INTRODUCTION TO THE MAGMA PROGRAM

Authors

  • Islamov Yorqin
  • Turdiev Sirojiddin

Keywords:

MAGMA, program, algebra, groups, geometry, fields, mathematical databases

Abstract

This article is designed to unlock the potential of magma. The article lists places where magma can be used.

References

G. Marsaglia. DIEHARD: a battery of tests of randomness. URL:http://stat.fsu.edu/pub/diehard/, 1995.

G. Marsaglia. The Monster, a random number generator with period 102857 times as long as the previously touted longest-period one. Preprint, 2000.

Криптографическая защита информации Блочные шифры // https://www.tc26.ru/standard/gost/ GOST_R_3412-2015.pdf.

Параллельные вычисления Cuda | Что такое Cuda| NVIDIA. [Электронный ресурс] URL: http://www.nvidia. ru/object/cuda-parallel-computing-ru.html.

W. Bosma and J. Cannon, editors. Discovering Mathematics with Magma. Springer-Verlag, Heidelberg, 2004.

Nils Bruin. Chabauty methods using elliptic curves. J. reine angew. Math., 562:27–49, 2003.

Nils Bruin. Some ternary Diophantine equations of signature (n, n, 2). In Bosma and Cannon

Nils Bruin and Michael Stoll. The Mordell-Weil sieve: Proving non-existence of rational points on curves. LMS J. Comput. Math., 13:272–306, 2010.

J. W. S. Cassels. Diophantine equations with special reference to elliptic curves. J. London Math. Soc., 41:150–158, 1966.

J.E. Cremona, T.A Fisher, and M Stoll. Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves. Algebra & Number Theory, 4(6):763–820, 2010.

B. Creutz and R.L. Miller. Second isogeny descents and the Birch and Swinnerton-Dyer conjectural formula. J.Algebra, 372:673–701, 2012.

N. Elkies. Rational Points Near Curves and Small Nonzero via Lattice Reduction, pages 33–63.

Tom Fisher. On 5 and 7 descents for elliptic curves. PhD thesis, University of Cambridge, 2000.

Tom Fisher. Some examples of 5 and 7 descent for elliptic curves over Q. J. Eur. Math. Soc., 3(Issue 2):169–201, 2001.

Tom Fisher. Finding rational points on elliptic curves using 6-descent and 12-descent. J. Algebra, 320(2):853–884, 2008.

Claus Fieker and David R. Kohel, editors. ANTS V, volume 2369 of LNCS. Springer-Verlag, 2002.

Gross and Zagier. Heegner Points and Derivatives of L-series. Invent. Math., 84:225–320, 1986.

D. Harvey. Efficient computation of p-adic heights. LMS J. Comput. Math., 11:40–59, 2008.

K. Kramer. Arithmetic of elliptic curves upon quadratic extension. Trans. Amer. Math. Soc., 264(1):121–135, 1981.

J. R. Merriman, S. Siksek, and N. P. Smart. Explicit 4-descents on an elliptic curve. Acta Arith., 77(4):385–404, 1996.

B. Mazur, W. Stein, and J. Tate. Computation of p-adic heights and log convergence. Documenta Mathematica, Extra:577–614, 2006.

Samir Siksek. Infinite descent on elliptic curves. Rocky Mountain J. Math., 25(4):1501–1538, 1995.

Edward F. Schaefer and Michael Stoll. How to do a p-descent on an elliptic curve. Trans. Amer. Math. Soc., 356(3):1209–1231 (electronic), 2004.

M. Watkins. Computing the modular degree of an elliptic curve. Experimental Mathematics, 11(4):487–502, 2002

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Published

2023-06-03