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  2. Ramanujan's ternary quadratic form - Wikipedia

    en.wikipedia.org/wiki/Ramanujan's_ternary...

    In number theory, a branch of mathematics, Ramanujan's ternary quadratic form is the algebraic expression x 2 + y 2 + 10z 2 with integral values for x, y and z. [ 1 ] [ 2 ] Srinivasa Ramanujan considered this expression in a footnote in a paper [ 3 ] published in 1916 and briefly discussed the representability of integers in this form.

  3. Quadratic form - Wikipedia

    en.wikipedia.org/wiki/Quadratic_form

    A mapping q : M → R : v ↦ b(v, v) is the associated quadratic form of b, and B : M × M → R : (u, v) ↦ q(u + v) − q(u) − q(v) is the polar form of q. A quadratic form q : M → R may be characterized in the following equivalent ways: There exists an R-bilinear form b : M × M → R such that q(v) is the associated quadratic form.

  4. Ternary quartic - Wikipedia

    en.wikipedia.org/wiki/Ternary_quartic

    The catalecticant of a ternary quartic is the resultant of its 6 second partial derivatives. It vanishes when the ternary quartic can be written as a sum of five 4th powers of linear forms. See also

  5. Category:Quadratic forms - Wikipedia

    en.wikipedia.org/wiki/Category:Quadratic_forms

    Ramanujan's ternary quadratic form; S. ... Quadratic form (statistics) Surgery structure set; Sylvester's law of inertia; T. Tensor product of quadratic forms; U. U ...

  6. Glossary of invariant theory - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_invariant_theory

    1. A contravariant of a ternary form, giving the equation of a dual curve. (Elliott 1895, p.400) reciprocity Exchanging the degree of a form with the degree of an invariant. For example, Hermite's law of reciprocity states that the degree p invariants of a form of degree n correspond to the degree n invariants of a form of degree p.

  7. Genus of a quadratic form - Wikipedia

    en.wikipedia.org/wiki/Genus_of_a_quadratic_form

    An integral quadratic form is a quadratic form on Z n, or equivalently a free Z-module of finite rank. Two such forms are in the same genus if they are equivalent over the local rings Z p for each prime p and also equivalent over R .

  8. Category:Squares in number theory - Wikipedia

    en.wikipedia.org/wiki/Category:Squares_in_number...

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  9. Glossary of biology - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_biology

    This glossary of biology terms is a list of definitions of fundamental terms and concepts used in biology, the study of life and of living organisms.It is intended as introductory material for novices; for more specific and technical definitions from sub-disciplines and related fields, see Glossary of cell biology, Glossary of genetics, Glossary of evolutionary biology, Glossary of ecology ...