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→The ring of invariants: degree 2 |
→The ring of invariants: ternary |
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The structure of the ring of invariants has been worked out for small degrees as follows:
# The only invariants are constants.
# The algebra of invariants of the binary form ''ax''<sup>2</sup> + ''bxy'' + ''cy''<sup>2</sup> is a polynomial
# The algebra of invariants of the ternary form ''ax''<sup>3</sup> + ''bx''<sup>2</sup>''y'' + ''cxy''<sup>2</sup> + ''dy''<sup>3</sup> is a polynomial algebra in 1 variable generated by the discriminant 3''b''<sup>2</sup>''c''<sup>2</sup> + 6''abcd'' −4''b''<sup>3</sup>''d'' − 4''c''<sup>3</sup>''a'' − ''a''<sup>2</sup>''d''<sup>2</sup> of degree 4.
# The algebra of invariants is generated by invariants of degrees 2, 3.
# The algebra of invariants is generated by invariants of degree 4, 8, 12, 18
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