A Database for Number Fields

We describe a database for number fields that has been integrated into the algebraic number theory system Kant. The database gives efficient access to the tables of number fields that have been computed during the last years and is easily extended.

[1]  Michael Pohst,et al.  Algorithmic algebraic number theory , 1989, Encyclopedia of mathematics and its applications.

[2]  Martin Gruber SQL Instant Reference , 1993 .

[3]  D. Ford Enumeration of totally complex quartic fields of small discriminant , 1991 .

[4]  Johannes Buchmann,et al.  On the computation of totally real quartic fields of small discriminant , 1989 .

[5]  László Lovász,et al.  Factoring polynomials with rational coefficients , 1982 .

[6]  Claus Fieker,et al.  Kant V4 , 1997, J. Symb. Comput..

[7]  Peter J. Weinberger,et al.  Factoring Polynomials Over Algebraic Number Fields , 1976, TOMS.

[8]  A. Schwarz,et al.  A table of quintic number fields , 1994 .

[9]  C. J. Date A guide to the SQL standard (2nd ed.) , 1989 .

[10]  Arjen K. Lenstra,et al.  Factoring polynominals over algebraic number fields , 1983, EUROCAL.

[11]  Bjarne Stroustrup,et al.  The C++ Programming Language, Second Edition , 1991 .

[12]  Arjen K. Lenstra,et al.  Lattices and Factorization of Polynomials over Algebraic Number Fields , 1982, EUROCAM.

[13]  C. J. Date A Guide to the SQL Standard , 1987 .

[14]  S. Lang Algebraic Number Theory , 1971 .

[15]  Johannes Buchmann,et al.  Enumeration of quartic fields of small discriminant , 1993 .

[16]  Kenneth J. Giuliani Factoring Polynomials with Rational Coeecients , 1998 .

[17]  Henri Cohen,et al.  A course in computational algebraic number theory , 1993, Graduate texts in mathematics.

[18]  Bjarne Stroustrup,et al.  C++ Programming Language , 1986, IEEE Softw..

[19]  Michael E. Pohst,et al.  A procedure for determining algebraic integers of given norm , 1983, EUROCAL.