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Triple Binary Forms; the complete system for a single (1, 1, 1) form with its geometrical interpretation

Published online by Cambridge University Press:  24 October 2008

W. Saddler
W. Saddler
Affiliation:
St John's College.
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Extract

In the Transactions of the American Math. Society, vol. I, 1900, and vol. IV, 1904, Mr E. Kasner treats exhaustively the (2, 2) double binary form and discusses the theory connected with double binary forms and multiple binary forms in general terms. He shows the relations between the systems of multiple binary forms with digredient variables and the forms with cogredient variables. Hitherto nothing seems to have been written on systems of triple binary forms (with regard to higher forms see a paper on the (1, 1, 1, 1) form by C. Segre); so here I propose to discuss the complete system of a (1, 1, 1) binary form which consists of six forms connected by one syzygy. When two of the variables are the same we naturally get the (2, 1) form and when the three are the same We get the (3) or cubic binary form.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 22 , Issue 5 , July 1925 , pp. 688 - 693
Copyright
Copyright © Cambridge Philosophical Society 1925

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References

* Annali di Mat. (3), 29, 105–140 (1920).Google Scholar

† The necessary x, y, z factors are to be added.

* Grace, and Young, , Algebra of Invariants, pp. 85–100Google Scholar; Peano, , Battaglini, vol. 20 (1882).Google Scholar

† In Φ2, Φ1, and in what follows, indicates the implied necessary x, y, z factors.