NAME

Sidef::Types::Number::Number

DESCRIPTION

The Number class implements support for numerical operations, supporting integers, rationals, floating-points and complex numbers at arbitrary precision.

This class also implements many useful mathematical methods, from basic arithmetical operations, to advanced number-theoretic functions, including primality testing and prime factorization methods.

SYNOPSIS

    var a = Num(string)
    var b = Number(string, base)

INHERITS

Inherits methods from:

       * Sidef::Object::Object

METHODS

!

n!

Factorial of n. (1*2*3*...*n)

Aliases: fac, factorial

!!

n!!

Double-factorial of n.

Aliases: dfac, dfactorial, double_factorial

%

    n % k

Remainder of n/k.

Aliases: mod

%%

    n %% k

Returns true if n is divisible by k. False otherwise.

Aliases: is_div

&

    a & b

Bitwise AND operation.

Aliases: and

*

    a * b

Multiplication of a and b.

Aliases: mul

**

    a**b

Exponentiation: a to power b.

Aliases: pow

+

    a + b

Addition of a and b.

Aliases: add

++

    n.inc

Increment n by 1 and return the result.

Aliases: inc

-

    a - b

Subtraction of a and b.

Aliases: sub

--

    n.dec

Decrement n by 1 and return the result.

Aliases: dec

..

    a .. b

Create an inclusive-inclusive RangeNum object, from a to b.

Equivalent with:

    RangeNum(a, b)

Aliases: to, upto

..^

    a ..^ b

Create an inclusive-exclusive RangeNum object, from a to b-1.

Equivalent with:

    RangeNum(a, b-1)

Aliases: xto, xupto

/

    a / b

Division of a by b.

Aliases: ÷, div

//

    a // b

Integer division of a and b.

Aliases: idiv

:

    a : b

Create a new complex number.

Equivalent with:

    Complex(a, b)

Aliases: pair

<

    a < b

Returns true if a is less than b.

Aliases: lt

<<

    a << b

Bitwise left-shift, equivalent with (assuming a and b are integers):

    int(a * 2**b)

Aliases: lsft, shift_left

<=>

    a <=> b

Comparison of a with b. Returns -1 if a is less than b, 0 if a and b are equal and +1 if a is greater than b.

Aliases: cmp

approx_cmp

    approx_cmp(a, b)
    approx_cmp(a, b, k)

Approximate comparison of a and b.

Equivalent with:

    a.round(k) <=> b.round(k)

When k is omitted, it uses the default floating-point precision to deduce k.

==

    a == b

Equality check. Returns true if a and b are equal.

Aliases: eq

>

    a > b

Returns true if a is greater than b. False otherwise.

Aliases: gt

>>

    a >> b

Bitwise right-shift, equivalent with (assuming a and b are integers):

    int(a / 2**b)

Aliases: rsft, shift_right

^

    a ^ b

Bitwise XOR operation.

Aliases: xor

^..

    a ^.. b

Creates a reversed exclusive-inclusive RangeNum object, from a-1 down to b.

Equivalent with:

    RangeNum(a-1, b, -1)

Aliases: xdownto

C

    Num.C
    Num.catalan_G

Returns the Catalan constant: 0.915965594177...

Aliases: catalan_G

Y

Number.Y() -> Obj

Return the

Aliases: γ, euler_gamma

|

Obj | Obj -> Obj

Return the

Aliases: or

~

Obj ~ Obj -> Obj

Return the

Aliases: not

Γ

Number.Γ() -> Obj

Return the

Aliases: gamma

δ

Number.δ() -> Obj

Return the

Aliases: kronecker_delta

ζ

Number.ζ() -> Obj

Return the

Aliases: zeta

η

Number.η() -> Obj

Return the

Aliases: eta

μ

Number.μ() -> Obj

Return the

Aliases: mu, mobius, möbius, moebius

Π

Number.Π() -> Obj

Return the

Aliases: prod

π

Number.π() -> Obj

Return the

Aliases: pi

Σ

Number.Σ() -> Obj

Return the

Aliases: sum

σ

Number.σ() -> Obj

Return the

Aliases: sigma

τ

Number.τ() -> Obj

Return the

Aliases: tau

φ

Number.φ() -> Obj

Return the

Aliases: phi

Ψ

Number.Ψ() -> Obj

Return the

Aliases: digamma

Ω

Number.Ω() -> Obj

Return the

Aliases: big_omega, bigomega, prime_power_sigma0

ω

Number.ω() -> Obj

Return the

Aliases: omega, prime_sigma0, prime_power_usigma0

≅

Obj ≅ Obj -> Obj

Return the

Aliases: =~=, approx_eq

≠

Obj ≠ Obj -> Obj

Return the

Aliases: !=, ne

≤

Obj ≤ Obj -> Obj

Return the

Aliases: <=, le

≥

Obj ≥ Obj -> Obj

Return the

Aliases: >=, ge

abs

    n.abs

Absolute value of n.

abundancy

Number.abundancy() -> Obj

Return the

Aliases: abundancy_index

acmp

Number.acmp() -> Obj

Return the

acos

    n.acos

Inverse cosine of n in radians.

acosh

    n.acosh

Inverse hyperbolic cosine of n.

acot

    n.acot

Inverse cotangent of n in radians.

acoth

    n.acoth

Inverse hyperbolic cotangent of n.

acsc

    n.acsc

Inverse cosecant of n in radians.

acsch

    n.acsch

Inverse hyperbolic cosecant of n.

agm

    agm(a, b)

Arithmetic-geometric mean of a and b.

ai

    x.ai
    Ai(x)

Airy function of the first kind: Ai(x).

Aliases: airy

all_composite

Number.all_composite() -> Obj

Return the

all_prime

Number.all_prime() -> Obj

Return the

approx_ge

    approx_ge(a, b)
    approx_ge(a, b, k)

True if a is approximately greater than or equal to b.

Equivalent with:

    a.round(k) >= b.round(k)

approx_gt

    approx_gt(a, b)
    approx_gt(a, b, k)

True if a is approximately greater than b.

Equivalent with:

    a.round(k) > b.round(k)

approx_le

    approx_le(a, b)
    approx_le(a, b, k)

True if a is approximately less than or equal to b.

Equivalent with:

    a.round(k) <= b.round(k)

approx_lt

    approx_lt(a, b)
    approx_lt(a, b, k)

True if a is approximately less than b.

Equivalent with:

    a.round(k) < b.round(k)

approx_ne

    approx_ne(a, b)
    approx_ne(a, b, k)

True if a is approximately different than b.

Equivalent with:

    a.round(k) != b.round(k)

as_bin

    n.as_bin

Returns a String with the binary representation of n.

Example:

    say 42.as_bin     # "101011"

as_dec

    n.as_dec
    n.as_dec(k)

Given a rational number n, it returns its decimal expansion as a String object, expanded at k decimal places.

Example:

    say (1/17 -> as_dec(10))      # 0.05882352941
    say (1/17 -> as_dec(30))      # 0.0588235294117647058823529411765

Aliases: as_float

asec

    n.asec

Inverse secant of n in radians.

asech

    n.asech

Inverse hyperbolic secant of n.

as_frac

    n.as_frac
    n.as_frac(base)

String-representation of n as fraction.

Example:

    say 24.as_frac                 # 24/1
    say bernoulli(10).as_frac      # 5/66
    say bernoulli(12).as_frac(36)  # -j7/23u

If n is an integer, it uses 1 for the denominator.

as_hex

    n.as_hex

Returns a String representing the integer part of n in hexadecimal (base 16).

Example:

    say 42.as_hex       # "2a"

Returns nil when n cannot be converted to an integer.

asin

    n.asin

Inverse sine of n in radians.

asinh

    n.asinh

Inverse hyperbolic sine of n.

as_int

    n.as_int
    n.as_int(base)

Returns a String representing the integer part of n in a given base, where the base must be between 2 and 62.

When the base is omitted, it defaults to base 10.

Example:

    say 255.as_int      # "255"
    say 255.as_int(16)  # "ff"

Returns nil when n cannot be converted to an integer.

as_oct

    n.as_oct

Returns a String representing the integer part of n in octal (base 8).

Example:

    say 42.as_oct   # 52

Returns nil when n cannot be converted to an integer.

as_rat

    n.as_rat
    n.as_rat(base)

Returns a rational string-representation of n in a given base, where the base must be between 2 and 62.

When the base is omitted, it defaults to base 10.

Example:

    say as_rat(42)          # "42"
    say as_rat(2/4)         # "1/2"
    say as_rat(255, 16)     # "ff"

Returns nil when n cannot be converted to a rational number.

atan

    n.atan

Inverse tangent of n in radians.

atan2

    atan2(a, b)

Four-quadrant inverse tangent of a and b.

atanh

    n.atanh

Inverse hyperbolic tangent of n.

base

    n.base(b)

Returns a String-representation of n in a given base b, which must be between 2 and 62.

Aliases: in_base

bell

    n.bell

Returns the n-th Bell number.

Aliases: bell_number

bern

    n.bern
    bernoulli(n)
    bernoulli(n, x)

Returns the n-th Bernoulli number. When an additional argument is provided, it returns the n-th Bernoulli polynomial.

Example:

    say bernoulli(10).as_rat       # B_10    = 5/66
    say bernoulli(10, 2).as_rat    # B_10(2) = 665/66

Aliases: bernfrac, bernoulli, bernoulli_number

bernoulli_polynomial

    bernoulli_polynomial(n, x)

Returns the n-th Bernoulli polynomial: B_n(x).

bernreal

    n.bernreal

Return an approximation to the n-th Bernoulli number as a floating-point number.

bessel_j

    bessel_j(x, n)

First order Bessel function: J_n(x).

bessel_y

    bessel_y(x, n)

Second order Bessel function: Y_n(x).

beta

    beta(a, b)

The beta function (also called the Euler integral of the first kind).

Defined as:

    beta(a, b) = gamma(a)*gamma(b) / gamma(a+b)

bit

    n.bit(k)
    n.getbit(k)

Returns 1 if bit k of n is set, and 0 if it is not set.

Return nil when n cannot be truncated to an integer or when k is negative.

Example:

    say getbit(0b1001, 0)   # 1
    say getbit(0b1000, 0)   # 0

Aliases: getbit, testbit

bits

Number.bits() -> Obj

Return the

bit_scan0

    n.bit_scan0
    n.bit_scan0(k)

Scan n, starting from bit index k, towards more significant bits, until a 0-bit is found.

When k is omitted, k=0 is assumed.

Returns nil if n cannot be truncated to an integer or if k is negative.

bit_scan1

    n.bit_scan1
    n.bit_scan1(k)

Scan n, starting from bit index k, towards more significant bits, until a 1-bit is found.

When k is omitted, k=0 is assumed.

Returns nil if n cannot be truncated to an integer or if k is negative.

bsearch

    bsearch(n, {...})
    bsearch(a, b, {...})

Binary search from to 0 to n, or from a to b, which can be any arbitrary large integers.

The last argument is a block which does the comparisons.

This function finds a value k such that f(k) = 0. Returns nil otherwise.

    say bsearch(20,      {|k| k*k  <=> 49   })   #=> 7   (7*7  = 49)
    say bsearch(3, 1000, {|k| k**k <=> 3125 })   #=> 5   (5**5 = 3125)

bsearch_ge

    bsearch_ge(n, {...})
    bsearch_ge(a, b, {...})

Binary search from to 0 to n, or from a to b, which can be any arbitrary large integers.

The last argument is a block which does the comparisons.

This function finds a value k such that f(k-1) < 0 and f(k) >= 0. Returns nil otherwise.

    bsearch_ge(1e6,       { .exp <=> 1e+9 })  #  21   (exp( 21) >= 1e+9)
    bsearch_ge(-1e6, 1e6, { .exp <=> 1e-9 })  # -20   (exp(-20) >= 1e-9)

bsearch_le

    bsearch_le(n, {...})
    bsearch_le(a, b, {...})

Binary search from to 0 to n, or from a to b, which can be any arbitrary large integers.

The last argument is a block which does the comparisons.

This function finds a value k such that f(k) <= 0 and f(k+1) > 0. Returns nil otherwise.

    bsearch_le(1e6,       { .exp <=> 1e+9 })  #  20   (exp( 20) <= 1e+9)
    bsearch_le(-1e6, 1e6, { .exp <=> 1e-9 })  # -21   (exp(-21) <= 1e-9)

bsearch_max

Number.bsearch_max() -> Obj

Return the

bsearch_min

Number.bsearch_min() -> Obj

Return the

bsearch_solve

Number.bsearch_solve() -> Obj

Return the

Aliases: bsearch_inverse

by

Number.by() -> Obj

Return the

Aliases: first

cadd

Number.cadd() -> Obj

Return the

Aliases: complex_add

catalan

    n.catalan
    n.catalan(k)

Returns the n-th Catalan number.

If two arguments are provided, it returns the C(n,k) entry in Catalan's triangle.

cbrt

    n.cbrt

Cube root of n.

cdiv

Number.cdiv() -> Obj

Return the

Aliases: complex_div

ceil

    n.ceil

Round n towards positive Infinity.

Aliases: ceiling

cfrac

    n.cfrac
    n.cfrac(k)

Compute k terms of the simple continued-fraction expansion of n.

Example:

    say sqrt(12).cfrac(6)    # [3, 2, 6, 2, 6, 2, 6]

Can also be used to compute very good rational approximations to a given real number:

    say Num.pi.cfrac(10).flip.reduce{|a,b| b + 1/a }.as_rat      # 4272943/1360120

When k is omitted, it uses the default floating-point precision to deduce k.

Aliases: as_cfrac

chebyshev_T

    chebyshevT(n, x)

Compute the Chebyshev polynomials of the first kind: T_n(x), where n must be a native integer.

Defined as:

    T(0, x) = 1
    T(1, x) = x
    T(n, x) = 2*x*T(n-1, x) - T(n-2, x)

Aliases: chebyshevt, chebyshevT

chebyshev_U

    chebyshevU(n, x)

Compute the Chebyshev polynomials of the second kind: U_n(x), where n must be a native integer.

Defined as:

    U(0, x) = 1
    U(1, x) = 2*x
    U(n, x) = 2*x*U(n-1, x) - U(n-2, x)

Aliases: chebyshevu, chebyshevU

chr

    n.chr

Convert the integer n into a character.

Example:

    say 97.chr      # "a"
    say 9786.chr    # "☺"

cinv

Number.cinv() -> Obj

Return the

Aliases: complex_inv

cinvmod

Number.cinvmod() -> Obj

Return the

Aliases: complex_invmod

circular_permutations

Number.circular_permutations() -> Obj

Return the

cis

Number.cis() -> Obj

Return the

clearbit

Number.clearbit() -> Obj

Return the

cmod

Number.cmod() -> Obj

Return the

Aliases: complex_mod

cmul

Number.cmul() -> Obj

Return the

Aliases: complex_mul

combinations

Number.combinations() -> Obj

Return the

combinations_with_repetition

Number.combinations_with_repetition() -> Obj

Return the

commify

Number.commify() -> Obj

Return the

complex

Number.complex() -> Obj

Return the

complex_cmp

Number.complex_cmp() -> Obj

Return the

complex_ipow

Number.complex_ipow() -> Obj

Return the

composite

Number.composite() -> Obj

Return the

Aliases: nth_composite

composite_count

Number.composite_count() -> Obj

Return the

conj

Number.conj() -> Obj

Return the

Aliases: conjug, conjugate

consecutive_lcm

Number.consecutive_lcm() -> Obj

Return the

Aliases: consecutive_integer_lcm

convergents

Number.convergents() -> Obj

Return the

cos

Number.cos() -> Obj

Return the

cosh

Number.cosh() -> Obj

Return the

cot

Number.cot() -> Obj

Return the

coth

Number.coth() -> Obj

Return the

cpow

Number.cpow() -> Obj

Return the

Aliases: complex_pow

cpowmod

Number.cpowmod() -> Obj

Return the

Aliases: complex_powmod

csc

Number.csc() -> Obj

Return the

csch

Number.csch() -> Obj

Return the

csub

Number.csub() -> Obj

Return the

Aliases: complex_sub

cyclotomic

Number.cyclotomic() -> Obj

Return the

Aliases: cyclotomic_polynomial

dconv

Number.dconv() -> Obj

Return the

Aliases: dirichlet_convolution

de

Number.de() -> Obj

Return the

Aliases: denominator

defs

Number.defs() -> Obj

Return the

deg2rad

Number.deg2rad() -> Obj

Return the

derangements

Number.derangements() -> Obj

Return the

Aliases: complete_permutations

derivative

Number.derivative() -> Obj

Return the

Aliases: arithmetic_derivative

digit

Number.digit() -> Obj

Return the

digits

Number.digits() -> Obj

Return the

digits2num

Number.digits2num() -> Obj

Return the

Aliases: from_digits

digits_sum

Number.digits_sum() -> Obj

Return the

Aliases: sum_digits, sumdigits

dirichlet_hyperbola

Number.dirichlet_hyperbola() -> Obj

Return the

divides

Number.divides() -> Obj

Return the

divisor_map

Number.divisor_map() -> Obj

Return the

divisor_prod

Number.divisor_prod() -> Obj

Return the

Aliases: divisors_prod

divisors

Number.divisors() -> Obj

Return the

divisor_sum

Number.divisor_sum() -> Obj

Return the

Aliases: divisors_sum

divmod

Number.divmod() -> Obj

Return the

downto

Number.downto() -> Obj

Return the

dump

Number.dump() -> Obj

Return the

e

Number.e() -> Obj

Return the

each_prime

Number.each_prime() -> Obj

Return the

Aliases: primes_each

each_squarefree

Number.each_squarefree() -> Obj

Return the

Aliases: squarefree_each

ecm_factor

Number.ecm_factor() -> Obj

Return the

ei

Number.ei() -> Obj

Return the

Aliases: eint

erf

Number.erf() -> Obj

Return the

erfc

Number.erfc() -> Obj

Return the

euler

Number.euler() -> Obj

Return the

Aliases: euler_number

euler_polynomial

Number.euler_polynomial() -> Obj

Return the

exp

Number.exp() -> Obj

Return the

exp10

Number.exp10() -> Obj

Return the

exp2

Number.exp2() -> Obj

Return the

exp_mangoldt

Number.exp_mangoldt() -> Obj

Return the

expmod

Number.expmod() -> Obj

Return the

Aliases: powmod

factor

Number.factor() -> Obj

Return the

Aliases: factors

factor_exp

Number.factor_exp() -> Obj

Return the

Aliases: factors_exp

factorialmod

Number.factorialmod() -> Obj

Return the

factorial_power

Number.factorial_power() -> Obj

Return the

factorial_sum

Number.factorial_sum() -> Obj

Return the

Aliases: left_factorial

factor_map

Number.factor_map() -> Obj

Return the

factor_prod

Number.factor_prod() -> Obj

Return the

Aliases: factors_prod

factor_sum

Number.factor_sum() -> Obj

Return the

Aliases: factors_sum

falling_factorial

Number.falling_factorial() -> Obj

Return the

faulhaber

Number.faulhaber() -> Obj

Return the

Aliases: faulhaber_sum

faulhaber_polynomial

Number.faulhaber_polynomial() -> Obj

Return the

fermat_factor

Number.fermat_factor() -> Obj

Return the

fib

Number.fib() -> Obj

Return the

Aliases: fibonacci

fibmod

Number.fibmod() -> Obj

Return the

Aliases: fibonacci_mod, fibonaccimod

flip

Number.flip() -> Obj

Return the

Aliases: reverse

flipbit

Number.flipbit() -> Obj

Return the

floor

Number.floor() -> Obj

Return the

gcd

Number.gcd() -> Obj

Return the

gcdext

Number.gcdext() -> Obj

Return the

geometric_sum

Number.geometric_sum() -> Obj

Return the

gpf

Number.gpf() -> Obj

Return the

hamdist

Number.hamdist() -> Obj

Return the

harm

Number.harm() -> Obj

Return the

Aliases: harmfrac, harmonic, harmonic_number

harmreal

Number.harmreal() -> Obj

Return the

hermite_H

Number.hermite_H() -> Obj

Return the

Aliases: hermiteH, hermite_polynomial_H, hermite_polynomialH

hermite_He

Number.hermite_He() -> Obj

Return the

Aliases: hermiteHe, hermite_polynomial_He, hermite_polynomialHe

holf_factor

Number.holf_factor() -> Obj

Return the

hyperfactorial

Number.hyperfactorial() -> Obj

Return the

hyperfactorial_ln

Number.hyperfactorial_ln() -> Obj

Return the

Aliases: lnhyperfactorial, hyperfactorial_log

hypot

Number.hypot() -> Obj

Return the

i

Number.i() -> Obj

Return the

iadd

Number.iadd() -> Obj

Return the

icbrt

Number.icbrt() -> Obj

Return the

ilog

Number.ilog() -> Obj

Return the

ilog10

Number.ilog10() -> Obj

Return the

ilog2

Number.ilog2() -> Obj

Return the

im

Number.im() -> Obj

Return the

Aliases: imag, imaginary

imod

Number.imod() -> Obj

Return the

imul

Number.imul() -> Obj

Return the

inf

Number.inf() -> Obj

Return the

int

Number.int() -> Obj

Return the

Aliases: to_i, to_int, trunc

inv

Number.inv() -> Obj

Return the

inverse_phi

Number.inverse_phi() -> Obj

Return the

Aliases: inverse_totient, inverse_euler_phi

inverse_polygonal

Number.inverse_polygonal() -> Obj

Return the

Aliases: polygonal_inverse

inverse_sigma

Number.inverse_sigma() -> Obj

Return the

inverse_totient_len

Number.inverse_totient_len() -> Obj

Return the

invmod

Number.invmod() -> Obj

Return the

ipolygonal_root

Number.ipolygonal_root() -> Obj

Return the

ipolygonal_root2

Number.ipolygonal_root2() -> Obj

Return the

ipow

Number.ipow() -> Obj

Return the

ipow10

Number.ipow10() -> Obj

Return the

ipow2

Number.ipow2() -> Obj

Return the

iquadratic_formula

Number.iquadratic_formula() -> Obj

Return the

Aliases: integer_quadratic_formula

irand

Number.irand() -> Obj

Return the

iroot

Number.iroot() -> Obj

Return the

irootrem

Number.irootrem() -> Obj

Return the

is_abundant

Number.is_abundant() -> Obj

Return the

is_aks_prime

Number.is_aks_prime() -> Obj

Return the

is_almost_prime

Number.is_almost_prime() -> Obj

Return the

is_between

Number.is_between() -> Obj

Return the

is_bpsw_prime

Number.is_bpsw_prime() -> Obj

Return the

is_bruckman_lucas_pseudoprime

Number.is_bruckman_lucas_pseudoprime() -> Obj

Return the

is_carmichael

Number.is_carmichael() -> Obj

Return the

is_chebyshev_pseudoprime

Number.is_chebyshev_pseudoprime() -> Obj

Return the

is_complex

Number.is_complex() -> Obj

Return the

is_composite

Number.is_composite() -> Obj

Return the

is_congruent

Number.is_congruent() -> Obj

Return the

is_coprime

Number.is_coprime() -> Obj

Return the

is_cube

Number.is_cube() -> Obj

Return the

is_cyclic

Number.is_cyclic() -> Obj

Return the

is_ecpp_prime

Number.is_ecpp_prime() -> Obj

Return the

iseed

Number.iseed() -> Obj

Return the

is_euler_pseudoprime

Number.is_euler_pseudoprime() -> Obj

Return the

is_even

Number.is_even() -> Obj

Return the

is_fibonacci_pseudoprime

Number.is_fibonacci_pseudoprime() -> Obj

Return the

is_frobenius_pseudoprime

Number.is_frobenius_pseudoprime() -> Obj

Return the

is_fundamental

Number.is_fundamental() -> Obj

Return the

is_gaussian_prime

Number.is_gaussian_prime() -> Obj

Return the

is_imag

Number.is_imag() -> Obj

Return the

is_inf

Number.is_inf() -> Obj

Return the

is_int

Number.is_int() -> Obj

Return the

is_khashin_pseudoprime

Number.is_khashin_pseudoprime() -> Obj

Return the

Aliases: is_frobenius_khashin_pseudoprime

is_lucas_carmichael

Number.is_lucas_carmichael() -> Obj

Return the

is_lucas_pseudoprime

Number.is_lucas_pseudoprime() -> Obj

Return the

is_mersenne_prime

Number.is_mersenne_prime() -> Obj

Return the

is_mone

Number.is_mone() -> Obj

Return the

is_nan

Number.is_nan() -> Obj

Return the

is_neg

Number.is_neg() -> Obj

Return the

Aliases: is_negative

is_ninf

Number.is_ninf() -> Obj

Return the

is_nm1_prime

Number.is_nm1_prime() -> Obj

Return the

Aliases: is_nminus1_prime

is_np1_prime

Number.is_np1_prime() -> Obj

Return the

Aliases: is_nplus1_prime

is_odd

Number.is_odd() -> Obj

Return the

is_one

Number.is_one() -> Obj

Return the

is_palindrome

Number.is_palindrome() -> Obj

Return the

Aliases: is_palindromic

is_pell_lucas_pseudoprime

Number.is_pell_lucas_pseudoprime() -> Obj

Return the

is_pell_pseudoprime

Number.is_pell_pseudoprime() -> Obj

Return the

is_perrin_pseudoprime

Number.is_perrin_pseudoprime() -> Obj

Return the

is_plumb_pseudoprime

Number.is_plumb_pseudoprime() -> Obj

Return the

Aliases: is_euler_plumb_pseudoprime

is_polygonal

Number.is_polygonal() -> Obj

Return the

is_polygonal2

Number.is_polygonal2() -> Obj

Return the

is_pos

Number.is_pos() -> Obj

Return the

Aliases: is_positive

is_pow

Number.is_pow() -> Obj

Return the

Aliases: is_power, is_perfect_power

is_powerful

Number.is_powerful() -> Obj

Return the

is_power_of

Number.is_power_of() -> Obj

Return the

is_prime

Number.is_prime() -> Obj

Return the

is_prime_power

Number.is_prime_power() -> Obj

Return the

is_primitive_root

Number.is_primitive_root() -> Obj

Return the

is_prob_prime

Number.is_prob_prime() -> Obj

Return the

is_prob_squarefree

Number.is_prob_squarefree() -> Obj

Return the

is_prov_prime

Number.is_prov_prime() -> Obj

Return the

Aliases: is_provable_prime

is_pseudoprime

Number.is_pseudoprime() -> Obj

Return the

Aliases: is_fermat_pseudoprime

isqrt

Number.isqrt() -> Obj

Return the

isqrtrem

Number.isqrtrem() -> Obj

Return the

is_rat

Number.is_rat() -> Obj

Return the

is_real

Number.is_real() -> Obj

Return the

is_rough

Number.is_rough() -> Obj

Return the

is_safe_prime

Number.is_safe_prime() -> Obj

Return the

is_semiprime

Number.is_semiprime() -> Obj

Return the

is_smooth

Number.is_smooth() -> Obj

Return the

is_smooth_over_prod

Number.is_smooth_over_prod() -> Obj

Return the

is_sqr

Number.is_sqr() -> Obj

Return the

Aliases: is_square, is_perfect_square

is_square_free

Number.is_square_free() -> Obj

Return the

Aliases: is_squarefree

is_stronger_lucas_pseudoprime

Number.is_stronger_lucas_pseudoprime() -> Obj

Return the

Aliases: is_extra_strong_lucas_pseudoprime

is_strong_fibonacci_pseudoprime

Number.is_strong_fibonacci_pseudoprime() -> Obj

Return the

is_strongish_lucas_pseudoprime

Number.is_strongish_lucas_pseudoprime() -> Obj

Return the

is_strong_lucas_pseudoprime

Number.is_strong_lucas_pseudoprime() -> Obj

Return the

is_strong_pseudoprime

Number.is_strong_pseudoprime() -> Obj

Return the

Aliases: is_strong_fermat_pseudoprime

is_super_pseudoprime

Number.is_super_pseudoprime() -> Obj

Return the

is_totient

Number.is_totient() -> Obj

Return the

isub

Number.isub() -> Obj

Return the

is_underwood_pseudoprime

Number.is_underwood_pseudoprime() -> Obj

Return the

Aliases: is_frobenius_underwood_pseudoprime

is_zero

Number.is_zero() -> Obj

Return the

jacobi

Number.jacobi() -> Obj

Return the

jordan_totient

Number.jordan_totient() -> Obj

Return the

kronecker

Number.kronecker() -> Obj

Return the

laguerre

Number.laguerre() -> Obj

Return the

Aliases: laguerreL, laguerre_polynomial

lambda

    lambda(n)

Carmichael lambda function: λ(n), defined as the smallest positive integer m such that:

    aᵐ ≡ 1 (mod n)

for every integer a between 1 and n that is coprime to n.

Alias: carmichael_lambda.

lambert_w

Number.lambert_w() -> Obj

Return the

lcm

Number.lcm() -> Obj

Return the

legendre

Number.legendre() -> Obj

Return the

legendre_P

Number.legendre_P() -> Obj

Return the

Aliases: legendrep, legendreP, legendre_polynomial

len

Number.len() -> Obj

Return the

Aliases: size, length

lgamma

Number.lgamma() -> Obj

Return the

Aliases: gamma_abs_log

lgrt

Number.lgrt() -> Obj

Return the

li

Number.li() -> Obj

Return the

li2

Number.li2() -> Obj

Return the

liouville

Number.liouville() -> Obj

Return the

liouville_sum

Number.liouville_sum() -> Obj

Return the

ln

Number.ln() -> Obj

Return the

ln2

Number.ln2() -> Obj

Return the

lnbern

Number.lnbern() -> Obj

Return the

Aliases: bern_log, lnbernreal, bernoulli_log

lngamma

Number.lngamma() -> Obj

Return the

Aliases: gamma_log

lnsuperfactorial

Number.lnsuperfactorial() -> Obj

Return the

Aliases: superfactorial_ln, superfactorial_log

log

Number.log() -> Obj

Return the

log10

Number.log10() -> Obj

Return the

log2

Number.log2() -> Obj

Return the

logarithmic_derivative

Number.logarithmic_derivative() -> Obj

Return the

lpf

Number.lpf() -> Obj

Return the

lsb

Number.lsb() -> Obj

Return the

lucas

Number.lucas() -> Obj

Return the

lucas_mod

Number.lucas_mod() -> Obj

Return the

Aliases: lucasmod

lucas_U

Number.lucas_U() -> Obj

Return the

Aliases: lucasu, lucasU

lucasumod

Number.lucasumod() -> Obj

Return the

Aliases: lucasUmod

lucasuvmod

Number.lucasuvmod() -> Obj

Return the

Aliases: lucasUVmod

lucas_V

Number.lucas_V() -> Obj

Return the

Aliases: lucasv, lucasV

lucasvmod

Number.lucasvmod() -> Obj

Return the

Aliases: lucasVmod

make_coprime

Number.make_coprime() -> Obj

Return the

mangoldt

Number.mangoldt() -> Obj

Return the

max

Number.max() -> Obj

Return the

mertens

Number.mertens() -> Obj

Return the

mfac

Number.mfac() -> Obj

Return the

Aliases: mfactorial, multi_factorial

miller_rabin_random

Number.miller_rabin_random() -> Obj

Return the

min

Number.min() -> Obj

Return the

mone

Number.mone() -> Obj

Return the

motzkin

Number.motzkin() -> Obj

Return the

msb

Number.msb() -> Obj

Return the

multinomial

Number.multinomial() -> Obj

Return the

nan

Number.nan() -> Obj

Return the

nd

Number.nd() -> Obj

Return the

Aliases: rd, st, th

neg

Number.neg() -> Obj

Return the

new

Number.new() -> Obj

Return the

Aliases: call

next_composite

Number.next_composite() -> Obj

Return the

next_palindrome

Number.next_palindrome() -> Obj

Return the

next_pow

Number.next_pow() -> Obj

Return the

Aliases: next_power

next_pow2

Number.next_pow2() -> Obj

Return the

Aliases: next_power2

next_prime

Number.next_prime() -> Obj

Return the

next_twin_prime

Number.next_twin_prime() -> Obj

Return the

ninf

Number.ninf() -> Obj

Return the

nok

Number.nok() -> Obj

Return the

Aliases: binomial

norm

Number.norm() -> Obj

Return the

nu

Number.nu() -> Obj

Return the

Aliases: numerator

nude

Number.nude() -> Obj

Return the

num2perm

Number.num2perm() -> Obj

Return the

numify

Number.numify() -> Obj

Return the

of

Number.of() -> Obj

Return the

one

Number.one() -> Obj

Return the

partitions

Number.partitions() -> Obj

Return the

Aliases: number_of_partitions

pbrent_factor

Number.pbrent_factor() -> Obj

Return the

perfect_power

Number.perfect_power() -> Obj

Return the

perfect_root

Number.perfect_root() -> Obj

Return the

permutations

Number.permutations() -> Obj

Return the

pi_k

Number.pi_k() -> Obj

Return the

Aliases: k_prime_count, almost_primepi, almost_prime_count

pm1_factor

Number.pm1_factor() -> Obj

Return the

Aliases: pminus1_factor

pn_primes

Number.pn_primes() -> Obj

Return the

pn_primorial

Number.pn_primorial() -> Obj

Return the

polygonal

Number.polygonal() -> Obj

Return the

polygonal_root

Number.polygonal_root() -> Obj

Return the

polygonal_root2

Number.polygonal_root2() -> Obj

Return the

polymod

Number.polymod() -> Obj

Return the

popcount

Number.popcount() -> Obj

Return the

Aliases: hammingweight

power_count

Number.power_count() -> Obj

Return the

Aliases: perfect_power_count

powerful

Number.powerful() -> Obj

Return the

powerful_count

Number.powerful_count() -> Obj

Return the

pp1_factor

Number.pp1_factor() -> Obj

Return the

Aliases: pplus1_factor

prev_prime

Number.prev_prime() -> Obj

Return the

prho_factor

Number.prho_factor() -> Obj

Return the

primality_pretest

Number.primality_pretest() -> Obj

Return the

prime

Number.prime() -> Obj

Return the

Aliases: nth_prime

prime_divisors

Number.prime_divisors() -> Obj

Return the

primepi

Number.primepi() -> Obj

Return the

Aliases: prime_count

primepi_lower

Number.primepi_lower() -> Obj

Return the

Aliases: prime_count_lower

primepi_upper

Number.primepi_upper() -> Obj

Return the

Aliases: prime_count_upper

prime_power

Number.prime_power() -> Obj

Return the

prime_power_count

Number.prime_power_count() -> Obj

Return the

prime_power_divisors

Number.prime_power_divisors() -> Obj

Return the

prime_power_sigma

Number.prime_power_sigma() -> Obj

Return the

prime_power_udivisors

Number.prime_power_udivisors() -> Obj

Return the

Aliases: prime_power_unitary_divisors, unitary_prime_power_divisors

prime_power_usigma

Number.prime_power_usigma() -> Obj

Return the

prime_root

Number.prime_root() -> Obj

Return the

primes

Number.primes() -> Obj

Return the

prime_sigma

Number.prime_sigma() -> Obj

Return the

primes_sum

Number.primes_sum() -> Obj

Return the

Aliases: sum_primes

prime_udivisors

Number.prime_udivisors() -> Obj

Return the

Aliases: prime_unitary_divisors, unitary_prime_divisors

prime_usigma

Number.prime_usigma() -> Obj

Return the

prime_usigma0

Number.prime_usigma0() -> Obj

Return the

primitive_part

Number.primitive_part() -> Obj

Return the

primorial

Number.primorial() -> Obj

Return the

primorial_deflation

Number.primorial_deflation() -> Obj

Return the

primorial_inflation

Number.primorial_inflation() -> Obj

Return the

psi

Number.psi() -> Obj

Return the

Aliases: dedekind_psi

qs_factor

Number.qs_factor() -> Obj

Return the

quadratic_formula

Number.quadratic_formula() -> Obj

Return the

rad

Number.rad() -> Obj

Return the

rad2deg

Number.rad2deg() -> Obj

Return the

ramanujan_sum

Number.ramanujan_sum() -> Obj

Return the

ramanujan_tau

Number.ramanujan_tau() -> Obj

Return the

rand

Number.rand() -> Obj

Return the

random_bytes

Number.random_bytes() -> Obj

Return the

random_maurer_nbit_prime

Number.random_maurer_nbit_prime() -> Obj

Return the

Aliases: random_nbit_maurer_prime

random_nbit_prime

Number.random_nbit_prime() -> Obj

Return the

random_nbit_strong_prime

Number.random_nbit_strong_prime() -> Obj

Return the

Aliases: random_strong_nbit_prime

random_ndigit_prime

Number.random_ndigit_prime() -> Obj

Return the

random_prime

Number.random_prime() -> Obj

Return the

random_safe_prime

Number.random_safe_prime() -> Obj

Return the

random_string

Number.random_string() -> Obj

Return the

range

Number.range() -> Obj

Return the

rat

Number.rat() -> Obj

Return the

Aliases: to_r, to_rat

rat_approx

Number.rat_approx() -> Obj

Return the

re

Number.re() -> Obj

Return the

Aliases: real

reals

Number.reals() -> Obj

Return the

remdiv

Number.remdiv() -> Obj

Return the

Aliases: remove

rising_factorial

Number.rising_factorial() -> Obj

Return the

root

Number.root() -> Obj

Return the

rough_count

Number.rough_count() -> Obj

Return the

round

Number.round() -> Obj

Return the

Aliases: roundf

run

Number.run() -> Obj

Return the

sec

Number.sec() -> Obj

Return the

secant_number

Number.secant_number() -> Obj

Return the

sech

Number.sech() -> Obj

Return the

seed

Number.seed() -> Obj

Return the

semiprime

Number.semiprime() -> Obj

Return the

Aliases: nth_semiprime

semiprime_count

Number.semiprime_count() -> Obj

Return the

setbit

Number.setbit() -> Obj

Return the

sgn

Number.sgn() -> Obj

Return the

Aliases: sign

sigma0

Number.sigma0() -> Obj

Return the

sin

Number.sin() -> Obj

Return the

sin_cos

Number.sin_cos() -> Obj

Return the

sinh

Number.sinh() -> Obj

Return the

smooth_count

Number.smooth_count() -> Obj

Return the

solve_pell

Number.solve_pell() -> Obj

Return the

sopfr

Number.sopfr() -> Obj

Return the

sqr

Number.sqr() -> Obj

Return the

sqrt

Number.sqrt() -> Obj

Return the

sqrt_cfrac

Number.sqrt_cfrac() -> Obj

Return the

sqrt_cfrac_period

Number.sqrt_cfrac_period() -> Obj

Return the

sqrt_cfrac_period_len

Number.sqrt_cfrac_period_len() -> Obj

Return the

sqrtmod

Number.sqrtmod() -> Obj

Return the

square_divisors

Number.square_divisors() -> Obj

Return the

squarefree

Number.squarefree() -> Obj

Return the

square_free_count

Number.square_free_count() -> Obj

Return the

Aliases: squarefree_count

squarefree_divisors

Number.squarefree_divisors() -> Obj

Return the

squarefree_sigma

Number.squarefree_sigma() -> Obj

Return the

squarefree_udivisors

Number.squarefree_udivisors() -> Obj

Return the

Aliases: squarefree_unitary_divisors, unitary_squarefree_divisors

squarefree_usigma

Number.squarefree_usigma() -> Obj

Return the

squarefree_usigma0

Number.squarefree_usigma0() -> Obj

Return the

square_sigma

Number.square_sigma() -> Obj

Return the

square_sigma0

Number.square_sigma0() -> Obj

Return the

square_udivisors

Number.square_udivisors() -> Obj

Return the

Aliases: square_unitary_divisors, unitary_square_divisors

square_usigma

Number.square_usigma() -> Obj

Return the

square_usigma0

Number.square_usigma0() -> Obj

Return the

squfof_factor

Number.squfof_factor() -> Obj

Return the

stirling

Number.stirling() -> Obj

Return the

Aliases: stirling1

stirling2

Number.stirling2() -> Obj

Return the

stirling3

Number.stirling3() -> Obj

Return the

subfactorial

Number.subfactorial() -> Obj

Return the

subsets

Number.subsets() -> Obj

Return the

superfactorial

Number.superfactorial() -> Obj

Return the

tan

Number.tan() -> Obj

Return the

tangent_number

Number.tangent_number() -> Obj

Return the

tanh

Number.tanh() -> Obj

Return the

times

Number.times() -> Obj

Return the

to_f

Number.to_f() -> Obj

Return the

Aliases: float, to_float

to_n

Number.to_n() -> Obj

Return the

Aliases: to_num

to_s

Number.to_s() -> Obj

Return the

Aliases: to_str

totient

Number.totient() -> Obj

Return the

Aliases: euler_phi, eulerphi, euler_totient

trial_factor

Number.trial_factor() -> Obj

Return the

tuples

Number.tuples() -> Obj

Return the

Aliases: variations

tuples_with_repetition

Number.tuples_with_repetition() -> Obj

Return the

Aliases: variations_with_repetition

udivisors

Number.udivisors() -> Obj

Return the

Aliases: unitary_divisors

uphi

Number.uphi() -> Obj

Return the

usigma

Number.usigma() -> Obj

Return the

usigma0

Number.usigma0() -> Obj

Return the

Aliases: squarefree_sigma0

valuation

Number.valuation() -> Obj

Return the

zero

Number.zero() -> Obj

Return the

znorder

Number.znorder() -> Obj

Return the

znprimroot

Number.znprimroot() -> Obj

Return the

To install Sidef, copy and paste the appropriate command in to your terminal.

cpanm

cpanm Sidef

CPAN shell

perl -MCPAN -e shell
install Sidef

For more information on module installation, please visit the detailed CPAN module installation guide.

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