h$Ʉ      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijkl m n o p q r s t u v w x y z { | } ~              !!!!!!""""""""""#$%%%%%%%%&&&&&&&&''''((((((((((())))))))))))))))))))))))))))****++++++++++++,-.///////000000001222222233333333344455555555555556777777778999999999 Safe-Inferred factory Describes an  exponential, in terms of its base and exponent.factory Accessor.factory Accessor.factory Construct an  merely raised to the 1st power.The value of the resulting exponential is the same as specified base;  .https://en.wikipedia.org/wiki/Identity_element.factoryEvaluate the specified !, returning the resulting number.factory True if the bases are equal.factoryRaise the specified  to a power.factory+Invert the value, by negating the exponent.factory The operand.factory3The power to which the exponential is to be raised.factory The result.48Nonew factoryGenerates multiples of the specified prime, starting from its square, skipping those multiples of the low primes from which the specified ') was composed, and which therefore, the wheel" won't generate as candidates. Eg:  Prime Rotating PrimeWheel 3 Output ===== ===================== ====== 7 [4,2,4,2,4,6,2,6] [49,77,91,119,133,161,203,217,259 ..] 11 [2,4,2,4,6,2,6,4] [121,143,187,209,253,319,341,407 ..] 13 [4,2,4,6,2,6,4,2] [169,221,247,299,377,403,481,533,559 ..]0factory!The number to square and multiplyfactoryA  rolling wheel0, the track of which, delimits the gaps between coprime candidates. $%&'()*+,-./0 $%&'(),0/.-*+None12factory5The list-length beneath which to terminate bisection.3factory9The ratio of the original list-length at which to bisect.CAVEAT: the value can overflow.4factory4Reduces a list to a single scalar encapsulated in a  , using a divide-and-conquer strategy, bisecting the list and recursively evaluating each part;  :https://en.wikipedia.org/wiki/Divide_and_conquer_algorithm.By choosing a bisectionRatio other than (1 % 2), the bisection can be made asymmetrical. The specified ratio represents the length of the left-hand portion, over the original list-length; eg. (1 % 3): results in the first part, half the length of the second.This process of recursive bisection, is terminated beneath the specified minimum list-length, after which the monoid's binary operator is directly folded over the list.One can view this as a  https://en.wikipedia.org/wiki/Hylomorphism_%28computer_science%29, in which the list is exploded into a binary tree-structure (each leaf of which contains a list of up to  minLength integers, and each node of which contains an associative binary operator), and then collapsed to a scalar, by application of the operators.5factory)Multiplies the specified list of numbers.Since the result can be large, 4 is used in an attempt to form operands of a similar order of magnitude, which creates scope for the use of more efficient multiplication-algorithms.6factory#Sums the specified list of numbers.Since the result can be large, 4 is used in an attempt to form operands of a similar order of magnitude, which creates scope for the use of more efficient multiplication-algorithms. Multiplication is required for the addition of  numbers by cross-multiplication; this function is unlikely to be useful for other numbers.4factory9The ratio of the original list-length at which to bisect.factoryFor efficiency, the list will not be bisected, when it's length has been reduced to this value.factoryThe list on which to operate.factoryThe resulting scalar.5factory9The ratio of the original list-length at which to bisect.factoryFor efficiency, the list will not be bisected, when it's length has been reduced to this value.factory&The numbers whose product is required.factoryThe resulting product.6factory9The ratio of the original list-length at which to bisect.factoryFor efficiency, the list will not be bisected, when it's length has been reduced to this value.factory"The numbers whose sum is required.factoryThe resulting sum.2345632456None6 7factoryfactorySquare the ring. 798=>:;:;<@A?8697=6?8None9JfactoryDefines a sub-class of 7#, in which division is implemented.Lfactory Returns the quotient&, after division of the two specified Js.Mfactory Returns the  remainder&, after division of the two specified Js.Nfactory if the two specified Js are  congruent in modulo-arithmetic, where the modulus is a third J. 3http://www.usna.edu/Users/math/wdj/book/node74.html.OfactoryTrue if the second operand divides the first.KfactoryDivides the first operand by the second, to yield a pair composed from the quotient and the  remainder.Lfactory Numerator.factory Denominator.Mfactory Numerator.factory Denominator.NfactoryLHS.factoryRHS.factoryModulus.Ofactory Numerator.factory Denominator.JKLMNOJKLMNONoneJPfactoryThe type of an arbitrary  univariate polynomial; actually it's more general, since it permits negative powers ( 0https://en.wikipedia.org/wiki/Laurent_polynomials). It can't describe  multivariate, polynomials, which would require a list of  exponents. Rather than requiring the exponent to implement the  type-class 9, this is implemented at the function-level, as required.#The structure permits gaps between  exponents , in which  coefficients are inferred to be zero, thus enabling efficient representation of sparse polynomials. CAVEAT: the  is required to; be ordered by  descending exponent (ie. reverse  ,https://en.wikipedia.org/wiki/Monomial_order9); have had zero coefficients removed; and to have had like; terms merged; so the raw data-constructor isn't exported.Qfactory+Transforms the data behind the constructor.CAVEAT: similar to :;, but P isn't an instance of :<& since we may want to operate on both type-parameters.%CAVEAT: the caller is required to re-T the resulting polynomial depending on the nature of the transformation of the data.Rfactory7Returns the number of non-zero terms in the polynomial.Sfactory#Return the highest-degree monomial.Tfactory Sorts into descending order of exponents, groups like exponents, and calls .UfactoryConstructs an arbitrary zeroeth-degree polynomial, ie. independent of the  indeterminate.VfactoryConstructs an arbitrary first-degree polynomial.Wfactory+Smart constructor. Constructs an arbitrary  polynomial.Xfactory Constructs a  polynomial with zero terms.YfactoryConstructs a constant monomial, independent of the  indeterminate.Zfactory True if the  exponents of successive terms are in  ascending order.[factory True if the  exponents of successive terms are in  descending order.\factoryTrue if no term has a  coefficient of zero and the  exponents of successive terms are in  descending order.]factory if the leading coefficient is one. >https://en.wikipedia.org/wiki/Monic_polynomial#Classifications.^factoryTrue if there are zero terms._factory!True if there's exactly one term.`factory True if all  exponents are positive integers as required.afactory if the two specified  polynomials are  congruent in modulo -arithmetic. =https://planetmath.org/encyclopedia/PolynomialCongruence.html.bfactory Return the degree (AKA order ) of the  polynomial. 4https://en.wikipedia.org/wiki/Degree_of_a_polynomial. 3https://mathworld.wolfram.com/PolynomialDegree.html.cfactoryScale-up the specified  polynomial by a constant monomial factor. 3https://en.wikipedia.org/wiki/Scalar_multiplication.dfactoryRaise a  polynomial5 to the specified positive integral power, but using modulo -arithmetic.+Whilst one could naively implement this as (x Data.Ring.=^ n)  m, this will result in arithmetic operatons on unnecessarily big integers.efactory#Reduces all the coefficients using modular arithmetic.ffactory Evaluate the  polynomial at a specific  indeterminate.CAVEAT: requires positive exponents; but it wouldn't really be a  polynomial otherwise.If the  polynomial4 is very sparse, this may be inefficient, since it memoizes8 the complete sequence of powers up to the polynomial's degree.gfactoryConvert the type of the  coefficients.hfactoryDefines the ability to divide  polynomials.ifactoryMakes  Polynomial a 7 , over the field composed from all possible  coefficients;  -https://en.wikipedia.org/wiki/Polynomial_ring.Vfactory Gradient.factory Constant.afactoryLHS.factoryRHS.factoryModulus.dfactory The base.factory0The exponent to which the base should be raised.factory The modulus.factory The result.efactoryModulus.ffactoryThe  indeterminate.factory The Result.PQRSTUVWXYZ[\]^_`abcdefgPXYfbSQeTdgRUVWcaZ[]_\`^c7 NoneLlfactory A type of P, in which the  leading term is required to have a  coefficient of one.nfactory+Smart constructor. Constructs an arbitrary monic polynomial.lmnlmn NoneRsfactory)Each element of this list represents one  prime-factor, expressed as an  exponential with a prime base, of the original integer.(Whilst it only makes sense for both the base and exponent to be integral, these constrains are applied at the function-level as required.tfactory'Sorts a list representing a product of  prime factors by increasing base. Multiplies  s of similar base.ufactory Insert a (, into a list representing a product of  prime factors), multiplying with any incumbent of like base.(The list should be sorted by increasing base.Preserves the sort-order.CAVEAT: this is tolerably efficient for sporadic insertion; to insert a list, use v.vfactory4Multiplies two lists each representing a product of  prime factors, and sorted by increasing base.Preserves the sort-order.wfactory2Divides two lists, each representing a product of  prime factors, and sorted by increasing base.Preserves the sort-order.xfactoryRaise the product of a list  prime factors to the specified power.CAVEAT: this merely involves raising each element to the specified power; cf. raising a  polynomial to a power.yfactoryMultiply a list of  prime factors.wfactory The list of  prime factors in the  numerator.factory The list of  prime factors in the  denominator.factory The ratio of  numerator and  denominator , after like  prime factors are cancelled.yfactoryThe list on which to operate.factory The result.stuvwxysuytvwxv7w7x8  Safe-InferredS^zfactory"Defines the methods expected of a  factorial -algorithm.z{z{  Safe-InferredTa|factoryA constant ordered list of the  Fibonacci -numbers.}factoryThe subset of |, indexed by a prime-number. 1)- which can be expressed as an integral power (> 1) of a smaller natural number.CAVEAT: zero and one% are normally excluded from this set. +https://en.wikipedia.org/wiki/Perfect_power. /https://mathworld.wolfram.com/PerfectPower.html.#A generalisation of the concept of perfect squares0, in which only the exponent '2' is significant. Safe-Inferredsfactory For each prime3, the infinite list of candidates greater than its square#, is filtered for indivisibility;  http://www.haskell.org/haskellwiki/Prime_numbers#Turner.27s_sieve_-_Trial_division.$CAVEAT: though one can easily add a =>, it proved counterproductive.NonetfactoryGenerates the constant bounded list of  prime-numbers. 0https://cr.yp.to/papers/primesieves-19990826.pdffactoryOther implementations effectively use a hard-coded value either 2 or 3, but 6 seems better.factoryThe maximum prime required.factoryThe bounded list of primes. Safe-Inferred| factory0A number of decimal digits; presumably positive.factoryThe rate of convergence;  1https://en.wikipedia.org/wiki/Rate_of_convergence.factoryThe order of convergence;  1https://en.wikipedia.org/wiki/Rate_of_convergence.factoryLinear1 convergence-rate; which may be qualified by the rate of convergence.factory Quadratic convergence-rate.factoryCubic convergence-rate.factoryQuartic convergence-rate.factoryThe predicted number of iterations, required to achieve a specific accuracy, at a given order of convergence.factoryThe predicted number of terms which must be extracted from a series, if it is to converge to the required accuracy, at the specified linear convergence-rate.The convergence-rate< of a series, is the error in the series after summation of (n+1)th) terms, divided by the error after only n9 terms, as the latter tends to infinity. As such, for a  convergent series (in which the error get smaller with successive terms), it's value lies in the range 0 .. 1. 1https://en.wikipedia.org/wiki/Rate_of_convergence.factory5Rounds the specified number, to a positive number of .factory7Promotes the specified number, by a positive number of .factory Reduces a : to the minimal form required for the specified number of  fractional decimal places; irrespective of the number of integral decimal places.A  approximation to an irrational number, may be very long, and provide an unknown excess precision. Whilst this doesn't sound harmful, it costs in performance and memory-requirement, and being unpredictable isn't actually useful.factory&The precision of the initial estimate.factoryThe required precision.factory0The additional number of correct decimal digits.factoryThe number of places after the decimal point, which are required.   Safe-Inferredrfactory#Categorises the various algorithms.factoryAlgorithms based on the Arithmetic-geometric Mean.factory https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula.factory 3https://en.wikipedia.org/wiki/Borwein%27s_algorithm.factory &http://www.pi314.net/eng/ramanujan.php.factory$Algorithms from which the digits of Pi slowly drip, one by one.factory"Defines the methods expected of a Pi -algorithm./Most of the implementations naturally return a 0, but the spigot-algorithms naturally produce a [Int]; though representing Pi as a big integer with the decimal point removed is clearly incorrect.Since representing Pi as either a  or promoted to an *, is inconvenient, an alternative decimal -representation is provided.factoryReturns the value of Pi as a .factoryReturns the value of Pi8, promoted by the required precision to form an integer.factoryReturns the value of Pi as a decimal .   Safe-InferredfactoryDefines a series composed from a sum of terms, each one of which is the product of a coefficient and a base.9The coefficents and bases of the series are described in  Horner form; .Pi = c1 + (b1 * (c2 + b2 * (c3 + b3 * (...)))).factoryThe width of the spigot-table, required to accurately generate the requested number of digits.factory Combines  and <, and as a side-effect, expresses the ratio in lowest terms. Safe-Inferredfactory:The constant base in which we want the resulting value of Pi to be expressed.factoryInitialises a spigot-table with the row of .Ensures that the row has suffient terms to accurately generate the required number of digits.?Extracts only those digits which are guaranteed to be accurate.%CAVEAT: the result is returned as an !, i.e. without any decimal point. Safe-Inferredfactory$Defines a series which converges to Pi. Safe-InferredRfactory$Defines a series which converges to Pi. Safe-Inferredpfactory Define those Spigot(-algorithms which have been implemented.factoryA continued fraction discovered by Gosper.factoryA continued fraction discovered by  Rabinowitz and Wagon. Safe-Inferredfactory-Defines a series corresponding to a specific  Ramanujan -formula.factoryThe sequence of terms, the sum to infinity of which defines the series.factoryThe ratio by which the sum to infinity of the sequence, must be scaled to result in Pi.factory!The expected number of digits of Pi, per term in the series. Safe-Inferredfactory-Defines a series corresponding to a specific Borwein -formula.factory!The expected number of digits of Pi, per term in the series. NonefactoryReturns Pi5, accurate to the specified number of decimal digits.factoryThis Pi-algorithm is parameterised by the type of other algorithms to use.factory The specific  square-root( algorithm to apply to the above series.factory The specific  factorial(-algorithm to apply to the above series.factory&The number of decimal digits required.! Safe-Inferredtfactory>Defines the methods expected of a primality-testing algorithm.factory# if the two specified integers are relatively prime<, i.e. if they share no common positive factors except one.1 and -1 are the only numbers which are coprime to themself. %https://en.wikipedia.org/wiki/Coprime. 2https://mathworld.wolfram.com/RelativelyPrime.html.factoryTests Fermat's Little Theorem> for all applicable values, as a probabilistic primality-test. 7https://en.wikipedia.org/wiki/Fermat%27s_little_theorem. 3https://en.wikipedia.org/wiki/Fermat_primality_test. 0https://en.wikipedia.org/wiki/Fermat_pseudoprime.*CAVEAT: this primality-test fails for the Carmichael numbers.-TODO: confirm that all values must be tested.factoryA Carmichael number is an odd  composite number which satisfies Fermat's little theorem. /https://en.wikipedia.org/wiki/Carmichael_number. 3https://mathworld.wolfram.com/CarmichaelNumber.html.factoryAn ordered list of the  Carmichael numbers;  /https://en.wikipedia.org/wiki/Carmichael_number."None factory"Defines the methods expected of a  factorisation -algorithm.factoryThe upper limit for a prime to be considered as a candidate factor of the specified number.+One might naively think that this limit is (x  2)0 for an even number, but though a prime-factor greater than the  square-root' of the number can exist, its smaller cofactor3 decomposes to a prime which must be less than the  square-root.N.B.: rather then using (primeFactor <= sqrt numerator) to filter the candidate prime-factors of a given numerator, one can alternatively use (numerator >= primeFactor ^ 2) to filter what can potentially be factored by a given prime-factor.CAVEAT: suffers from rounding-errors, though no consequence has been witnessed.factory>A constant, zero-indexed, conceptually infinite, list, of the smoothness of all positive integers. +https://en.wikipedia.org/wiki/Smooth_number. /https://mathworld.wolfram.com/SmoothNumber.html.factory=A constant, zero-indexed, conceptually infinite, list of the  power-smoothness of all positive integers. ?https://en.wikipedia.org/wiki/Smooth_number#Powersmooth_numbers.factoryFilters !, to derive the constant list of Hamming-numbers. ,https://en.wikipedia.org/wiki/Regular_number.factoryEuler's Totient for a power of a prime-number.By Olofsson; (phi(n^k) = n^(k - 1) * phi(n)) and since (phi(prime) = prime - 1)CAVEAT: checks neither the primality nor the bounds of the specified value; therefore for internal use only.factoryThe number of coprimes6 less than or equal to the specified positive integer. 8https://en.wikipedia.org/wiki/Euler%27s_totient_function. 2https://mathworld.wolfram.com/TotientFunction.html.AKA EulerPhi.factory=A constant, zero-indexed, conceptually infinite, list of the  small omega numbers (i.e. the number of distinct prime factors); cf.  big omega. https://oeis.org/wiki/Omega%28n%29,_number_of_distinct_primes_dividing_n. 7https://mathworld.wolfram.com/DistinctPrimeFactors.html https://planetmath.org/encyclopedia/NumberOfDistinctPrimeFactorsFunction.html.factory/A constant, conceptually infinite, list of the  square-free3 numbers, i.e. those which aren't divisible by any perfect square. 1https://en.wikipedia.org/wiki/Square-free_integer.factory The operand  #NonefactoryThe smallest positive integral power to which the specified integral base must be raised, to be congruent with one, in the specified modular arithmetic. Based on  9https://rosettacode.org/wiki/Multiplicative_order#Haskell. 2https://en.wikipedia.org/wiki/Multiplicative_order. 6https://mathworld.wolfram.com/MultiplicativeOrder.html.factoryBase.factoryModulus.factoryResult.$Nonefactory3For each candidate, confirm indivisibility, by all primes smaller than its  square-root.,The candidates to sieve, are generated by a '', of parameterised, but static, size;  1https://en.wikipedia.org/wiki/Wheel_factorization.%NonefactoryThe algorithms by which prime-factorisation has been implemented.factory =https://en.wikipedia.org/wiki/Fermat%27s_factorization_method.factory ,https://en.wikipedia.org/wiki/Trial_division.&NonefactoryThe algorithms by which  primality-testing has been implemented.factory 0https://en.wikipedia.org/wiki/AKS_primality_test.factory https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test.' Safe-Inferredfactory"Defines the methods expected of a  prime-number generator.factory(Returns the constant list, defining the  Primorial. 'https://en.wikipedia.org/wiki/Primorial. ,https://mathworld.wolfram.com/Primorial.html.factory.Returns the constant ordered infinite list of Mersenne numbers.Only the subset composed from a prime exponent is returned; which is a strict superset of the Mersenne Primes. ,https://en.wikipedia.org/wiki/Mersenne_prime. 1https://mathworld.wolfram.com/MersenneNumber.htmlfactory/Returns the constant, infinite, list of primes.(Nonefactory=The implemented methods by which the primes may be generated.factoryThe Sieve of Atkin, optimised using a ' of optimal size, for primes up to the specified maximum bound;  ,https://en.wikipedia.org/wiki/Sieve_of_Atkin.factoryThe Sieve of Eratosthenes ( 3https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes), optimised using a '.factory3For each candidate, confirm indivisibility, by all primes smaller than its  square-root, optimised using a '.factory For each prime3, the infinite list of candidates greater than its square", is filtered for indivisibility;  https://www.haskell.org/haskellwiki/Prime_numbers#Turner.27s_sieve_-_Trial_division.factory.)None}factory9Defines a common interface for probability-distributions.factory Describes "discrete probability-distributions;  https://en.wikipedia.org/wiki/List_of_probability_distributions#Discrete_distributions.factory Defines an Poisson -distribution with a particular lambda;  2https://en.wikipedia.org/wiki/Poisson_distribution.factory Defines an  Geometric8-distribution with a particular probability of success;  4https://en.wikipedia.org/wiki/Geometric_distribution.factory Describes $continuous probability-distributions;  https://en.wikipedia.org/wiki/List_of_probability_distributions#Continuous_distributions.factory Defines an  Exponential -distribution with a particular lambda;  6https://en.wikipedia.org/wiki/Exponential_distribution.factoryDefines a distribution whose logarithm is normally distributed with a particular mean & variance;  'https://en.wikipedia.org/wiki/Lognormal.factory Defines a Normal -distribution with a particular mean & variance;  1https://en.wikipedia.org/wiki/Normal_distribution.factory Defines a Uniform-distribution within a closed interval;  2https://en.wikipedia.org/wiki/Uniform_distribution.factoryThe maximum integer which can be accurately represented as a Double.factoryConverts a pair of independent uniformly distributed random numbers, within the semi-closed unit interval (0,1], to a pair of independent normally distributed! random numbers, of standardized mean=0, and variance=1. :https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform.factoryUses the supplied random-number generator, to generate a conceptually infinite list, of normally distributed# random numbers, with standardized mean=0, and variance=1. 1https://en.wikipedia.org/wiki/Normal_distribution,  5https://mathworld.wolfram.com/NormalDistribution.html.factoryUses the supplied random-number generator, to generate a conceptually infinite population, with the specified continuous probability-distribution.factoryUses the supplied random-number generator, to generate a conceptually infinite population, with the specified discrete probability-distribution.factoryA generator of uniformly distributed random numbers.factoryCAVEAT: the integers generated for discrete distributions are represented by a fractional type; use  if this is a problem.factoryThe theoretical mean.factory#The theoretical standard-deviation.factoryThe theoretical variance.factory Independent, uniformly distributed* random numbers, which must be within the semi-closed unit interval, (0,1].factory Independent, normally distributed# random numbers, with standardized mean=0 and variance=1.factoryA generator of uniformly distributed random numbers.factoryA generator of uniformly distributed random numbers.* Safe-InferredfactoryConvert the specified integral quantity, to an alternative base, and represent the result as a .:Both negative integers and negative bases are permissible.The conversion to  can only succeed where printable and intelligible characters exist to represent all digits in the chosen base; which in practice means (-36 <= base <= 36).factory Convert the -representation of a number in the specified base, to an integer.9Both negative numbers and negative bases are permissible.factory +https://mathworld.wolfram.com/DigitSum.html. 'https://en.wikipedia.org/wiki/Digit_sum.factory *https://en.wikipedia.org/wiki/Digital_root.+ Safe-InferredfactoryThe interface required to iterate, from an estimate of the required value, to the next approximation.factory"Defines the methods expected of a  square-root algorithm.factoryContains an estimate for the  square-root of a value, and its accuracy.factory 4*a[N]^2 / (1 - sum [2^n * (a[n]^2 - 2*a[n]*g[n] + g[n]^2)]) => 4*a[N]^2 / (1 - sum [2^n * (a[n]^2 + 2*a[n]*g[n] + g[n]^2 - 4*a[n]*g[n])]) => 4*a[N]^2 / (1 - sum [2^n * ((a[n] + g[n])^2 - 4*a[n]*g[n])]) => 4*a[N]^2 / (1 - sum [2^(n-1) * 4 * (a[n-1]^2 - g[n-1]^2)]) where n = [1 .. N] => 4*a[N]^2 / (1 - sum [2^(n+1) * (a[n-1]^2 - g[n-1]^2)])2Nonefactory!Defines the available algorithms.3None> factoryDetermines the mean of the specified numbers;  "https://en.wikipedia.org/wiki/Mean.,Should the caller define the result-type as ,, then it will be free from rounding-errors.factoryDetermines the root mean square of the specified numbers;  .https://en.wikipedia.org/wiki/Root_mean_square.factoryDetermines the  weighted mean of the specified numbers;  6https://en.wikipedia.org/wiki/Weighted_arithmetic_mean.The specified value is only evaluated if the corresponding weight is non-zero.CAVEAT: because the operand is more general than a list, no optimisation is performed when supplied a singleton.factoryDetermines the exact variance of the specified numbers;  &https://en.wikipedia.org/wiki/Variance.,Should the caller define the result-type as ,, then it will be free from rounding-errors.factoryDetermines the standard-deviation of the specified numbers;  0https://en.wikipedia.org/wiki/Standard_deviation.factoryDetermines the average absolute deviation of the specified numbers;  https://en.wikipedia.org/wiki/Absolute_deviation#Average_absolute_deviation.,Should the caller define the result-type as ,, then it will be free from rounding-errors.factoryDetermines the coefficient-of-variance of the specified numbers;  6https://en.wikipedia.org/wiki/Coefficient_of_variation.factoryThe number of unordered  combinations of r objects taken from n;  )https://en.wikipedia.org/wiki/Combination.factoryThe number of  permutations of r objects taken from n;  *https://en.wikipedia.org/wiki/Permutations.factory9Each pair consists of a value & the corresponding weight.factory/The total number of items from which to select.factory The number of items in a sample.factoryThe number of combinations.factory/The total number of items from which to select.factory The number of items in a sample.factoryThe number of permutations.  4Noneӟfactory)Sums a list of numbers of arbitrary type.Sparks the summation of (list-length / chunk-size) chunks from the list, each of the specified size (thought the last chunk may be smaller), then recursively sums the list of results from each spark.&CAVEAT: unless the numbers are large,  (requiring cross-multiplication), or the list long,  is too light-weight for sparking to be productive, therefore it is more likely to be the parallelised deep  evaluation# of list-elements which saves time.factorySums a list of rational type numbers.CAVEAT: though faster than , this algorithm has poor space-complexity, making it unsuitable for unrestricted use.factorySums a list of rational numbers.Sparks the summation of (list-length / chunk-length) chunks from the list, each of the specified size (thought the last chunk may be smaller), then recursively sums the list of results from each spark.1CAVEAT: memory-use is proportional to chunk-size.5None factoryThe algorithms by which the  square-root has been implemented.factory https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Bakhshali_approximationfactory https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Continued_fraction_expansion.factory /https://en.wikipedia.org/wiki/Halley%27s_method.factory /https://en.wikipedia.org/wiki/Newton%27s_method.factory https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Taylor_series.factory The number of terms in a series.6NonefactoryReturns Pi5, accurate to the specified number of decimal digits.factoryThis Pi-algorithm is parameterised by the type of other algorithms to use.factory The specific  square-root( algorithm to apply to the above series.factory The specific  factorial(-algorithm to apply to the above series.factory&The number of decimal digits required.7Noneخfactory Define those  Ramanujan$-series which have been implemented.factoryThe original version.factoryA variant found by the Chudnovsky brothers.8NonefactoryReturns Pi5, accurate to the specified number of decimal digits.factoryThis Pi-algorithm is parameterised by the type of other algorithms to use.factory&The number of decimal digits required.9NoneڹfactoryDefines those BBP)-type series which have been implemented.factoryA base-2^16 version of the formula.factoryA  nega-base 2^10 version of the formula.?@ABCDEFGHIJKLMNOPQRSTUAVWDXYZ[\]^_`abc>defghijklmnopSqrstuvwxZySqz{|}~PV_C              S                 Z !!!!!!""""""""""#$%%%%%%%%&&&&&&&&''''((((((((((())))))))))))))))))))))))))))****++++++++++++,-.///////00000000122222223333333334q445555555555555677777777899999999p&factory-0.3.2.3-5gVcPpoBqpO4IK4vqJjbw0Factory.Data.ExponentialFactory.Data.IntervalFactory.Data.MonomialFactory.Data.PrimeWheelFactory.Math.DivideAndConquerFactory.Data.RingFactory.Data.QuotientRingFactory.Data.PolynomialFactory.Data.MonicPolynomialFactory.Data.PrimeFactorsFactory.Math.FactorialFactory.Math.FibonacciFactory.Math.Hyperoperation&Factory.Math.Implementations.Factorial*Factory.Math.Implementations.Pi.BBP.Series+Factory.Math.Implementations.Pi.BBP.Bellard-Factory.Math.Implementations.Pi.BBP.Base655367Factory.Math.Implementations.Primes.SieveOfEratosthenesFactory.Math.PowerFactory.Math.PerfectPower0Factory.Math.Implementations.Primes.TurnersSieve0Factory.Math.Implementations.Primes.SieveOfAtkinFactory.Math.PrecisionFactory.Math.Pi-Factory.Math.Implementations.Pi.Spigot.Series-Factory.Math.Implementations.Pi.Spigot.Spigot6Factory.Math.Implementations.Pi.Spigot.RabinowitzWagon-Factory.Math.Implementations.Pi.Spigot.Gosper0Factory.Math.Implementations.Pi.Spigot.Algorithm0Factory.Math.Implementations.Pi.Ramanujan.Series.Factory.Math.Implementations.Pi.Borwein.Series6Factory.Math.Implementations.Pi.Borwein.ImplementationFactory.Math.PrimalityFactory.Math.PrimeFactorisation 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