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XXVIII.—The Discriminant of a Certain Ternary Quartic

Published online by Cambridge University Press:  14 February 2012

W. L. Edge
W. L. Edge
Affiliation:
Mathematical Institute, University of Edinburgh
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Extract

I. By the discriminant D of a homogeneous polynomial ø is, in accordance with the general custom, to be understood that function of its coefficients whose vanishing is the necessary and sufficient condition for the locus ø = o to have a node. It is the resultant, or eliminant, of the set of equations obtained by equating all the first partial derivatives of ø simultaneously to zero. If ø contains n variables and is of order p, the degree of D in the coefficients of ø is n(p–I)n−1.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 62 , Issue 3 , 1948 , pp. 268 - 272
Copyright
Copyright © Royal Society of Edinburgh 1946

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References

REFERENCES TO LITERATURE

Dersch, O., 1874. “Doppeltangenten einer Curve n ter Ordnung”, Math. Ann., VII, 497–511.CrossRefGoogle Scholar
Klein, F., 1890. “Zur Theorie der Abelschen Functionen”, Math, Ann., XXXVI, 1–83; Gesammelte Mathematische Abhandlungen, III, 388–473.CrossRefGoogle Scholar
Salmon, G., 1879. A treatise on the higher plane curves, Third Edition, Dublin.Google Scholar