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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 [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
[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 [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 [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 [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. |