Combinants of a pencil of quadric surfaces (III)
John A. Todd
Abstract
John A. Todd
Abstract
The two previous papers of this series dealt with the determination of the complete system of combinantal covariants and contravariants of a pencil of quadric surfaces. The present paper is concerned with combinantal forms involving line-complexes, and with certain syzygies which exist between these forms. It is essentially a preparation for the determination of the complete system of combinantal line-complexes of the pencil, which will be carried out explicitly in the next paper of the series.
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The two previous papers of this series dealt with the determination of the complete system of combinantal covariants and contravariants of a pencil of quadric surfaces. The present paper is concerned with combinantal forms involving line-complexes, and with certain syzygies which exist between these forms. It is essentially a preparation for the determination of the complete system of combinantal line-complexes of the pencil, which will be carried out explicitly in the next paper of the series.
Key concepts: Pencil (optics), Quadric, Series (stratigraphy), Mathematics, Line (geometry), Algebra over a field, Pure mathematics, Geometry