Korkin-Zolotarev bases and successive minima of a lattice and its reciprocal lattice
Tóm tắt
Từ khóa
Tài liệu tham khảo
L. Babai: On Lovász' lattice reduction and the nearest lattice point problem,Combinatorica,6 (1986), 1–13.
J. W. S. Cassels:An introduction to the geometry of numbers, Springer-Verlag, Berlin,1971.
J. H. Conway, andN. J. A. Sloane:Sphere packings, lattices and groups, Springer-Verlag, New York,1988.
M. Grötschel, L. Lovász, andA. Schrijver:Geometric algorithms and combinatorial optimization, Springer-Verlag, Berlin,1988.
P. M. Gruber, andC. G. Lekkerkerker:Geometry of numbers, North-Holland, Amsterdam,1987.
C. Hermite: Extraits de lettres de M. Ch. Hermite à M. Jacobi sur différents objets de la théorie des nombres, Deuxième lettre,J. Reine Angew. Math. 40 (1850), 279–290.
F. John: Extremum problems with inequalities as subsidiary conditions, K. O. Friedrichs, O. E. Neugebauer, J. J. Stoker (eds),Studies and essays presented to R. Courant on his 60th birthday, 187–204, Interscience Publishers, New York,1948.
R. Kannan: Minkowski's convex body theorem and integer programming,Math. Oper. Res. 12 (1987), 415–440.
J. L.Lagrange: Recherches d'arithmétique,Nouv. Mém. Acad. Berlin (1773), 265–312; ∄uvres, vol. VIII, 693–753.
A. K. Lenstra, H. W. Lenstra, Jr., andL. Lovász: Factoring polynomials with rational coefficients,Math. Ann. 261 (1982), 515–534.
H. W. Lenstra, Jr.: Integer programming with a fixed number of variables,Math. Oper. Res. 8 (1983), 538–548.
L. Lovász: An algorithmic theory of numbers, graphs and convexity,CBMS-NSF Regional Conference Series in Applied Mathematics 50, SIAM, Philadelphia, Pennsylvania,1986.
K. Mahler: A theorem on inhomogeneous diophantine inequalities,Nederl. Akad. Wetensch., Proc. 41 (1938), 634–637.
K.Mahler:The geometry of numbers, duplicated lectures, Boulder, Colorado,1950.
N. V. Novikova: Korkin-Zolotarev reduction domains of positive quadratic forms inn≤8 variables and a reduction algorithm for these domains,Dokl. Akad. Nauk SSSR 270 (1983), 48–51; English translation:Soviet Math. Dokl. 27 (1983), 557–560.
C. A. Rogers:Packing and covering, Cambridge University Press, Cambridge,1964.
S. S. Ryshkov: Geometry of positive quadratic forms (Russian),Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974),1, 501–506,Canad. Math. Congress, Montreal, Que., 1975.
S. S. Ryshkov, andE. P. Baranovskii: Classical methods in the theory of lattice packings,Uspekhi Mat. Nauk 34, 4 (208) (1979), 3–63; English translation:Russian Math. Surveys 34 (4) (1979), 1–68.
C. P. Schnorr: A hierarchy of polynomial time lattice basis reduction algorithms,Theoret. Comput. Sci. 53 (1987), 201–224.
B. L. van der Waerden: Die Reduktionstheorie der positiven quadratischen Formen,Acta Math. 96 (1956), 265–309.
B. L. van der Waerden: H. Gross (eds),Studien zur Theorie der quadratischen Formen, BirkhÄuser-Verlag, Basel,1968.
P. van Emde Boas: AnotherNP-complete partition problem and the complexity of computing short vectors in a lattice,Report 81-04, Department of Mathematics, University of Amsterdam, Amsterdam,1981.