chunky

# Feature Release steps

 - tests passing
 - mix format
 - inline documentation
 - top of module documentation
 - version bump in mix.exs
 - version bump in README.md
 - version bump in CHANGELOG
 - version bump in library.md
 - update OEIS stats for release version
 - git tag -a v0.x.x -m "v0.x.x - summary"
 - git push
 - git push --tags
 - mix hex.publish

# CHANGELOG

## v0.11.2

### Build/Development changes

 - Module requiring HTTPoison and Jason excluded from packaging
 - HTTPoison and Jason moved to `dev` and `test` only requirements
 - Credo is now being used for style/consistency checks (with specific configuration to make credo run in a reasonable time frame)
 - new documentation as main page for hexdocs (library.md)
 
### Libraries

 - Refactored Fractions.lcm/1 and Fractions.lcm/2 to Math.lcm/1 and Math.lcm/2
 - Refactored nth_root/3, integer_nth_root?/3, and floats_equal?/3 from Fractions to Math
 - Updated all cached Math functions to use CacheAgent.cache_as macro

### Sequences

 - Moved A000045/Fibonacci from Sequence.OEIS to Sequence.OEIS.Core
  

## v0.11.1

### Enhancements

 - Chunky.Math
  - `analyze_number/2` - Run all predicates against `n` to generate labels for `n`
  - `is_odd?/1` - New predicate
  - `is_even?/1` - New predicate
  - `is_zero?/1` - New predicate
  - `is_positive?/1` - New predicate
  - `is_negative?/1` - New predicate
  - all predicates of form `is_*?/1` now work for all integers in range `(-∞..+∞)


## v0.11.0

```
OEIS Coverage
        210 total sequences
By Module
        Elixir.Chunky.Sequence.OEIS - 3 sequences
        Elixir.Chunky.Sequence.OEIS.Core - 88 sequences
        Elixir.Chunky.Sequence.OEIS.Factors - 98 sequences
        Elixir.Chunky.Sequence.OEIS.Primes - 1 sequences
        Elixir.Chunky.Sequence.OEIS.Sigma - 20 sequences
Sequence Groups
        OEIS Core Sequences - 89 / 177 (50.28%)
        OEIS Core::Easy Sequences - 75 / 146 (51.37%)
        OEIS Core::Hard Sequences - 12 / 12 (100.0%)
        OEIS Core::Multiplicative Sequences - 22 / 22 (100.0%)
        OEIS Core::Eigen Sequences - 5 / 5 (100.0%)
```

### Enhancements

 - added Chunky.CacheAgent - caching agent for particularly recursive functions
 - Chunky.Math
  - ramanujan_tau/1 - Find the ramanujan tau error value for `n`
  - partition_count/1 - Recursive (and cached) Partition Function for `n`
  - abelian_group_count/1 - Number of Abelian groups of order `n`
  - p_adic_valuation/2 - The _p-adic_ valuation function (for prime `p` and integer `n`)
  - rooted_tree_count/1 - Rooted trees of N nodes
  - is_of_form_mx_plus_b/3 - Does number have form `mx + b` for strict values of `m` and `b`?
  - divisors_of_form_mx_plus_b/3 - Find divisors of `n` that are of form `mx + b`
  - hurwitz_radon_number/1 - find the hurwitz-radon number of `n`
  - catalan_number/1 - Find `C(n)`, the Catalan number, of `n`
  - euler_zig_zag/1 - Permutation set sizes
  - factorial/1 - Factorial `n!`
  - binomial/2 - Binomial coefficient over `(n k)`
  - wedderburn_etherington_number/1 - Count of permutations of binary rooted trees of size `n`
  - functions for calculating positions in euler/pascal/element triangles
  - eulerian_number/2
  - euler_number
  - combinatorics counting methods
  - ...
  
  
### New Sequences

 - OEIS Core
     - A000001 - Number of groups of order n
     - A000002 - Kolakoski sequence
     - A000004 - The zero sequence
     - A000007 - The characteristic function of {0}: a(n) = 0^n
     - A000012 - The simplest sequence of positive numbers: the all 1's sequence
     - A000027 - The positive integers
     - A000032 - Lucas numbers beginning at 2
     - A000035 - Period 2: repeat [0, 1]
     - A000040 - The prime numbers.
     - A000043 - Mersenne exponents: primes p such that 2^p - 1 is prime.
     - A000069 - Odious numbers: numbers with an odd number of 1's in their binary expansion
     - A000081 - Number of unlabeled rooted trees with n nodes
     - A000085 - Number of self-inverse permutations on n letters, also known as involutions
     - A000105 - Number of free polyominoes (or square animals) with n cells
     - A000108 - Catalan numbers: C(n), Also called Segner numbers.
     - A000109 - Number of simplicial polyhedra with n nodes
     - A000110 - Bell or exponential numbers: number of ways to partition a set of n labeled elements
     - A000111 - Euler or up/down numbers
     - A000112 - Number of partially ordered sets ("posets") with n unlabeled elements
     - A000120 - 1's-counting sequence: number of 1's in binary expansion of n (or the binary weight of n)
     - A000124 - Central polygonal numbers (the Lazy Caterer's sequence)
     - A000129 - Pell numbers: a(n) = 2*a(n-1) + a(n-2)
     - A000142 - Factorial numbers: n! = 1*2*3*4*...*n 
     - A000166 - Subfactorial or rencontres numbers, or derangements of `n`
     - A000169 - Number of labeled rooted trees with n nodes: n^(n-1)
     - A000204 - Lucas numbers (beginning with 1)
     - A000217 - Triangular numbers: a(n) = binomial(n+1,2)
     - A000219 - Number of planar partitions (or plane partitions) of n
     - A000225 - a(n) = 2^n - 1
     - A000262 - Number of "sets of lists"
     - A000272 - Number of trees on n labeled nodes
     - A000292 - Tetrahedral (or triangular pyramidal) numbers
     - A000312 - a(n) = n^n; number of labeled mappings from n points to themselves
     - A000326 - Pentagonal numbers: a(n) = n*(3*n-1)/2.
     - A000330 - Square pyramidal numbers
     - A000364 - Euler (or secant or "Zig") numbers
     - A000521 - Coefficients of modular function j as power series in q = e^(2 Pi i t)
     - A000583 - Fourth powers: a(n) = n^4.
     - A000594 - Ramanujan's tau function
     - A000609 - Number of threshold functions of n or fewer variables
     - A000670 - Fubini numbers
     - A000688 - Number of Abelian groups of order n
     - A000720 - pi(n), the number of primes <= n.
     - A000796 - Decimal expansion of Pi
     - A000798 - Number of different quasi-orders (or topologies, or transitive digraphs) with n labeled elements
     - A001190 - Wedderburn-Etherington numbers: unlabeled binary rooted trees
     - A001227 - Number of odd divisors of n.
     - A001477 - The nonnegative integers.
     - A001511 - The ruler function: 2^a(n) divides 2n
     - A002106 - Number of transitive permutation groups of degree n
     - A002654 - Number of ways of writing n as a sum of at most two nonzero squares, where order matters
     - A003094 - Number of unlabeled connected planar simple graphs with n nodes
     - A003484 - Radon function, also called Hurwitz-Radon numbers
     - A005470 - Number of unlabeled planar simple graphs with n nodes
     - A006966 - Number of lattices on n unlabeled nodes
     - A008292 - Triangle of Eulerian numbers T(n,k)
     - A055512 - Lattices with n labeled elements

 - OEIS Factors
 
     - A001826 - Number of divisors of n of form 4k+1
     - A001842 - Expansion of Sum_{n>=0} x^(4*n+3)/(1 - x^(4*n+3))
     
     
## v0.10.0

```
OEIS Coverage
        144 total sequences
By Module
        Elixir.Chunky.Sequence.OEIS - 3 sequences
        Elixir.Chunky.Sequence.OEIS.Core - 24 sequences
        Elixir.Chunky.Sequence.OEIS.Factors - 96 sequences
        Elixir.Chunky.Sequence.OEIS.Primes - 1 sequences
        Elixir.Chunky.Sequence.OEIS.Sigma - 20 sequences
Sequence Groups
        OEIS Core Sequences - 25 / 177 (14.12%)
```

### Enhancements

 - Chunky.Math
  - jordan_totient/2 - Jordan totient `J-k(n)`
  - mobius_function/1 - Classical mobius function
  - omega/1 - Count of distinct prime factors
  - bigomega/1 - Count of distinct prime factors, with multiplicity
  - greatest_prime_factor/1 - largest prime factor of `n`
  - least_prime_factor/1 - smallest prime factor of `n`
  - tau/1 - Tau function, number of divisors of `n`
  - is_squarefree?/1 - Are any factors of `n` perfect squares?
  - is_cubefree?/1 - Are any factors of `n` perfect cubes?
  - radical/1 - Square-free kernel, or `rad(n)` - product of distict prime factors
  - prime_factor_exponents/1 - Find the exponents of all prime factors of `n`
  - is_power_of?/2 - Is `n` a power of `m`?
  - is_sphenic_number?/1 - Is `n` the product of three distinct primes?
  
### New Sequences

 - A007434 - Jordan-2 totient `J_2(n)`
 - A059376 - Jordan function J_3(n)
 - A059377 - Jordan function J_4(n)
 - A059378 - Jordan function J_5(n)
 - A065958 - a(n) = n^2*Product_{distinct primes p dividing n} (1+1/p^2)
 - A065959 - a(n) = n^3*Product_{distinct primes p dividing n} (1+1/p^3)
 - A065960 - a(n) = n^4*Product_{distinct primes p dividing n} (1+1/p^4)
 - A069091 - Jordan function J_6(n)
 - A069092 - Jordan function J_7(n)
 - A069093 - Jordan function J_8(n)
 - A069094 - Jordan function J_9(n)
 - A069095 - Jordan function J_10(n)
 - A160889 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 4
 - A160891 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 5
 - A160893 - a(n) = Sum_{d|n} Möbius(n/d)*d^5/phi(n)
 - A160895 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 7
 - A160897 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 8
 - A160908 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 9
 - A160953 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 10
 - A160957 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 11
 - A160960 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 12
 - A001615 - Dedekind psi function
 - A008683 - Möbius (or Moebius) function mu(n)
 - A001221 - Number of distinct primes dividing n (also called omega(n))
 - A001222 - Number of prime divisors of n counted with multiplicity (also called bigomega(n) or Omega(n))
 - A006530 - Gpf(n): greatest prime dividing n
 - A020639 - Lpf(n): least prime dividing n
 - A000244 - Powers of 3
 - A000290 - The squares: a(n) = n^2
 - A000302 - Powers of 4: a(n) = 4^n
 - A000578 - The cubes: a(n) = n^3.
 - A001358 - Semiprimes (or biprimes): products of two primes
 - A005117 - Squarefree numbers: numbers that are not divisible by a square greater than 1
 - A000037 - Numbers that are not squares
 - A000977 - Numbers that are divisible by at least three different primes
 - A004709 - Cubefree numbers: numbers that are not divisible by any cube > 1
 - A006881 - Squarefree semiprimes: Numbers that are the product of two distinct primes
 - A007018 - a(n) = a(n-1)^2 + a(n-1), a(0)=1
 - A007304 - Sphenic numbers: products of 3 distinct primes
 - A007412 - The noncubes: n + [ (n + [ n^{1/3} ])^{1/3} ]
 - A007774 - Numbers that are divisible by exactly 2 different primes
 - A007947 - Largest squarefree number dividing n
 - A008966 - 1 if n is squarefree, else 0.
 - A013929 - Numbers that are not squarefree.
 - A014612 - Numbers that are the product of exactly three primes, including multiplicity.
 - A014613 - Numbers that are products of 4 primes
 - A014614 - Numbers that are products of 5 primes
 - A030513 - Numbers with 4 divisors
 - A030515 - Numbers with exactly 6 divisors
 - A033273 - Number of nonprime divisors of n
 - A033942 - At least 3 prime factors (counted with multiplicity).
 - A033987 - Numbers that are divisible by at least 4 primes (counted with multiplicity)
 - A033992 - Numbers that are divisible by exactly three different primes
 - A033993 - Numbers that are divisible by exactly four different primes
 - A036537 - Numbers whose number of divisors is a power of 2.
 - A037143 - Numbers with at most 2 prime factors (counted with multiplicity).
 - A038109 - Divisible exactly by the square of a prime.
 - A039956 - Even squarefree numbers.
 - A046099 - Numbers that are not cubefree. Numbers divisible by a cube greater than 1. 
 - A046306 - Numbers that are divisible by exactly 6 primes with multiplicity.
 - A046308 - Numbers that are divisible by exactly 7 primes counting multiplicity.
 - A046310 - Numbers that are divisible by exactly 8 primes counting multiplicity
 - A046312 - Numbers that are divisible by exactly 9 primes with multiplicity
 - A046314 - Numbers that are divisible by exactly 10 primes with multiplicity
 - A046321 - Odd numbers divisible by exactly 8 primes (counted with multiplicity)
 - A046386 - Products of four distinct primes
 - A046387 - Products of 5 distinct primes
 - A046660 - Excess of n = Ω(n) - ω(n)
 - A048272 - Number of odd divisors of n minus number of even divisors of n
 - A051270 - Numbers that are divisible by exactly 5 different primes
 - A056911 - Odd squarefree numbers.
 - A059269 - Numbers n for which tau(n) is divisible by 3.
 - A067259 - Cubefree numbers which are not squarefree
 - A067885 - Product of 6 distinct primes
 - A069272 - 11-almost primes (generalization of semiprimes)
 - A069273 - 12-almost primes (generalization of semiprimes)
 - A069274 - 13-almost primes (generalization of semiprimes)
 - A069275 - 14-almost primes (generalization of semiprimes)
 - A069276 - 15-almost primes (generalization of semiprimes)
 - A069277 - 16-almost primes (generalization of semiprimes)
 - A069278 - 17-almost primes (generalization of semiprimes)
 - A069279 - Products of exactly 18 primes (generalization of semiprimes)
 - A069280 - 19-almost primes (generalization of semiprimes)
 - A069281 - 20-almost primes (generalization of semiprimes)
 - A074969 - Numbers with six distinct prime divisors
 - A076479 - a(n) = mu(rad(n)), where mu is the Moebius-function
 - A117805 - Start with 3. Square the previous term and subtract it.
 - A123321 - Products of 7 distinct primes
 - A123322 - Products of 8 distinct primes
 - A130897 - Numbers that are not exponentially squarefree.
 - A162643 - Numbers such that their number of divisors is not a power of 2.
 - A209061 - Exponentially squarefree numbers
 - A211337 - Numbers n for which the number of divisors, tau(n), is congruent to 1 modulo 3
 - A211338 - Numbers n for which the number of divisors, tau(n), is congruent to 2 modulo 3
 

## v0.9.0

### Changes/Refactorizations

### Enhancements

 - Chunky.Math
  - is_abundant?/1 - Is a number `n` an Abundant number
  - next_abundant/1 - Find the next abundant number after `n`
  - is_perfect?/1 - Is a number `n` a perfect number
  - is_deficient?/1 - Is a number `n` a deficient number
  - next_deficient/1 - Find the next deficient number
  - is_arithmetic_number?/1 - Is a number `n` an arithmetic number
  - aliquot_sum/1 - Aliquot Sum of `n`
  - is_highly_abundant?/1` - Is a number `n` highly abundant?
  - is_powerful_number?/1 - Is a number `n` a powerful number?
  - product_of_prime_factors/1 - Number theoretical function for product of prime factor exponents of `n`
  - is_highly_powerful_number?/1 - Is a number a _highly powerful_ number?
  - is_perfect_power?/1 - Is integer `n` a perfect power?
  - is_perfect_square?/1 - Is integer `n` a perfect square?
  - is_perfect_cube?/1 - Is integer `n` a perfect cube?
  - is_root_of?/2 - Is integer `n` any k-th root of `m`?
  - is_achilles_number?/1 - Is integer `n` an achilles number?
  - is_coprime?/2 - Test if `m` and `n` are co-prime
  - totient/1 - Calculate Euler's totient for `n`
  
 - Chunky.Sequence
  - drop/2 - Like Enum.drop
  
### New Sequences
 
 - A001065 - Aliquot parts of N
 - A005101 - Abundant Numbers
 - A000396 - Perfect Numbers
 - A005100 - Deficient Numbers
 - A003601 - Arithmetic Numbers
 - A002093 - Highly Abundant Numbers
 - Added Sequences.OEIS.Factors module
 - A001694 - Powerful Numbers
 - A005361 - Product of Prime Exponents of factors of N
 - A005934 - Highly powerful numbers: numbers with record value
 - A001597 - Perfect Powers
 - A052486 - Achilles Numbers
 - A000010 - Euler's totient function

## v0.8.0

### Changes/Refactorizations

### Enhancements

 - Chunky.Sequence
  - sequences are now marked as finite or infinite (as computable/stored in Squence library)
  - sequences can now have initial index/offset other than 0 (like A000593)
  - New Functions:
   - `is_finite?/1` - Is a sequence finite or infinite is sequence library?
 - Chunky.Math
  - `factors/1` - All divisors of N
  - `sigma/1` - Sigma-1 function of factors of N
  - `sigma/2` - Generalized Sigma function
  - `pow/2` - Pure integer exponentiation
  
### New Sequences

 - A000593 - Sum of Odd Divisors of N
 - A000009 - Number of partitions of n into distinct parts
 - A000079 - Powers of 2
 - A000203 - Sigma-1 of N
 - A001057 through A001060 - sigma2 through sigma5 of N
 - A013954 through A013968 - sigma6 through sigma20 of N
 
 
## v0.7.0

### Enhancements

 - `Chunky.Math` - Extended math for integers and floating point
  - `pow/3` - Modular arithmetic exponentiation
  - `is_prime?/1` - Primality test for integers
  - `prime_factors/1` - Factorize an integer to prime factors
  
 - `Chunky.Sequences` - Create, inspect, manipulate, iterate, and compare finite and infinite value sequences
  - New functions:
   - `create/3` - Create a new sequence instance
   - `available/0` - List all loaded sequences from all loaded applications and modules
   - `available/1` - List available sequences from a module
   - `has_next?/1` - Check that a sequence has at least one more available value
   - `is_available?/2` - Check if a specific sequence is available
   - `is_instance/2` - Check if a sequence is an instance of a specific sequence identifier
   - `is_instance/3` - Check if a sequence is an instance of a specific sequence identifier
   - `get_references/1` - Retrieve reference sources and links for a sequence
   - `has_reference?/2 - Check if a sequence has a specific reference source
   - `readable_name/1` - Find the human readable name of a sequence
   - `next/1` - Retrieve the next sequence value and updated sequence struct as a tuple
   - `next!/1` - Retrieve the next sequence as just an updated sequence struct
   - `take/2` - Like `Enum.take/2` - retrieve a list of values from a sequence
   - `take!/2` - Like `take/2`, but only return the updated sequence struct
   - `sequence_for_function/1` - Wrap a function as a sequence - see Developing New Sequences
   - `sequence_for_list/1` - Wrap a list as a sequence - see Developing New Sequences
   - `map/2` - Apply a function to values in a sequence, and collect the result
  - New Sequences:
   - `{Basic, :whole_numbers}` - Whole number sequence, starting from `1` or any other digit
   - `{Basic, :empty}` - The empty sequence
   - `{Basic, :decimal_digits}` - The decimal digits
   - `{OEIS, :a000045}` - OEIS - Fibonacci sequence
   - `{OEIS, :fibonacci}` - OEIS - alternate name, Fibonacci sequence
   - `{OEIS, :keyword_core}` - OEIS - List of core sequences, according to OEIS
   - `{OEIS, :a000041}` - OEIS - Partitions of Integers
   - Various test sequences

 
## v0.6.5

### Enhancements

 - `Chunky.Fractions`
  - added `uniq/2` for finding distinct fractions in a list
  - added `sort/2` for sorting value lists
  - added `clamp/2` for constraining value lists
  
## v0.6.4

### Enhancements

 - `Chunky.Fraction`
  - Most functions now use type coercion to handle any value that can be converted to a fraction via `new/1`
  
## v0.6.3

### Enhancements

 - `Chunky.Fraction`
  - `to_float/2` - convert to a float, with optional precision rounding
  - `min_of/1` - find the smallest from a list of fractions
  - `min_of/2` - find the smallest of two fractions
 - `Chunky.Grid`
  - `put_all/2` - basic function for putting `{x, y, v}` tuples  or `%{x: x, y: y, value: value}` maps into the grid
  - `find_index/2` - Find coordinates in grid of a value
  
## v0.6.2

### Documentation

 - `Chunky.Fraction` - Enhancements to documentation. Extended doctests


## v0.6.1

### Enhancements

 - `Chunky.Grid`
  - `put_at/3` and `put_at/4` - put values into the grid
  
## v0.6.0

### Enhancements

 - `Chunky.Fraction` module for manipulating fractions
  - `new/2` - create a new fraction
  - `new/1` - create a new fraction from a tuple or integer
  - `has_whole?/1` - fractions is greater than 1, and has a whole component
  - `is_whole?/1` - does a fraction exactly represent a whole number
  - `components/1` - tuple of numerator an denominator
  - `get_whole/1` - get reduced whole component of a fraction
  - `get_remainder/1` - get remainder of fraction after removing whole components
  - `split/1` - combine `get_whole/1` and `get_remainder/1` into one call
  - `is_simplified?/1` - is fraction in reduced form?
  - `simplify/1` - reduce fraction
  - `is_zero?/1` - does fraction represent zero?
  - `add/3` - Add two fractions, or a fraction and an integer
  - `subtract/3` - Subtract two fractions, or a fraction and an integer
  - `String.Chars` - Fractions now work properly with IO functions
  - `multiply/3` - Multiply two fractions, or a fraction and an integer
  - `reciprocal/2` - Take the reciprocal of a fraction
  - `divide/3` - Divide two fractions, or a fraction and an integer
  - `normalize/2` - Normalize two fractions to a common denominator
  - `is_positive?/1` - Test if a fraction is positive
  - `is_negative?/2` - Test if a fraction is negative
  - `power/3` - Fractional and integer powers of integers and fractions
  - `gt?/2`, `gte?/2`, `lt?/2`, `lte?/2`, and `eq?/2` added for comparison between fractions and fractions and integers
  - `normalize_all/1` - normalize a list of fractions and integers, like `normalize/2`
  - `sum/2` - sum a list of fractions and integers
  - `lcm/1` - find Least Common Multiple from a list of integers

 - `Chunky.Grid` module for working with two dimensional data
  - `Grid.new/3` - generate a grid from a value or a function
  - `Grid.get_at/2` and `Grid.get_at/3` - access cell value by 2d index
  - `Grid.valid_coordinate/*` and `Grid.valid_coordinate?/*` - determine if a coordinate is within grid bounds
  
## v0.5.0

### Enhancements

 - `Chunky.combinations_size/2` - pre-calculate the size of a combination using a closed form equation, instead of running the combination
 
## v0.4.1

### Documentation

 - Fixes for embedded `@moduledoc` for better Hexdocs layout
 
## v0.4.0

### Enhancements

 - `Chunky.permutations_size/1` - pre-calculate the size of a permutation using a closed form equation, instead of running the permutation
 
## v0.3.0

### Enhancements

 - Added `Chunky.combinations/2` for nCr unordered set generation
 
### Documentation

 - move all TODO items out of Chunky module
 - remove references to incomplete/unimplemented functions

## v0.2.1

### Documentation

 - Fix reference to `Chunky.chunk_length/2` in moduledoc
 
## v0.2.0

### Enhancements

 - `Chunky.chunk_length/2` added. Supports `list`, `tuple`, `binary`, and `range` types
 
### Documentation

 - Cleanup of readme and top level documentation
 - Hexdocs now have embedded readme data
 
## v0.1.1

### Documentation

 - Expanded documentation for `Chunky.permutations/1`
 
## v0.1.0

### Enhancements

 - `Chunky.permutations/1` added. Supports `list`, `tuple`, `binary`, and `range` types