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67 publications using GAP in the category "Field theory and polynomials"

[AV97] Arnaudiès, J. and Valibouze, A., Lagrange resolvents, J. Pure Appl. Algebra, 117/118 (1997), 23–40
(Algorithms for algebra (Eindhoven, 1996)).

[AV12] Aubry, P. and Valibouze, A., Parallel computation of resolvents by multimodular techniques and decomposition formula, Internat. J. Algebra Comput., 22 (5) (2012), 1250043, 21.

[BBL19] Badr, E., Bars, F., and Lorenzo García, E., On twists of smooth plane curves, Math. Comp., 88 (315) (2019), 421–438.

[B19] Bors, A., Finite groups with an automorphism inverting, squaring or cubing a non-negligible fraction of elements, J. Algebra Appl., 18 (3) (2019), 1950055, 30.

[B18] Bouazizi, F., Algebraic certification of numerical algorithms computing Lagrange resolvents, J. Algebra Appl., 17 (1) (2018), 1850007, 15.

[BH16] Boykett, T. and Howell, K., The multiplicative automorphisms of a finite nearfield, with an application, Comm. Algebra, 44 (6) (2016), 2336–2350.

[BW16] Boykett, T. and Wendt, G., Units in near-rings, Comm. Algebra, 44 (4) (2016), 1478–1495.

[CCD20] Campedel, E., Caranti, A., and Del Corso, I., Hopf-Galois structures on extensions of degree $p^2q$ and skew braces of order $p^2 q$: the cyclic Sylow $p$-subgroup case, J. Algebra, 556 (2020), 1165–1210.

[CC99] Carnahan, S. and Childs, L., Counting Hopf Galois structures on non-abelian Galois field extensions, J. Algebra, 218 (1) (1999), 81–92.

[CH+15] Chu, H., Hoshi, A., Hu, S., and Kang, M., Noether's problem for groups of order 243, J. Algebra, 442 (2015), 233–259.

[CH+10] Chu, H., Hu, S., Kang, M., and Kunyavskii, B. E., Noether's problem and the unramified Brauer group for groups of order 64, Int. Math. Res. Not. IMRN (12) (2010), 2329–2366.

[CCS99] Cohen, A. M., Cuypers, H., and Sterk, H., Algebra interactive!, Springer-Verlag, Berlin (1999), viii+159 pages
(Learning algebra in an exciting way, With 1 CD-ROM (Windows, LINUX and UNIX)).

[DF+97] Daberkow, M., Fieker, C., Klüners, J., Pohst, M., Roegner, K., Schörnig, M., and Wildanger, K., KANT V4, J. Symbolic Comput., 24 (3-4) (1997), 267–283
(Computational algebra and number theory (London, 1993)).

[D95] Dentzer, R., On geometric embedding problems and semiabelian groups, Manuscripta Math., 86 (2) (1995), 199–216.

[D97] Dèvenport, D., Galois groups and the factorization of polynomials, Programmirovanie (1) (1997), 43–58.

[DJ15] Dubickas, A. and Jankauskas, J., Simple linear relations between conjugate algebraic numbers of low degree, J. Ramanujan Math. Soc., 30 (2) (2015), 219–235.

[E05] Eick, B., Computational group theory, Jahresber. Deutsch. Math.-Verein., 107 (3) (2005), 155–170.

[FG04] Fernandez-Ferreiros, P. and Gomez-Molleda, M. A., Deciding the nilpotency of the Galois group by computing elements in the centre, Math. Comp., 73 (248) (2004), 2043–2060.

[FGM02] Frohardt, D., Guralnick, R., and Magaard, K., Genus 0 actions of groups of Lie rank 1, in Arithmetic fundamental groups and noncommutative algebra (Berkeley, CA, 1999), Amer. Math. Soc., Providence, RI, Proc. Sympos. Pure Math., 70 (2002), 449–483.

[GG14] Gal, I. and Grizzard, R., On the compositum of all degree $d$ extensions of a number field, J. Théor. Nombres Bordeaux, 26 (3) (2014), 655–673.

[GK00] Geissler, K. and Klüners, J., Galois group computation for rational polynomials, J. Symbolic Comput., 30 (6) (2000), 653–674
(Algorithmic methods in Galois theory).

[G95] Greenhill, C. S., Theoretical and experimental comparison of efficiency of finite field extensions, J. Symbolic Comput., 20 (4) (1995), 419–429.

[GS09] Grundman, H. G. and Smith, T. L., Galois realizability of a central $C_4$-extension of $D_8$, J. Algebra, 322 (10) (2009), 3492–3498.

[GS10] Grundman, H. G. and Smith, T. L., Galois realizability of groups of order 64, Cent. Eur. J. Math., 8 (5) (2010), 846–854.

[GS10] Grundman, H. G. and Smith, T. L., Realizability and automatic realizability of Galois groups of order 32, Cent. Eur. J. Math., 8 (2) (2010), 244–260.

[GS04] Grundman, H. G. and Stewart, G. L., Galois realizability of non-split group extensions of $C_2$ by $(C_2)^r \times (C_4)^s \times (D_4)^t$, J. Algebra, 272 (2) (2004), 425–434.

[GMP17] Guralnick, R. M., Maróti, A., and Pyber, L., Normalizers of primitive permutation groups, Adv. Math., 310 (2017), 1017–1063.

[HHY20] Hasegawa, S., Hoshi, A., and Yamasaki, A., Rationality problem for norm one tori in small dimensions, Math. Comp., 89 (322) (2020), 923–940.

[H12] Hoshi, A., On the simplest sextic fields and related Thue equations, Funct. Approx. Comment. Math., 47 (part 1) (2012), 35–49.

[H16] Hoshi, A., Birational classification of fields of invariants for groups of order 128, J. Algebra, 445 (2016), 394–432.

[H17] Hoshi, A., Complete solutions to a family of Thue equations of degree 12, J. Théor. Nombres Bordeaux, 29 (2) (2017), 549–568.

[HKK14] Hoshi, A., Kang, M., and Kitayama, H., Quasi-monomial actions and some 4-dimensional rationality problems, J. Algebra, 403 (2014), 363–400.

[HKY11] Hoshi, A., Kitayama, H., and Yamasaki, A., Rationality problem of three-dimensional monomial group actions, J. Algebra, 341 (2011), 45–108.

[HM10] Hoshi, A. and Miyake, K., On the field intersection problem of solvable quintic generic polynomials, Int. J. Number Theory, 6 (5) (2010), 1047–1081.

[HY17] Hoshi, A. and Yamasaki, A., Rationality problem for algebraic tori, Mem. Amer. Math. Soc., 248 (1176) (2017), v+215.

[H95] Hulpke, A., Block systems of a Galois group, Experiment. Math., 4 (1) (1995), 1–9.

[H99] Hulpke, A., Galois groups through invariant relations, in Groups St. Andrews 1997 in Bath, II, Cambridge Univ. Press, Cambridge, London Math. Soc. Lecture Note Ser., 261 (1999), 379–393.

[H99] Hulpke, A., Techniques for the computation of Galois groups, in Algorithmic algebra and number theory (Heidelberg, 1997), Springer, Berlin (1999), 65–77.

[J13] Jones, J. W., Minimal solvable nonic fields, LMS J. Comput. Math., 16 (2013), 130–138.

[JKZ08] Jouve, F., Kowalski, E., and Zywina, D., An explicit integral polynomial whose splitting field has Galois group $W(E_8)$, J. Théor. Nombres Bordeaux, 20 (3) (2008), 761–782.

[K10] Kitayama, H., Noether's problem for four- and five-dimensional linear actions, J. Algebra, 324 (4) (2010), 591–597.

[KY09] Kitayama, H. and Yamasaki, A., The rationality problem for four-dimensional linear actions, J. Math. Kyoto Univ., 49 (2) (2009), 359–380.

[KM00] Klüners, J. and Malle, G., Explicit Galois realization of transitive groups of degree up to 15, J. Symbolic Comput., 30 (6) (2000), 675–716
(Algorithmic methods in Galois theory).

[KK+19] Koch, A., Kohl, T., Truman, P. J., and Underwood, R., Normality and short exact sequences of Hopf-Galois structures, Comm. Algebra, 47 (5) (2019), 2086–2101.

[K07] Kohl, T., Groups of order $4p$, twisted wreath products and Hopf-Galois theory, J. Algebra, 314 (1) (2007), 42–74.

[K13] Kohl, T., Regular permutation groups of order $mp$ and Hopf Galois structures, Algebra Number Theory, 7 (9) (2013), 2203–2240.

[L10] Lalande, F., À propos de la relation galoisienne $x_1=x_2+x_3$, J. Théor. Nombres Bordeaux, 22 (3) (2010), 661–673.

[L17] Lorenzo García, E., Twists of non-hyperelliptic curves, Rev. Mat. Iberoam., 33 (1) (2017), 169–182.

[LM99] Lübeck, F. and Malle, G., $(2,3)$-generation of exceptional groups, J. London Math. Soc. (2), 59 (1) (1999), 109–122.

[MSV03] Magaard, K., Shpectorov, S., and Völklein, H., A GAP package for braid orbit computation and applications, Experiment. Math., 12 (4) (2003), 385–393.

[MSV98] Magaard, K., Strambach, K., and Völklein, H., Finite quotients of the pure symplectic braid group, Israel J. Math., 106 (1998), 13–28.

[M11] Michailov, I. M., On Galois cohomology and realizability of 2-groups as Galois groups, Cent. Eur. J. Math., 9 (2) (2011), 403–419.

[M11] Michailov, I. M., The rationality problem for three- and four-dimensional permutational group actions, Internat. J. Algebra Comput., 21 (8) (2011), 1317–1337.

[M98] Müller, P., Kronecker conjugacy of polynomials, Trans. Amer. Math. Soc., 350 (5) (1998), 1823–1850.

[M13] Müller, P., Permutation groups with a cyclic two-orbits subgroup and monodromy groups of Laurent polynomials, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 12 (2) (2013), 369–438.

[N10] Nagy, G. P., On the multiplication groups of semifields, European J. Combin., 31 (1) (2010), 18–24.

[N08] Nomura, A., Notes on the minimal number of ramified primes in some $l$-extensions of $\bf Q$, Arch. Math. (Basel), 90 (6) (2008), 501–510.

[R04] Rennert, N., A parallel multi-modular algorithm for computing Lagrange resolvents, J. Symbolic Comput., 37 (5) (2004), 547–556.

[RV99] Rennert, N. and Valibouze, A., Calcul de résolvantes avec les modules de Cauchy, Experiment. Math., 8 (4) (1999), 351–366.

[S03] Shiina, T., Rigid braid orbits related to $\rm PSL_2(p^2)$ and some simple groups, Tohoku Math. J. (2), 55 (2) (2003), 271–282.

[S19] Sun, H., Existence of simple BIBDs from a prime power difference family with minimum index, J. Algebra Appl., 18 (9) (2019), 1950166, 17.

[S01] Swallow, J. R., Quadratic descent for quaternion algebras, Comm. Algebra, 29 (10) (2001), 4523–4544.

[ST02] Swallow, J. R. and Thiem, F. N., Quadratic corestriction, $C_2$-embedding problems, and explicit construction, Comm. Algebra, 30 (7) (2002), 3227–3258.

[T17] Tsunogai, H., Toward Noether's problem for the fields of cross-ratios, Tokyo J. Math., 39 (3) (2017), 901–922.

[V95] Valibouze, A., Computation of the Galois groups of the resolvent factors for the direct and inverse Galois problems, in Applied algebra, algebraic algorithms and error-correcting codes (Paris, 1995), Springer, Berlin, Lecture Notes in Comput. Sci., 948 (1995), 456–468.

[V08] Valibouze, A., Sur les relations entre les racines d'un polyn\^ome, Acta Arith., 131 (1) (2008), 1–27.

[Y12] Yamasaki, A., Negative solutions to three-dimensional monomial Noether problem, J. Algebra, 370 (2012), 46–78.