1 and 36.
`static int`	`digitIndex(char digitChar)`	Digit index based on digit character for numeral systems with base between 1 and 36.
`private static double[]`	`fractionToDoubleArray(double sign, double numerator, double denominator)`	Creates array representing fraction (sign, numerator and denominator).
`static java.lang.String`	`fractionToString(double[] fraction)`	Converts array representing fraction to fraction string representation.
`static double`	`gcd(double... numbers)`	Greatest common divisor (GCD)
`static double`	`gcd(double a, double b)`	Greatest common divisor (GCD)
`static long`	`gcd(long... numbers)`	Greatest common divisor (GCD)
`static long`	`gcd(long a, long b)`	Greatest common divisor (GCD)
`static double[][]`	`getDistValues(double[] array, boolean returnOrderByDescFreqAndAscOrigPos)`	Returns list of distinct values found in a given array.
`static int`	`getNumeralSystemBase(java.lang.String numberLiteral)`	Recognition of numeral system base in which number literal represents number.
`private static java.lang.String`	`getRegExpForNumeralSystem(int numeralSystemBase)`	Return regular expression representing number literal string in given numeral system with base between 1 and 36.
`static long`	`getToFractionInitSearchSize()`	Gets initial search size used by the toFraction method
`static double`	`lcm(double... numbers)`	Latest common multiply (LCM)
`static double`	`lcm(double a, double b)`	Latest common multiply (LCM)
`static long`	`lcm(long... numbers)`	Latest common multiply (LCM)
`static long`	`lcm(long a, long b)`	Latest common multiply (LCM)
`static double`	`max(double... numbers)`	Maximum function.
`static double`	`max(double a, double b)`	Maximum function.
`static double`	`max(Expression f, Argument index, double from, double to, double delta)`	Maximum value - iterative operator.
`static double`	`min(double... numbers)`	Minimum function.
`static double`	`min(double a, double b)`	Minimum function.
`static double`	`min(Expression f, Argument index, double from, double to, double delta)`	Minimum value - iterative operator.
`private static double[]`	`mixedFractionToDoubleArray(double sign, double whole, double numerator, double denominator)`	Creates array representing mixed fraction (sign, whole number, numerator and denominator).
`static double`	`numberOfDigits(double number)`	Number of digits needed to represent given number in base 10 numeral system.
`static double`	`numberOfDigits(double number, double numeralSystemBase)`	Number of digits needed to represent given number (its integer part) in numeral system with given base.
`static int`	`numberOfDigits(long number)`	Number of digits needed to represent given number in base 10 numeral system.
`static long`	`numberOfDigits(long number, long numeralSystemBase)`	Number of digits needed to represent given number in numeral system with given base.
`static double`	`numberOfDistValues(double... numbers)`	Returns number of unique values found the list of numbers
`static double`	`numberOfPrimeFactors(double number)`	Prime decomposition (prime factorization) - returns number of distinct prime factors
`static double`	`piProduct(Expression f, Argument index, double from, double to, double delta)`	Product operator
`static double`	`primeCount(double n)`	Prime counting function
`static long`	`primeCount(long n)`	Prime counting function
`static double`	`primeFactorExponent(double number, double id)`	Prime decomposition (prime factorization) - returns prime factor exponent
`static double[]`	`primeFactors(double number)`	Prime decomposition (prime factorization)
`static long[]`	`primeFactors(long number)`	Prime decomposition (prime factorization)
`static double`	`primeFactorValue(double number, double id)`	Prime decomposition (prime factorization) - returns prime factor value
`static double`	`primeTest(double n)`	Prime test
`static boolean`	`primeTest(long n)`	Prime test
`static double`	`prod(double... numbers)`	Numbers multiplication.
`static void`	`setToFractionInitSearchSize(long n)`	Sets initial search size for the toFraction method
`static double`	`sigmaSummation(Expression f, Argument index, double from, double to, double delta)`	Summation operator (SIGMA FROM i = a, to b, f(i) by delta
`static int[]`	`sortAsc(double[] array)`	Array sort - ascending - quick sort algorithm.
`private static void`	`sortAsc(double[] array, int[] initOrder, int leftIndex, int rightIndex)`	Sorting array - ascending - quick sort algorithm.
`static double`	`sum(double... numbers)`	Adding numbers.
`static double[]`	`toFraction(double value)`	Converts double value to its fraction representation.
`static java.lang.String`	`toFractionString(double value)`	Converts number to its fraction string representation.
`static double[]`	`toMixedFraction(double value)`	Converts double value to its mixed fraction representation.
`static java.lang.String`	`toMixedFractionString(double value)`	Converts number to its mixed fraction string representation.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - DEFAULT_TO_FRACTION_INIT_SEARCH_SIZE
```
public static final long DEFAULT_TO_FRACTION_INIT_SEARCH_SIZE
```
    See Also:
    
    Constant Field Values
  - TO_FRACTION_INIT_SEARCH_SIZE
```
private static long TO_FRACTION_INIT_SEARCH_SIZE
```
    Initial search size 1 ... n for the toFraction method
    
    See Also:
    
    toFraction(double)
- Constructor Detail
  - NumberTheory
```
public NumberTheory()
```
- Method Detail
  - setToFractionInitSearchSize
```
public static void setToFractionInitSearchSize(long n)
```
    Sets initial search size for the toFraction method
    
    Parameters:
    
    n - initial search size, has to be non-zero positive.
    
    See Also:
    
    toFraction(double)
  - getToFractionInitSearchSize
```
public static long getToFractionInitSearchSize()
```
    Gets initial search size used by the toFraction method
    
    Returns:
    
    initial search size used by the toFraction method
    
    See Also:
    
    toFraction(double)
  - min
```
public static double min(double a,
                         double b)
```
    Minimum function.
    
    Parameters:
    
    a - the a function parameter
    
    b - the b function parameter
    
    Returns:
    
    if a,b <> Double.NaN returns Math.min(a, b), otherwise returns Double.NaN.
  - min
```
public static double min(double... numbers)
```
    Minimum function.
    
    Parameters:
    
    numbers - the a function parameter
    
    Returns:
    
    if each number form numbers <> Double.NaN returns the smallest number, otherwise returns Double.NaN.
  - argmin
```
public static double argmin(double... numbers)
```
    Arg-Min function.
    
    Parameters:
    
    numbers - the a function parameter
    
    Returns:
    
    Returns the index of the first smallest number, otherwise returns Double.NaN.
  - max
```
public static double max(double a,
                         double b)
```
    Maximum function.
    
    Parameters:
    
    a - the a function parameter
    
    b - the b function parameter
    
    Returns:
    
    if a,b <> Double.NaN returns Math.max(a, b), otherwise returns Double.NaN.
  - max
```
public static double max(double... numbers)
```
    Maximum function.
    
    Parameters:
    
    numbers - the a function parameter
    
    Returns:
    
    if each number form numbers <> Double.NaN returns the highest number, otherwise returns Double.NaN.
  - argmax
```
public static double argmax(double... numbers)
```
    Arg-Max function.
    
    Parameters:
    
    numbers - the a function parameter
    
    Returns:
    
    Returns the index of the first biggest number, otherwise returns Double.NaN.
  - sortAsc
```
private static void sortAsc(double[] array,
                            int[] initOrder,
                            int leftIndex,
                            int rightIndex)
```
    Sorting array - ascending - quick sort algorithm. Initial ordering swapped according to sort order.
    
    Parameters:
    
    array - Array to be sorted
    
    initOrder - Array to be swapped together with sorted array
    
    leftIndex - Starting left index.
    
    rightIndex - Starting right index.
  - sortAsc
```
public static int[] sortAsc(double[] array)
```
    Array sort - ascending - quick sort algorithm.
    
    Parameters:
    
    array - Array to be sorted
    
    Returns:
    
    Sorts array and additionally returns initial ordering swapped according to sort order.
  - getDistValues
```
public static double[][] getDistValues(double[] array,
                                       boolean returnOrderByDescFreqAndAscOrigPos)
```
    Returns list of distinct values found in a given array.
    
    Parameters:
    
    array - The array
    
    returnOrderByDescFreqAndAscOrigPos - Indicator whether to apply final ordering based on descending value frequency and ascending initial position.
    
    Returns:
    
    List of values in the form of: first index - value index, second index: 0 - value, 1 - value count, 2 - minimal value position in original array
  - numberOfDistValues
```
public static double numberOfDistValues(double... numbers)
```
    Returns number of unique values found the list of numbers
    
    Parameters:
    
    numbers - The list of numbers
    
    Returns:
    
    Number of unique values. If list is null or any Double.NaN is found then Double.NaN is returned.
  - gcd
```
public static long gcd(long a,
                       long b)
```
    Greatest common divisor (GCD)
    
    Parameters:
    
    a - the a function parameter
    
    b - the b function parameter
    
    Returns:
    
    GCD(a,b)
  - gcd
```
public static double gcd(double a,
                         double b)
```
    Greatest common divisor (GCD)
    
    Parameters:
    
    a - the a function parameter
    
    b - the b function parameter
    
    Returns:
    
    if a, b <> Double.NaN returns gcd( (int)Math.round(a),(int)Math.round(b) ), otherwise returns Double.NaN.
  - gcd
```
public static long gcd(long... numbers)
```
    Greatest common divisor (GCD)
    
    Parameters:
    
    numbers - the numbers
    
    Returns:
    
    GCD(a_1,...,a_n) a_1,...,a_n in numbers
  - gcd
```
public static double gcd(double... numbers)
```
    Greatest common divisor (GCD)
    
    Parameters:
    
    numbers - the numbers
    
    Returns:
    
    if each number form numbers <> Double.NaN returns GCD(a_1,...,a_n) a_1,...,a_n in numbers, otherwise returns Double.NaN.
  - lcm
```
public static long lcm(long a,
                       long b)
```
    Latest common multiply (LCM)
    
    Parameters:
    
    a - the a function parameter
    
    b - the b function parameter
    
    Returns:
    
    LCM(a,b)
  - lcm
```
public static double lcm(double a,
                         double b)
```
    Latest common multiply (LCM)
    
    Parameters:
    
    a - the a function parameter
    
    b - the b function parameter
    
    Returns:
    
    if a, b <> Double.NaN returns lcm( (int)Math.round(a), (int)Math.round(b) ), otherwise returns Double.NaN.
  - lcm
```
public static long lcm(long... numbers)
```
    Latest common multiply (LCM)
    
    Parameters:
    
    numbers - the numbers
    
    Returns:
    
    LCM(a_1,...,a_n) a_1,...,a_n in numbers
  - lcm
```
public static double lcm(double... numbers)
```
    Latest common multiply (LCM)
    
    Parameters:
    
    numbers - the numbers
    
    Returns:
    
    if each number form numbers <> Double.NaN returns LCM(a_1,...,a_n) a_1,...,a_n in numbers, otherwise returns Double.NaN.
  - sum
```
public static double sum(double... numbers)
```
    Adding numbers.
    
    Parameters:
    
    numbers - the numbers
    
    Returns:
    
    if each number from numbers <> Double.NaN returns sum(a_1,...,a_n) a_1,...,a_n in numbers, otherwise returns Double.NaN.
  - prod
```
public static double prod(double... numbers)
```
    Numbers multiplication.
    
    Parameters:
    
    numbers - the numbers
    
    Returns:
    
    if each number from numbers <> Double.NaN returns prod(a_1,...,a_n) a_1,...,a_n in numbers, otherwise returns Double.NaN.
  - primeTest
```
public static boolean primeTest(long n)
```
    Prime test
    
    Parameters:
    
    n - The number to be tested.
    
    Returns:
    
    true if number is prime, otherwise false
  - primeTest
```
public static double primeTest(double n)
```
    Prime test
    
    Parameters:
    
    n - The number to be tested.
    
    Returns:
    
    true if number is prime, otherwise false
  - primeCount
```
public static long primeCount(long n)
```
    Prime counting function
    
    Parameters:
    
    n - number
    
    Returns:
    
    Number of primes below or equal x
  - primeCount
```
public static double primeCount(double n)
```
    Prime counting function
    
    Parameters:
    
    n - number
    
    Returns:
    
    Number of primes below or equal x
  - sigmaSummation
```
public static double sigmaSummation(Expression f,
                                    Argument index,
                                    double from,
                                    double to,
                                    double delta)
```
    Summation operator (SIGMA FROM i = a, to b, f(i) by delta
    
    Parameters:
    
    f - the expression
    
    index - the name of index argument
    
    from - FROM index = form
    
    to - TO index = to
    
    delta - BY delta
    
    Returns:
    
    summation operation (for empty summation operations returns 0).
  - piProduct
```
public static double piProduct(Expression f,
                               Argument index,
                               double from,
                               double to,
                               double delta)
```
    Product operator
    
    Parameters:
    
    f - the expression
    
    index - the name of index argument
    
    from - FROM index = form
    
    to - TO index = to
    
    delta - BY delta
    
    Returns:
    
    product operation (for empty product operations returns 1).
    
    See Also:
    
    Expression, Argument
  - min
```
public static double min(Expression f,
                         Argument index,
                         double from,
                         double to,
                         double delta)
```
    Minimum value - iterative operator.
    
    Parameters:
    
    f - the expression
    
    index - the name of index argument
    
    from - FROM index = form
    
    to - TO index = to
    
    delta - BY delta
    
    Returns:
    
    product operation (for empty product operations returns 1).
    
    See Also:
    
    Expression, Argument
  - max
```
public static double max(Expression f,
                         Argument index,
                         double from,
                         double to,
                         double delta)
```
    Maximum value - iterative operator.
    
    Parameters:
    
    f - the expression
    
    index - the name of index argument
    
    from - FROM index = form
    
    to - TO index = to
    
    delta - BY delta
    
    Returns:
    
    product operation (for empty product operations returns 1).
    
    See Also:
    
    Expression, Argument
  - getRegExpForNumeralSystem
```
private static java.lang.String getRegExpForNumeralSystem(int numeralSystemBase)
```
    Return regular expression representing number literal string in given numeral system with base between 1 and 36.
    
    Parameters:
    
    numeralSystemBase - Base of numeral system, base between 1 and 36
    
    Returns:
    
    Regular expression string if base between 1 and 36, otherwise empty string "" is returned.
  - digitIndex
```
public static int digitIndex(char digitChar)
```
    Digit index based on digit character for numeral systems with base between 1 and 36.
    
    Parameters:
    
    digitChar - Digit character (lower or upper case) representing digit in numeral systems with base between 1 and 36. Digits: 0:0, 1:1, 2:2, 3:3, 4:4, 5:5, 6:6, 7:7, 8:8, 9:9, 10:A, 11:B, 12:C, 13:D, 14:E, 15:F, 16:G, 17:H, 18:I, 19:J, 20:K, 21:L, 22:M, 23:N, 24:O, 25:P, 26:Q, 27:R, 28:S, 29:T, 30:U, 31:V, 32:W, 33:X, 34:Y, 35:Z
    
    Returns:
    
    Returns digit index if digit char was recognized, otherwise returns -1.
  - digitChar
```
public static char digitChar(int digitIndex)
```
    Character representing digit for numeral systems with base between 1 and 36.
    
    Parameters:
    
    digitIndex - Digit index between 0 and 35
    
    Returns:
    
    Digit character representing digit for numeral systems with base between 1 and 36. Digits: 0:0, 1:1, 2:2, 3:3, 4:4, 5:5, 6:6, 7:7, 8:8, 9:9, 10:A, 11:B, 12:C, 13:D, 14:E, 15:F, 16:G, 17:H, 18:I, 19:J, 20:K, 21:L, 22:M, 23:N, 24:O, 25:P, 26:Q, 27:R, 28:S, 29:T, 30:U, 31:V, 32:W, 33:X, 34:Y, 35:Z. If digit index is put of range '?' is returned.
  - getNumeralSystemBase
```
public static int getNumeralSystemBase(java.lang.String numberLiteral)
```
    Recognition of numeral system base in which number literal represents number. Examples: 2 for b2.1001 or b.1001, 1 for b1.111, 23 for b23.123afg 16 for b16.123acdf or h.123acdf.
    
    Parameters:
    
    numberLiteral - Number literal string. Base format: b1. b2. b. b3. b4. b5. b6. b7. b8. o. b9. b10. b11. b12. b13. b14. b15. b16. h. b17. b18. b19. b20. b21. b22. b23. b24. b25. b26. b27. b28. b29. b30. b31. b32. b33. b34. b35. b36. Digits: 0:0, 1:1, 2:2, 3:3, 4:4, 5:5, 6:6, 7:7, 8:8, 9:9, 10:A, 11:B, 12:C, 13:D, 14:E, 15:F, 16:G, 17:H, 18:I, 19:J, 20:K, 21:L, 22:M, 23:N, 24:O, 25:P, 26:Q, 27:R, 28:S, 29:T, 30:U, 31:V, 32:W, 33:X, 34:Y, 35:Z
    
    Returns:
    
    If number literal fits numeral system definition then numeral system base is returned (base between 1 and 36), otherwise -1 is returned.
  - convOthBase2Decimal
```
public static double convOthBase2Decimal(java.lang.String numberLiteral,
                                         int numeralSystemBase)
```
    Other base (base between 1 and 36) number literal conversion to decimal number.
    
    Parameters:
    
    numberLiteral - Number literal in given numeral system with base between 1 and 36. Digits: 0:0, 1:1, 2:2, 3:3, 4:4, 5:5, 6:6, 7:7, 8:8, 9:9, 10:A, 11:B, 12:C, 13:D, 14:E, 15:F, 16:G, 17:H, 18:I, 19:J, 20:K, 21:L, 22:M, 23:N, 24:O, 25:P, 26:Q, 27:R, 28:S, 29:T, 30:U, 31:V, 32:W, 33:X, 34:Y, 35:Z
    
    numeralSystemBase - Numeral system base, between 1 and 36
    
    Returns:
    
    Decimal number after conversion. If conversion was not possible the Double.NaN is returned.
  - convOthBase2Decimal
```
public static double convOthBase2Decimal(java.lang.String numberLiteral)
```
    Other base (base between 1 and 36) number literal conversion to decimal number. Base specification included in number literal. Examples: 2 for b2.1001 or b.1001, 1 for b1.111, 23 for b23.123afg 16 for b16.123acdf or h.123acdf.
    
    Parameters:
    
    numberLiteral - Number literal string. Base format: b1. b2. b. b3. b4. b5. b6. b7. b8. o. b9. b10. b11. b12. b13. b14. b15. b16. h. b17. b18. b19. b20. b21. b22. b23. b24. b25. b26. b27. b28. b29. b30. b31. b32. b33. b34. b35. b36. Digits: 0:0, 1:1, 2:2, 3:3, 4:4, 5:5, 6:6, 7:7, 8:8, 9:9, 10:A, 11:B, 12:C, 13:D, 14:E, 15:F, 16:G, 17:H, 18:I, 19:J, 20:K, 21:L, 22:M, 23:N, 24:O, 25:P, 26:Q, 27:R, 28:S, 29:T, 30:U, 31:V, 32:W, 33:X, 34:Y, 35:Z
    
    Returns:
    
    Decimal number after conversion. If conversion was not possible the Double.NaN is returned.
  - convOthBase2Decimal
```
public static double convOthBase2Decimal(int numeralSystemBase,
                                         int... digits)
```
    Other base to decimal conversion.
    
    Parameters:
    
    numeralSystemBase - Numeral system base has to be above 0.
    
    digits - List of digits
    
    Returns:
    
    Number after conversion. If conversion is not possible then Double.NaN is returned.
  - convOthBase2Decimal
```
public static double convOthBase2Decimal(double numeralSystemBase,
                                         double... digits)
```
    Other base to decimal conversion.
    
    Parameters:
    
    numeralSystemBase - Numeral system base has to be above 0.
    
    digits - List of digits
    
    Returns:
    
    Number after conversion. If conversion is not possible then Double.NaN is returned.
  - convOthBase2Decimal
```
public static double convOthBase2Decimal(int[] baseAndDigits)
```
    Other base to decimal conversion.
    
    Parameters:
    
    baseAndDigits - Numeral system base and digits specification. Numeral system base is placed at index 0, rest of array is interpreted as digits. Numeral system base has to be above 0.
    
    Returns:
    
    Number after conversion. If conversion is not possible then Double.NaN is returned.
  - convOthBase2Decimal
```
public static double convOthBase2Decimal(double[] baseAndDigits)
```
    Other base to decimal conversion.
    
    Parameters:
    
    baseAndDigits - Numeral system base and digits specification. Numeral system base is placed at index 0, rest of array is interpreted as digits. Numeral system base has to be above 0.
    
    Returns:
    
    Number after conversion. If conversion is not possible then Double.NaN is returned.
  - convDecimal2OthBase
```
public static java.lang.String convDecimal2OthBase(double decimalNumber,
                                                   int numeralSystemBase)
```
    Decimal number to other numeral system conversion with base between 1 and 36.
    
    Parameters:
    
    decimalNumber - Decimal number
    
    numeralSystemBase - Numeral system base between 1 and 36
    
    Returns:
    
    Number literal representing decimal number in given numeral system. Digits 0:0, 1:1, 2:2, 3:3, 4:4, 5:5, 6:6, 7:7, 8:8, 9:9, 10:A, 11:B, 12:C, 13:D, 14:E, 15:F, 16:G, 17:H, 18:I, 19:J, 20:K, 21:L, 22:M, 23:N, 24:O, 25:P, 26:Q, 27:R, 28:S, 29:T, 30:U, 31:V, 32:W, 33:X, 34:Y, 35:Z. If conversion was not possible the "NaN" string is returned.
  - convDecimal2OthBase
```
public static java.lang.String convDecimal2OthBase(double decimalNumber,
                                                   int numeralSystemBase,
                                                   int format)
```
    Decimal number to other numeral system conversion with base between 1 and 36.
    
    Parameters:
    
    decimalNumber - Decimal number
    
    numeralSystemBase - Numeral system base between 1 and 36
    
    format - If 1 then always bxx. is used, i.e. b1. or b16. If 2 then for binary b. is used, for octal o. is used, for hexadecimal h. is used, otherwise bxx. is used where xx is the numeral system base specification.
    
    Returns:
    
    Number literal representing decimal number in given numeral system. Base format: b1. b2. b. b3. b4. b5. b6. b7. b8. o. b9. b10. b11. b12. b13. b14. b15. b16. h. b17. b18. b19. b20. b21. b22. b23. b24. b25. b26. b27. b28. b29. b30. b31. b32. b33. b34. b35. b36. Digits: 0:0, 1:1, 2:2, 3:3, 4:4, 5:5, 6:6, 7:7, 8:8, 9:9, 10:A, 11:B, 12:C, 13:D, 14:E, 15:F, 16:G, 17:H, 18:I, 19:J, 20:K, 21:L, 22:M, 23:N, 24:O, 25:P, 26:Q, 27:R, 28:S, 29:T, 30:U, 31:V, 32:W, 33:X, 34:Y, 35:Z If conversion was not possible the "NaN" string is returned.
  - numberOfDigits
```
public static int numberOfDigits(long number)
```
    Number of digits needed to represent given number in base 10 numeral system.
    
    Parameters:
    
    number - The number
    
    Returns:
    
    Number of digits needed to represent given number in base 10 numeral system.
  - numberOfDigits
```
public static double numberOfDigits(double number)
```
    Number of digits needed to represent given number in base 10 numeral system.
    
    Parameters:
    
    number - The number
    
    Returns:
    
    Number of digits needed to represent given number in base 10 numeral system. If number is NaN the NaN is returned. If number is infinite then Double.POSITIVE_INFINITY is returned.
  - numberOfDigits
```
public static long numberOfDigits(long number,
                                  long numeralSystemBase)
```
    Number of digits needed to represent given number in numeral system with given base.
    
    Parameters:
    
    number - The number
    
    numeralSystemBase - Numeral system base above 0
    
    Returns:
    
    Returns number of digits. In case when numeralSystemBase is lower than 1 then -1 is returned.
  - numberOfDigits
```
public static double numberOfDigits(double number,
                                    double numeralSystemBase)
```
    Number of digits needed to represent given number (its integer part) in numeral system with given base.
    
    Parameters:
    
    number - The number
    
    numeralSystemBase - Numeral system base above 0
    
    Returns:
    
    Returns number of digits. In case when numeralSystemBase is lower than 1 then Double.NaN is returned. If number or numeralSystemBase is Double.NaN then Double.NaN is returned. If numeralSystemBase is infinite then Double.NaN is returned.
  - digitAtPosition
```
public static int digitAtPosition(long number,
                                  int position,
                                  int numeralSystemBase)
```
    Digit at position - numeral system with given base
    
    Parameters:
    
    number - The number
    
    position - Position from 1 ... n (left to right) or from 0 ... -(n-1) (right to left).
    
    numeralSystemBase - Base of numeral system - above 0
    
    Returns:
    
    Return digit at given position. If digit finding was not possible then -1 is returned.
  - digitAtPosition
```
public static int digitAtPosition(long number,
                                  int position)
```
    Digit at position - numeral system with base 10
    
    Parameters:
    
    number - The number
    
    position - Position from 1 ... n (left to right) or from 0 ... -(n-1) (right to left).
    
    Returns:
    
    Return digit at given position. If digit finding was not possible then -1 is returned.
  - digitAtPosition
```
public static double digitAtPosition(double number,
                                     double position,
                                     double numeralSystemBase)
```
    Digit at position - numeral system with given base
    
    Parameters:
    
    number - The number
    
    position - Position from 1 ... n (left to right) or from 0 ... -(n-1) (right to left).
    
    numeralSystemBase - Base of numeral system - above 0
    
    Returns:
    
    Return digit at given position. If digit finding was not possible then Double.NaN is returned.
  - digitAtPosition
```
public static double digitAtPosition(double number,
                                     double position)
```
    Digit at position - numeral system with base 10
    
    Parameters:
    
    number - The number
    
    position - Position from 1 ... n (left to right) or from 0 ... -(n-1) (right to left).
    
    Returns:
    
    Return digit at given position. If digit finding was not possible then Double.NaN is returned.
  - primeFactors
```
public static long[] primeFactors(long number)
```
    Prime decomposition (prime factorization)
    
    Parameters:
    
    number - Number to be decomposed
    
    Returns:
    
    List of prime factors (non-distinct)
  - primeFactors
```
public static double[] primeFactors(double number)
```
    Prime decomposition (prime factorization)
    
    Parameters:
    
    number - Number to be decomposed
    
    Returns:
    
    List of prime factors (non-distinct)
  - numberOfPrimeFactors
```
public static double numberOfPrimeFactors(double number)
```
    Prime decomposition (prime factorization) - returns number of distinct prime factors
    
    Parameters:
    
    number - Number to be decomposed
    
    Returns:
    
    Number of distinct prime factors
  - primeFactorValue
```
public static double primeFactorValue(double number,
                                      double id)
```
    Prime decomposition (prime factorization) - returns prime factor value
    
    Parameters:
    
    number - Number to be decomposed
    
    id - Factor id
    
    Returns:
    
    Factor value if factor id between 1 and numberOfPrimeFactors, otherwise 1 is returned. For NaN of infinite parameters Double NaN is returned. For number eq 0 Double.NaN is returned.
  - primeFactorExponent
```
public static double primeFactorExponent(double number,
                                         double id)
```
    Prime decomposition (prime factorization) - returns prime factor exponent
    
    Parameters:
    
    number - Number to be decomposed
    
    id - Factor id
    
    Returns:
    
    Factor exponent if factor id between 1 and numberOfPrimeFactors, otherwise 0 is returned. For NaN of infinite parameters Double NaN is returned. For number eq 0 Double.NaN is returned.
  - fractionToDoubleArray
```
private static double[] fractionToDoubleArray(double sign,
                                              double numerator,
                                              double denominator)
```
    Creates array representing fraction (sign, numerator and denominator).
    
    Parameters:
    
    sign - Sign of the number represented by fraction
    
    numerator - Numerator from the fraction
    
    denominator - Denominator from the fraction
    
    Returns:
    
    Returns array containing sign, numerator and denominator. Sign at index 0, numerator at index 1, denominator at index 2.
  - mixedFractionToDoubleArray
```
private static double[] mixedFractionToDoubleArray(double sign,
                                                   double whole,
                                                   double numerator,
                                                   double denominator)
```
    Creates array representing mixed fraction (sign, whole number, numerator and denominator).
    
    Parameters:
    
    sign - Sign of the number represented by fraction
    
    whole - Whole number
    
    numerator - Numerator from the fraction
    
    denominator - Denominator from the fraction
    
    Returns:
    
    Returns array containing whole number, numerator and denominator. Sign at index 0, whole number at index 1, numerator at index 2, denominator at index 3.
  - toFraction
```
public static double[] toFraction(double value)
```
    Converts double value to its fraction representation.
    
    Parameters:
    
    value - Value to be converted
    
    Returns:
    
    Array representing fraction. Sign at index 0, numerator at index 1, denominator at index 2. If conversion is not possible then Double.NaN is assigned to all the fields.
  - toMixedFraction
```
public static double[] toMixedFraction(double value)
```
    Converts double value to its mixed fraction representation.
    
    Parameters:
    
    value - Value to be converted
    
    Returns:
    
    Array representing fraction. Sign at index 0, whole number at index 1, numerator at index 2, denominator at index 3. If conversion is not possible then Double.NaN is assigned to both numerator and denominator.
  - fractionToString
```
public static java.lang.String fractionToString(double[] fraction)
```
    Converts array representing fraction to fraction string representation.
    
    Parameters:
    
    fraction - Array representing fraction (including mix fractions)
    
    Returns:
    
    String representation of fraction.
    
    See Also:
    
    toFraction(double), toMixedFraction(double)
  - toFractionString
```
public static java.lang.String toFractionString(double value)
```
    Converts number to its fraction string representation.
    
    Parameters:
    
    value - Given number
    
    Returns:
    
    String representation of fraction.
    
    See Also:
    
    toFraction(double), fractionToString(double[])
  - toMixedFractionString
```
public static java.lang.String toMixedFractionString(double value)
```
    Converts number to its mixed fraction string representation.
    
    Parameters:
    
    value - Given number
    
    Returns:
    
    String representation of fraction.
    
    See Also:
    
    toMixedFraction(double), fractionToString(double[])

Modifier and Type	Field	Description
`static long`	`DEFAULT_TO_FRACTION_INIT_SEARCH_SIZE`
`private static long`	`TO_FRACTION_INIT_SEARCH_SIZE`	Initial search size 1 ...

Class NumberTheory

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

DEFAULT_TO_FRACTION_INIT_SEARCH_SIZE

TO_FRACTION_INIT_SEARCH_SIZE

Constructor Detail

NumberTheory

Method Detail

setToFractionInitSearchSize

getToFractionInitSearchSize

min

min

argmin

max

max

argmax

sortAsc

sortAsc

getDistValues

numberOfDistValues

gcd

gcd

gcd

gcd

lcm

lcm

lcm

lcm

sum

prod

primeTest

primeTest

primeCount

primeCount

sigmaSummation

piProduct

min

max

getRegExpForNumeralSystem

digitIndex

digitChar

getNumeralSystemBase

convOthBase2Decimal

convOthBase2Decimal

convOthBase2Decimal

convOthBase2Decimal

convOthBase2Decimal

convOthBase2Decimal

convDecimal2OthBase

convDecimal2OthBase

numberOfDigits

numberOfDigits

numberOfDigits

numberOfDigits

digitAtPosition

digitAtPosition

digitAtPosition

digitAtPosition

primeFactors

primeFactors

numberOfPrimeFactors

primeFactorValue

primeFactorExponent

fractionToDoubleArray

mixedFractionToDoubleArray

toFraction

toMixedFraction

fractionToString

toFractionString

toMixedFractionString