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III.—Double Binary Forms

Published online by Cambridge University Press:  15 September 2014

H. W. Turnbull
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Extract

In the Quarterly Journal, No. 162, 1910, Professor A. R. Forsyth considered some of the problems arising from a homographic transformation of plane curves whose equations could be written in the form

where F is a rational integral function of z and z′, and where z = x + iy, z′ = x − iy determine the rectangular Cartesian coordinates of the plane. It was suggested that the theory could be developed algebraically by using the symbolic methods of the German school which proved so powerful in furthering the theory of binary forms.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 43 , 1924 , pp. 43 - 50
Copyright
Copyright © Royal Society of Edinburgh 1924

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References

page 46 note * Turnbull, H. W., “On the General Theory of Quadrics,” Proc. London Math. Soc., ser. 2, vol. xxi (1922).Google Scholar

page 46 note † See Algebra of Invariants, p 358.

page 47 note * Cf. Algebra of Invariants, chapter iii.

page 48 note * This only happens when ƒ involves two or more symbols a, b.