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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. 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

  4. 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.

  5. Quadric (algebraic geometry) - Wikipedia

    en.wikipedia.org/wiki/Quadric_(algebraic_geometry)

    By definition, a quadric X of dimension n over a field k is the subspace of + defined by q = 0, where q is a nonzero homogeneous polynomial of degree 2 over k in variables , …, +. (A homogeneous polynomial is also called a form , and so q may be called a quadratic form .)

  6. Category:Quadratic forms - Wikipedia

    en.wikipedia.org/wiki/Category:Quadratic_forms

    Ramanujan's ternary quadratic form; S. Signature (topology) Smith–Minkowski–Siegel mass formula; Spinor genus; Quadratic form (statistics) Surgery structure set;

  7. Carl Friedrich Gauss - Wikipedia

    en.wikipedia.org/wiki/Carl_Friedrich_Gauss

    This is an accepted version of this page This is the latest accepted revision, reviewed on 8 January 2025. German mathematician, astronomer, geodesist, and physicist (1777–1855) "Gauss" redirects here. For other uses, see Gauss (disambiguation). Carl Friedrich Gauss Portrait by Christian Albrecht Jensen, 1840 (copy from Gottlieb Biermann, 1887) Born Johann Carl Friedrich Gauss (1777-04-30 ...

  8. Degenerate bilinear form - Wikipedia

    en.wikipedia.org/wiki/Degenerate_bilinear_form

    The study of real, quadratic algebras shows the distinction between types of quadratic forms. The product zz* is a quadratic form for each of the complex numbers, split-complex numbers, and dual numbers. For z = x + ε y, the dual number form is x 2 which is a degenerate quadratic form. The split-complex case is an isotropic form, and the ...

  9. 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 .

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