# Robin S. Hankin

#### approximator

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Performs Bayesian prediction of complex computer codes when fast approximations are available. It uses a hierarchical version of the Gaussian process, originally proposed by Kennedy and O'Hagan (2000), Biometrika 87(1):1.

#### aylmer

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A generalization of Fisher's exact test that allows for structural zeros.

#### BACCO

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The BACCO bundle of packages is replaced by the BACCO package, which provides a vignette that illustrates the constituent packages (emulator, approximator, calibrator) in use.

#### Brobdingnag

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Handles very large numbers in R. Real numbers are held using their natural logarithms, plus a logical flag indicating sign. The package includes a vignette that gives a step-by-step introduction to using S4 methods.

#### contfrac

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Various utilities for evaluating continued fractions.

#### Davies

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Various utilities for the Davies distribution.

#### freegroup

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Provides functionality for manipulating elements of the free group (juxtaposition is represented by a plus) including inversion, multiplication by a scalar, group-theoretic power operation, and Tietze forms. The package is fully vectorized.

#### hypergeo

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The Gaussian hypergeometric function for complex numbers.

#### knotR

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Makes nice pictures of knots using Bezier curves and numerical optimization.

#### magic

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A collection of efficient, vectorized algorithms for the creation and investigation of magic squares and hypercubes, including a variety of functions for the manipulation and analysis of arbitrarily dimensioned arrays. The package includes methods for creating normal magic squares of any order greater than 2. The ultimate intention is for the package to be a computerized embodiment all magic square knowledge, including direct numerical verification of properties of magic squares (such as recent results on the determinant of odd-ordered semimagic squares). Some antimagic functionality is included. The package also serves as a rebuttal to the often-heard comment "I thought R was just for statistics".

#### MM

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Various utilities for the Multiplicative Multinomial distribution.

#### multipol

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Various utilities to manipulate multivariate polynomials.

#### multivator

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A multivariate generalization of the emulator package.

#### onion

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Quaternions and Octonions are four- and eight- dimensional extensions of the complex numbers. They are normed division algebras over the real numbers and find applications in spatial rotations (quaternions) and string theory and relativity (octonions). The quaternions are noncommutative and the octonions nonassociative. See RKS Hankin 2006, Rnews Volume 6/2: 49-51, and the package vignette, for more details.

#### partitions

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Additive partitions of integers. Enumerates the partitions, unequal partitions, and restricted partitions of an integer; the three corresponding partition functions are also given. Set partitions are now included.