The number of distinct alleles observed in a DNA mixture is informative of the number of contributors to the mixture. The package provides methods for computing the probability distribution of the number of distinct alleles in a mixture for a given set of allele frequencies. The mixture contributors may be related according to a provided pedigree.

Provides number-theoretic functions for factorization, prime 
    numbers, twin primes, primitive roots, modular logarithm and
    inverses, extended GCD, Farey series and continued fractions.
    Includes Legendre and Jacobi symbols, some divisor functions,
    Euler's Phi function, etc.

Validate, format and compare identification numbers used in Brazil.
  These numbers are used to identify individuals (CPF), vehicles (RENAVAN),
  companies (CNPJ) and etc.
  Functions to format, validate and compare these numbers have been 
  implemented in a vectorized way in order to speed up
  validations and comparisons in big datasets.

Methods for calculating (usually) accurate
	numerical first and second order derivatives. Accurate calculations 
	are done using 'Richardson''s' extrapolation or, when applicable, a
	complex step derivative is available. A simple difference 
	method is also provided. Simple difference is (usually) less accurate
	but is much quicker than 'Richardson''s' extrapolation and provides a 
	useful cross-check. 
	Methods are provided for real scalar and vector valued functions.

High-dimensional datasets that do not exhibit a clear intrinsic clustered structure pose a challenge to conventional clustering algorithms. For this reason, we developed an unsupervised framework that helps scientists to better subgroup their datasets based on visual cues, please see Gao S, Mutter S, Casey A, Makinen V-P (2019) Numero: a statistical framework to define multivariable subgroups in complex population-based datasets, Int J Epidemiology, 48:369-37, <doi:10.1093/ije/dyy113>. The framework includes the necessary functions to construct a self-organizing map of the data, to evaluate the statistical significance of the observed data patterns, and to visualize the results.