rational arithmetics
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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 , where and 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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3: Annie A. M. Cuyt
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►As a consequence her expertise spans a wide range of activities from pure abstract mathematics to computer arithmetic and different engineering applications.
A lot of her research has been devoted to rational approximations, in one as well as in many variables, and sparse interpolation.
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4: 24.10 Arithmetic Properties
§24.10 Arithmetic Properties
… ►Here and elsewhere two rational numbers are congruent if the modulus divides the numerator of their difference. …5: Bibliography
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Rational solutions of Painlevé equations.
Stud. Appl. Math. 61 (1), pp. 31–53.
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A -beta integral on the unit circle and some biorthogonal rational functions.
Proc. Amer. Math. Soc. 121 (2), pp. 553–561.
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Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, , and the Ladies Diary.
Amer. Math. Monthly 95 (7), pp. 585–608.
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Rational function approximations for Fermi-Dirac integrals.
The Astrophysical Journal Supplement Series 84, pp. 101–108.
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The MasPar MP-1 as a computer arithmetic laboratory.
J. Res. Nat. Inst. Stand. Technol. 101 (2), pp. 165–174.
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6: Bibliography S
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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean.
SIAM J. Math. Anal. 20 (6), pp. 1514–1528.
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A Course in Arithmetic.
Graduate Texts in Mathematics, Vol. 7, Springer-Verlag, New York.
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Staudt and arithmetical properties of Bernoulli numbers.
Historia Sci. (2) 5 (1), pp. 69–74.
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Algorithm 786: Multiple-precision complex arithmetic and functions.
ACM Trans. Math. Software 24 (4), pp. 359–367.
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Algorithm 693: A FORTRAN package for floating-point multiple-precision arithmetic.
ACM Trans. Math. Software 17 (2), pp. 273–283.
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7: Bibliography H
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A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation.
Arch. Rational Mech. Anal. 73 (1), pp. 31–51.
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The higher arithmetic.
American Scientist 97, pp. 364–368.
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Über die Integration logarithmisch-rationaler Differentiale.
J. Reine Angew. Math. 3, pp. 101–159.
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8: Bibliography Y
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On rational solutions of the second Painlevé equation.
Vesti Akad. Navuk. BSSR Ser. Fiz. Tkh. Nauk. 3, pp. 30–35 (Russian).
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Software for interval arithmetic: A reasonably portable package.
ACM Trans. Math. Software 5 (1), pp. 50–63.
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9: Bibliography G
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What every computer scientist should know about floating-point arithmetic.
ACM Computing Surveys 23 (1), pp. 5–48.
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Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials.
J. Phys. A 47 (1), pp. 015203, 26 pp..
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10: Bibliography C
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Special polynomials associated with rational solutions of the fifth Painlevé equation.
J. Comput. Appl. Math. 178 (1-2), pp. 111–129.
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Level-Index Arithmetic: An Introductory Survey.
In Numerical Analysis and Parallel Processing (Lancaster, 1987), P. R. Turner (Ed.),
Lecture Notes in Math., Vol. 1397, pp. 95–168.
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Rational Chebyshev approximations for the error function.
Math. Comp. 23 (107), pp. 631–637.
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The arithmetic-geometric mean of Gauss.
Enseign. Math. (2) 30 (3-4), pp. 275–330.
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Gauss and the arithmetic-geometric mean.
Notices Amer. Math. Soc. 32 (2), pp. 147–151.
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