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Application of thue equations to computing power integral bases in algebraic number fields

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Algorithmic Number Theory (ANTS 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1122))

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References

  1. A.M.Bergé, J.Martinet and M.Olivier, The computation of sextic fields with a quadratic subfield, Math. Comp., 54(1990), 869–884.

    Google Scholar 

  2. I.Gaál, On the resolution of inhomogeneous norm form equations in two dominating variables, Math. Comp., 51(1988), 359–373.

    Google Scholar 

  3. I.Gaál, Power integral bases in orders of families of quartic fields, Publ. Math. (Debrecen), 42 (1993), 253–263.

    Google Scholar 

  4. I.Gaál, Computing all power integral bases in orders of totally real cyclic sextic number fields, Math. Comp., 65(1996), 801–822.

    Google Scholar 

  5. I.Gaál, Computing elements of given index in totally complex cyclic sextic fields, J.Symbolic Computation, to appear.

    Google Scholar 

  6. I.Gaál, A.Pethő and M.Pohst, On the resolution of index form equations in biquadratic number fields, I, J.Number Theory, 38 (1991), 18–34.

    Google Scholar 

  7. I.Gaál, A.Pethő and M.Pohst, On the resolution of index form equations in biquadratic number fields, II, J.Number Theory, 38 (1991), 35–51.

    Google Scholar 

  8. I.Gaál, A.Pethő and M.Pohst, On the resolution of index form equations in biquadratic number fields, III. The bicyclic biquadratic case, J.Number Theory, 53 (1995), 100–114.

    Google Scholar 

  9. I.Gaál, A.Pethő and M.Pohst, On the indices of biquadratic number fields having Galois group V 4, Arch. Math., 57 (1991), 357–361.

    Google Scholar 

  10. I.Gaál, A.Pethő and M.Pohst, On the resolution of index form equations in quartic number fields, J.Symbolic Computation, 16 (1993), 563–584.

    Google Scholar 

  11. I.Gaál, A.Pethő and M.Pohst, Simultaneous representation of integers by a pair of ternary quadratic forms — with an application to index form equations in quartic number fields, J.Number Theory, to appear.

    Google Scholar 

  12. I.Gaál, A.Pethő and M.Pohst, On the resolution of index form equations in dihedral number fields, J. Experimental Math., 3(1994), 245–254.

    Google Scholar 

  13. I.Gaál and M.Pohst, On the resolution of index form equations in sextic fields with an imaginary quadratic subfield, in preparation.

    Google Scholar 

  14. I.Gaál and N.Schulte, Computing all power integral bases of cubic number fields, Math. Comp., 53 (1989), 689–696.

    Google Scholar 

  15. D.Koppenhöfer, Über projektive Darstellungen von Algebren kleinen Ranges, Dissertation, Univ. Tübingen, 1994.

    Google Scholar 

  16. M.Olivier, Corps sextiques contenant un corps quadratique (I), Séminaire de Théorie des Nombres Bordeaux, 1(1989), 205–250.

    Google Scholar 

  17. N.P.Smart, Solving discriminant form equations via unit equations, J.Symbolic Comp., to appear.

    Google Scholar 

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Henri Cohen

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© 1996 Springer-Verlag Berlin Heidelberg

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Gaál, I. (1996). Application of thue equations to computing power integral bases in algebraic number fields. In: Cohen, H. (eds) Algorithmic Number Theory. ANTS 1996. Lecture Notes in Computer Science, vol 1122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61581-4_51

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  • DOI: https://doi.org/10.1007/3-540-61581-4_51

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  • Print ISBN: 978-3-540-61581-1

  • Online ISBN: 978-3-540-70632-8

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