Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-13T10:54:32.428Z Has data issue: false hasContentIssue false
  • English
  • Français

L’Elimination. Par H. Laurent. Pp. 75. Scientia, Mars, 1900. Carré et Naud. Paris

Published online by Cambridge University Press:  03 November 2016

T. J. I’a Bromwich
Get access Rights & Permissions [Opens in a new window]

Abstract

An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Reviews
Information
The Mathematical Gazette , Volume 2 , Issue 26 , March 1901 , pp. 27 - 29
Copyright
Copyright © Mathematical Association 1901

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

page note 27 1 Here (-1)n should be (-1)mn.

page note 27 2 This is an extension of the familiar theorem

where f(x) is a polynomial of degree m, a is a root of f(x)−0 (all the roots being different) and g(x) is a polynomial of degree less than (m -1).

page note 28 1 The exact statement is Cij=cj ; presumably a printer’s error.

page note 28 2 Coll. Math. Papers, vol. ii., p. 475; Laurent himself published a paper in Liouville’s Journal (1898) where similar results are obtained.

page note 28 3 Crelle’s Journal, Bd. 26, 1843, p. 268; Salmon’s Modern Higher Algebra, Lesson vi., p. 55, 4th Ed.

page note 28 4 This reduction is always possible if the use of imaginary substitutions is admissible; but there is then no guarantee that g = 0 = x1 2+ = x2 2 +… +xn 2 really necessitates x1=0=x2 = … =xn Thus, in the case quoted below, g=0 can be satisfied by x=0, z=0 for any value of y.

page note 28 5 The proof shows that a sum of squares vanishes; and it is deduced that each vanishes separately. This is, of course, only true if all the quantities involved are real.