Revision as of 23:49, 8 June 2015 edit JoergenB (talk \| contribs) Extended confirmed users 6,038 edits m →Terminology: The invariants "are" not an algebra. They form an algebra (together). Alternatively, the set of invariants is a subalgebra of the polynomial ring over the variables a_0,..., a_n ← Previous edit		Revision as of 17:47, 8 December 2015 edit undo 77.172.209.42 (talk) →Covariants of a binary quartic: fixed typo Next edit →
Line 56: ===Covariants of a binary quartic=== The algebra of invariants of a quartic form is generated by invariants ''i'', ''j'' of degrees 2, 3. This ring is naturally isomorphic to the ring of modular forms of level 1, with the two generators corresponding to the Eisenstein series ''E''<sub>4</sub> and ''E''</sub>6</sub>. The algebra of covariants is generated by these two invariants together with the form ''f'' of degree 1 and order 4, the Hessian ''H'' of degree 2 and order 4, and a covariant ''T'' of degree 3 and order 6. They are related by a syzygy ''jf''<sup>3</sup>−''Hf''<sup>2</sup>''i''+4''H''<sup>3</sup>+''T''<sup>2</sup>=0 of degree 6 and order 12. {{harv\|Schur\|1968\|loc=II.8}} {{harv\|Hilbert\|1993\|loc=XVIII, XXII}} ===Covariants of a binary quintic===

Invariant of a binary form: Difference between revisions