pseudoprime test

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11: Philip J. Davis

… ►This immediately led to discussions among some of the project members about what might be possible, and the discovery that some interactive graphics work had already been done for the NIST Matrix Market, a publicly available repository of test matrices for comparing the effectiveness of numerical linear algebra algorithms. …

12: 1.10 Functions of a Complex Variable

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$M$-test

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$M$-test

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13: 2.6 Distributional Methods

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2.6.11 $$⟨f,\varphi ⟩={\int }_0^{\mathrm{\infty }}f(t)\varphi (t)dt,$$ $\varphi \in 𝒯$.

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Symbols:

$dx$: differential of $x$ , $⟨\mathrm{\Lambda },\varphi ⟩$: action of distribution on test function, $\in$: element of, $\int$: integral, $f(t)$: locally integrable function and $𝒯$: space of decreasing functions

Referenced by:

§2.6(ii)

Permalink:

http://dlmf.nist.gov/2.6.E11

Encodings:

pMML, png, TeX

See also:

Annotations for §2.6(ii), §2.6 and Ch.2

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2.6.12 $$⟨t^{-\alpha },\varphi ⟩={\int }_0^{\mathrm{\infty }}{t}^{-\alpha }\varphi (t)dt,$$ $\varphi \in 𝒯$,

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Symbols:

$dx$: differential of $x$ , $⟨\mathrm{\Lambda },\varphi ⟩$: action of distribution on test function, $\in$: element of, $\int$: integral and $𝒯$: space of decreasing functions

Referenced by:

§2.6(iii), §2.6(iii)

Permalink:

http://dlmf.nist.gov/2.6.E12

Encodings:

pMML, png, TeX

See also:

Annotations for §2.6(ii), §2.6 and Ch.2

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2.6.13 $$⟨t^{-s-\alpha },\varphi ⟩=\frac{1}{{\left(\alpha \right)}_s}{\int }_0^{\mathrm{\infty }}{t}^{-\alpha }{\varphi }^{(s)}(t)dt,$$ $\varphi \in 𝒯$,

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Symbols:

${\left(a\right)}_n$: Pochhammer’s symbol (or shifted factorial), $dx$: differential of $x$ , $⟨\mathrm{\Lambda },\varphi ⟩$: action of distribution on test function, $\in$: element of, $\int$: integral and $𝒯$: space of decreasing functions

Referenced by:

§2.6(ii), §2.6(iii)

Permalink:

http://dlmf.nist.gov/2.6.E13

Encodings:

pMML, png, TeX

See also:

Annotations for §2.6(ii), §2.6 and Ch.2

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2.6.14 $$⟨t^{-s-1},\varphi ⟩=-\frac{1}{s!}{\int }_0^{\mathrm{\infty }}(\ln t){\varphi }^{(s+1)}(t)dt,$$ $\varphi \in 𝒯$.

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Symbols:

$dx$: differential of $x$ , $⟨\mathrm{\Lambda },\varphi ⟩$: action of distribution on test function, $\in$: element of, $!$: factorial (as in $n!$), $\int$: integral, $\ln z$: principal branch of logarithm function and $𝒯$: space of decreasing functions

Referenced by:

§2.6(ii), §2.6(iii)

Permalink:

http://dlmf.nist.gov/2.6.E14

Encodings:

pMML, png, TeX

See also:

Annotations for §2.6(ii), §2.6 and Ch.2

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2.6.19 $$⟨{\delta }^{(s)},\varphi ⟩={(-1)}^s{\varphi }^{(s)}(0),$$ $s=0,1,2,\mathrm{\dots }$;

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Symbols:

${\delta }_x$: Dirac delta distribution and $⟨\mathrm{\Lambda },\varphi ⟩$: action of distribution on test function

Permalink:

http://dlmf.nist.gov/2.6.E19

Encodings:

pMML, png, TeX

See also:

Annotations for §2.6(ii), §2.6 and Ch.2

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14: Bibliography P

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Unbiasedness of invariant tests for MANOVA and other multivariate problems. Ann. Statist. 8 (6), pp. 1326–1341.

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External Links:

ISSN 0090-5364, FullText, MathReview (Takeaki Kariya), ZentralBlatt

Referenced by:

§35.9.

Encodings:

BibTeX

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Notes:

Information on primes, primality testing, and factorization including links to programs and lists of primes.

External Links:

Home Page

Referenced by:

7th item.

Encodings:

BibTeX

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15: Software Index

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	Open Source													With Book						Commercial
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4.48(v) Testing
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Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.

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16: Bibliography B

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On the power function of the likelihood ratio test for MANOVA. J. Multivariate Anal. 82 (2), pp. 416–421.

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External Links:

ISSN 0047-259X, Document, MathReview (Yasuko Chikuse), ZentralBlatt

Referenced by:

§35.9.

Encodings:

BibTeX

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Faster Primality Testing. In Advances in Cryptology—EUROCRYPT ’89 Proceedings, J.-J. Quisquater and J. Vandewalle (Eds.), Lecture Notes in Computer Science, Vol. 434, New York, pp. 652–656.

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External Links:

ZentralBlatt

Referenced by:

§27.18.

Encodings:

BibTeX

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Factorization and Primality Testing. Springer-Verlag, New York.

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External Links:

ISBN 0-387-97040-1, MathReview (Brigitte Vallée), ZentralBlatt

Referenced by:

§23.20(iii), §27.19, Profile David M. Bressoud.

Encodings:

BibTeX

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17: Bibliography M

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Rational approximations, software and test methods for sine and cosine integrals. Numer. Algorithms 12 (3-4), pp. 259–272.

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Notes:

Includes Fortran code, maximum accuracy 20S.

External Links:

ISSN 1017-1398, Document, MathReview, ZentralBlatt

Referenced by:

§6.13, 4th item, §6.21(ii).

Encodings:

BibTeX

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Loud Speakers: Theory, Performance, Testing and Design. Oxford University Press, New York.

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Notes:

Reprinted, with corrections, by Dover Publications Inc., 1960.

External Links:

MathReview, ZentralBlatt

Referenced by:

§11.12.

Encodings:

BibTeX

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Algorithm 346: F-test probabilities [S14]. Comm. ACM 12 (3), pp. 184–185.

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Notes:

Includes Algol program, maximum accuracy 12S. For a remark see ACM Trans. Math. Software 14(1988), pp. 288-289

External Links:

ISSN 0001-0782, Document, Remark

Referenced by:

§8.28(iv).

Encodings:

BibTeX

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18: 1.9 Calculus of a Complex Variable

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Weierstrass $M$-test

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19: Bibliography C

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Algorithm 714: CELEFUNT – A portable test package for complex elementary functions. ACM Trans. Math. Software 19 (1), pp. 1–21.

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External Links:

ISSN 0098-3500, Document, GAMS (module 714; package TOMS), ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

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Algorithm 715: SPECFUN – A portable FORTRAN package of special function routines and test drivers. ACM Trans. Math. Software 19 (1), pp. 22–32.

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Notes:

Double precision, maximum accuracy 18S.

External Links:

ISSN 0098-3500, Document, Remark. GAMS (module 715; package TOMS), ZentralBlatt

Referenced by:

3rd item, 6th item, 4th item, 2nd item, 2nd item, 2nd item, 2nd item.

Encodings:

BibTeX

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20: Bibliography E

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Notes:

Links to software for elliptic curve methods of factorization and primality testing.

External Links:

Home Page

Referenced by:

4th item.

Encodings:

BibTeX

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