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I.—The Theory of Bigradients from 1861 to 1919

Published online by Cambridge University Press:  15 September 2014

Thomas Muir
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Extract

The number of writings dealt with here is very slightly in excess of the number under the same heading for the period 1880–1900, and there is also little alteration in the general character of them. The bigradient which still receives most attention is that resulting from Sylvester's dialytic method of elimination, and others are close relatives of it.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 49 , 1930 , pp. 1 - 15
Copyright
Copyright © Royal Society of Edinburgh 1930

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References

LIST OF AUXILIARY WRITINGS

1885. Laurent, H.Théorie des substitutions linéaires. Sur Félimination. Traité d'Analyse, i, pp. 227–285, 286–342.Google Scholar
1886. Mertens, F.Ueber die bestimmenden Eigenschaften der Resultante von n formen mit n Veränderlichen, Sitzungsb. … Akad. d. Wiss. (Wien), xciii, Abt. 2, pp. 527–566.Google Scholar
1894. Biermann, O, Ueber die Bildung der Eliminanten eines Systems algebraischer Gleichungen, Monatshefte f. Math. u. Phys., v, pp, 17–32.CrossRefGoogle Scholar
1899. Mertens, F. Zur Theorie der Elimination, Sitzungsb. … Akad. d. Wiss. (Wien), cviii, Abt. 2a, pp. 1173–1228.Google Scholar
1899. Bes, K.Over de Vorming der Eindvergelijking, Verslagen … Akad. van Wetensch. (Amsterdam), viii, pp, 173–177 : or English Translation, pp. 85–88.Google Scholar
1900. Laurent, H. L'Elimination, 75 pp., Paris.Google Scholar
1900. Poussart, A. Théorèmes de Bezout et d'Euler, L'Enseignement Math, ii, pp. 136–138.Google Scholar
1901. Dellac, H. Note sur l'élimination; méthode de parallélogramme, Annales … Sci. de Marseille, xi, pp. 141–164.Google Scholar
1901. Bes, K. L'equation finale, Verhand. … Akad. … (Amsterdam) (1), viii, No. 1, 57 pp.Google Scholar
1902. Macaulay, F. S. Some formulæ in elimination, Proceed. London Math. Soc., xxxv, pp. 3–27.CrossRefGoogle Scholar
1903. Jung, H. Arithmetischer Beweis eines Satzes über deo Grad der. Eliminante zweier ganzen Funktionen zweier Veränderlichen, Crelle's Journ., cxxv, pp. 293–298.Google Scholar
1904. Muir, T. The eliminant of a set of general ternary quadrics, Pt. III., Transac. R. Soc. Edinburgh, xli, pp. 387–397.Google Scholar
1905. Giudice, F. Sull'eliminazione, Giornale di Mat., xliii, pp. 305–313.Google Scholar
1906. Gordan, P. Die Resultante binärer Formen, Rendic. del Circolo Mat. (Palermo), xxii, pp. 161–196.CrossRefGoogle Scholar
1906. Kürschák, J.Contributions to the theory of elimination (In Magyar), Math. és termész. értesitö (Budapest), xxiv, pp. 780–794.Google Scholar
1908. Dixon, A. L. The eliminant of three quantics in two independent variables, Proceed. London Math. Soc., (2), vii, pp. 49–69, 473–492.Google Scholar
1908. White, H. S. Bezout's theory of resultants, and its influence on geometry, Bull. American Math. Soc., xv, pp. 325–338.Google Scholar
1909. Dixon, A. L. Symbolical expressions for the eliminant of two binary quantics, Proceed. London Math. Soc., (2), viii, pp. 265–276.Google Scholar
1909. Dixon, A. L. The eliminant of the equations of four quadric surfaces, Proceed. London Math. Soc., (2), viii, pp. 340–352.Google Scholar
1909. Dixon, A. L. Some results in the theory of elimination, Proceed. R. Soc. (London), A, lxxxii, pp. 384–386.Google Scholar
1911. Dines, L. L. The highest common factor of a system of polynomials in one variable, American Journ. of Math., xxxv, pp. 129–150.Google Scholar
1911. Fontene, G.Discussion des équations de degrés 2, 3, 4, 5 au point de vue des racines multiples, Nouv. Annales de Math. (4), xi, pp. 340–355 (see esp. § 9).Google Scholar
1912. Meuli, M. Untersuchungen über die Darstellung der Mertens-schen Resultante in Determinantenform, Dissert., 53 pp., Bonn.Google Scholar
1912. Tiedemann, K. Zur Theorie der Elimination, Dissert., vii + 64 pp., Königsberg.Google Scholar
1914. Liénard, K.—, et Chipart, — Sur la signe de la partie réelle des racines d'une équation algébrique, Journ. (de Liouville) de Math. (6), x, pp. 338–346.Google Scholar
1914. Stuyvaert, M.Elimination d'une inconnue entre plusieurs équations algébriques, American Journ. of Math., xxxvii, pp. 272–280.Google Scholar
1916. Palomby, A.Studio sulle risultanti, Periodico di Mat. (3), xiii, pp. 178–191.Google Scholar
1917. Datta, H.On the failure of Heilermann's theorem, Proceed. Edinburgh Math. Soc., xxxv, pp. 83–106.Google Scholar
1917. Carmichael, R. D.Repeated solutions of a certain class of linear functional equations, Tôhoku Math. Journ., xiii, pp. 304–313.Google Scholar
1919. Riquier, C.Sur 1'élimination algébrique, L'Enseignement Math., xx, pp. 405–421.Google Scholar
1919. Stuyvaert, M.Elimination d'une inconnue entre trois equations algébriques, Comptes rendus … Acad. des Sci. (Paris), clxix, pp. 459–462.Google Scholar