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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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The minimum discriminant of totally real algebraic number fields of degree $9$ with cubic subfields
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by Hiroyuki Fujita PDF
Math. Comp. 60 (1993), 801-810 Request permission

Abstract:

With the help of the computer language UBASIC86, the minimum discriminant $d(K)$ of totally real algebraic number fields K of degree 9 with cubic subfields F is determined. It is given by $d(K) = 16240385609$. The defining equation for K is given by $f(x) = {x^9} - {x^8} - 9{x^7} + 4{x^6} + 26{x^5} - 2{x^4} - 25{x^3} - {x^2} + 7x + 1$, and K is uniquely determined by $d(K)$ up to Q-isomorphism. The field K has the cubic subfield F with $d(F) = 49$ defined by the polynomial $f(x) = {x^3} + {x^2} - 2x - 1$.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Math. Comp. 60 (1993), 801-810
  • MSC: Primary 11R16; Secondary 11R29, 11R80, 11Y40
  • DOI: https://doi.org/10.1090/S0025-5718-1993-1176709-6
  • MathSciNet review: 1176709