exact rational arithmetic

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1: 3.1 Arithmetics and Error Measures

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§3.1(iii) Rational Arithmetics

►Computer algebra systems use exact rational arithmetic with rational numbers $p/q$, where $p$ and $q$ are multi-length integers. …

2: Bibliography M

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Foundations of Finite Precision Rational Arithmetic. In Fundamentals of Numerical Computation (Computer-oriented Numerical Analysis), G. Alefeld and R. D. Grigorieff (Eds.), Comput. Suppl., Vol. 2, Vienna, pp. 85–111.

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External Links:

MathReview (G. Blanch), ZentralBlatt

Referenced by:

§3.1(iii).

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Exact remainders for asymptotic expansions of fractional integrals. J. Inst. Math. Appl. 24 (2), pp. 139–147.

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ISSN 0020-2932, Document, MathReview, ZentralBlatt

Referenced by:

§2.6(iii).

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Exact misclassification probabilities for plug-in normal quadratic discriminant functions. I. The equal-means case. J. Multivariate Anal. 77 (1), pp. 21–53.

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ISSN 0047-259X, Document, MathReview (Peter A. Lachenbruch), ZentralBlatt

Referenced by:

§35.9.

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Exact misclassification probabilities for plug-in normal quadratic discriminant functions. II. The heterogeneous case. J. Multivariate Anal. 82 (2), pp. 299–330.

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ISSN 0047-259X, Document, MathReview (Peter A. Lachenbruch), ZentralBlatt

Referenced by:

§35.9.

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Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions. Ramanujan J. 6 (1), pp. 7–149.

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External Links:

Document, ZentralBlatt

Referenced by:

§27.13(iv).

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3: Bibliography P

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Evaluation of Fermi-Dirac Integral. In Nonlinear Numerical Methods and Rational Approximation (Wilrijk, 1987), A. Cuyt (Ed.), Mathematics and Its Applications, Vol. 43, pp. 435–444.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§25.18(i).

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Complex Interval Arithmetic and its Applications. Mathematical Research, Vol. 105, Wiley-VCH Verlag Berlin GmbH, Berlin.

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ISBN 3-527-40134-2, MathReview (G. Alefeld), ZentralBlatt

Referenced by:

§3.1(ii).

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The exact distribution of the Wald statistic. Econometrica 54 (4), pp. 881–895.

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ISSN 0012-9682, FullText, MathReview (Sadanori Konishi), ZentralBlatt

Referenced by:

§35.9.

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4: Bibliography C

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Nonclassical Symmetry Reductions and Exact Solutions for Physically Significant Nonlinear Evolution Equations. In Nonlinear and Chaotic Phenomena in Plasmas, Solids and Fluids (Edmonton, AB, 1990), W. Rozmus and J. A. Tuszynski (Eds.), pp. 72–79.

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External Links:

MathReview

Referenced by:

§29.19(ii).

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Rational Chebyshev approximations for the error function. Math. Comp. 23 (107), pp. 631–637.

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FullText, MathReview, ZentralBlatt

Referenced by:

2nd item.

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Exact elliptic compactons in generalized Korteweg-de Vries equations. Complexity 11 (6), pp. 30–34.

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ISSN 1076-2787, Document, MathReview

Referenced by:

§19.6(i).

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The arithmetic-geometric mean of Gauss. Enseign. Math. (2) 30 (3-4), pp. 275–330.

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ISSN 0013-8584, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§19.8(i).

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Gauss and the arithmetic-geometric mean. Notices Amer. Math. Soc. 32 (2), pp. 147–151.

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ISSN 0002-9920, MathReview (Willard Parker)

Referenced by:

§19.8(i).

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5: Bibliography S

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Exact recursive evaluation of $3j$- and $6j$-coefficients for quantum-mechanical coupling of angular momenta. J. Mathematical Phys. 16 (10), pp. 1961–1970.

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External Links:

Document, MathReview (J.-L. Calais)

Referenced by:

§34.13, §34.3(iii).

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Exact analytical solutions of $z{e}^z=a$ . J. Math. Anal. Appl. 43 (3), pp. 626–632.

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Document, MathReview (Pl. Kannappan), ZentralBlatt

Referenced by:

§4.13.

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Staudt and arithmetical properties of Bernoulli numbers. Historia Sci. (2) 5 (1), pp. 69–74.

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ISSN 0285-4821, MathReview (Peter M. Neumann), ZentralBlatt

Referenced by:

§24.10(ii).

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Exact error terms in the asymptotic expansion of a class of integral transforms. I. Oscillatory kernels. SIAM J. Math. Anal. 11 (5), pp. 828–841.

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ISSN 0036-1410, Document, MathReview (John S. Lew), ZentralBlatt

Referenced by:

§2.5(ii).

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Root-rational-fraction package for exact calculation of vector-coupling coefficients. Comput. Phys. Comm. 21 (2), pp. 195–205.

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Notes:

Double-precision Fortran, maximum accuracy 16D

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Document, Code

Referenced by:

10th item.

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