Algebraic calculations that depend upon a full partition can be automated through the use of an operator P for the derivation of such a partition. Calculations that require the repeated use of P are automated by simply iterating the operator. The resulting output is general and contains sufficient structure to identify the result of a calculation for a variety of settings.
Unable to display preview. Download preview PDF.
- Andrews, D. F. (1994) The analytic bootstrap. University of Toronto Technical Report.Google Scholar
- Andrews, D. F. and Stafford, J. E. (1993) Tools for the symbolic computation of asymptotic expansions. Journal of the Royal Statistical Society, B, 55, 613–28; 16, 421–36.Google Scholar
- Barndorff-Nielsen, O. E. and Cox, D. R. (1989) Asymptotic Techniques for Use in Statistics. New York: Chapman and Hall.Google Scholar
- Kendall, W. S. (1994) Computer algebra and yoke geometry I: when is an expression a tensor? Warwick University Technical Report.Google Scholar
- Leonov, V. P. and Shiryaev, A. N. (1959) On a method of calculation of semi-invariants. Theory of Probability and Applications, 4, 319–29.Google Scholar
- McCullagh, P. (1987) Tensor Methods in Statistics. New York: Chapman & Hall.Google Scholar
- McCullagh, P. and Wilks, A. (1988) Complementary set partitions. Proceedings of the Royal Society of London Series A, 415, 347–62.Google Scholar
- Stafford, J. E. (1994) Automating the partition of indexes. Journal of Computer Graphics and Statistics, 3, 249–60.Google Scholar
- Stafford, J. E. and Bellhouse, D. R.(1995) A computer algebra for sample survey theory. University of Western Ontario Technical Report.Google Scholar
- Wolfram, S. (1988) Mathematica: A System for Doing Mathematics by Computer, 2nd edn. New York: Addison Wesley.Google Scholar