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==The ring of invariants==
The structure of the ring of invariants has been worked out for small degrees. {{harvtxt|Sylvester|Franklin|1879}} gave tables of the numbers of generators of invariants and covariants for forms of degree up to 10, though the tables have a few minor errors for large degrees, mostly where a few invariants or covariants are omitted.
===Covariants of a binary linear form===
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===Covariants of a binary octavic===
{{harvtxt|Sylvester|Franklin|1879}} showed that the ring of invariants of a degree 8 form is generated by 9 invariants of degrees 2, 3, 4, 5, 6, 7, 8, 9, 10, and the ring of covariants is generated by 69 covariants. August von Gall ({{harvtxt|von Gall|1880}}) and {{harvtxt|Shioda|1967}} confirmed the generators for the ring of invariants and showed that the ideal of relations between them is generated by elements of degrees 16, 17, 18, 19, 20.
===Covariants of a binary nonic===
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==Invariants of several binary forms==
The covariants of a binary form are essentially the same as joint invariants of a binary form and a binary linear form. More generally, on can ask for the joint invariants (and covariants) of any collection of binary forms. Some cases that have been studied are listed below.
===Covariants of two linear forms===
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==External links==
*{{citation|first=Andries E. |last=Brouwer|url=http://www.win.tue.nl/~aeb/math/invar.html |title=Invariants of binary forms}}
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