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Ternary Cubic
In mathematics, a ternary cubic form is a homogeneous degree 3 polynomial in three variables. Invariant theory The ternary cubic is one of the few cases of a form of degree greater than 2 in more than 2 variables whose ring of invariants was calculated explicitly in the 19th century. The ring of invariants The algebra of invariants of a ternary cubic under SL3(C) is a polynomial algebra generated by two invariants ''S'' and ''T'' of degrees 4 and 6, called Aronhold invariants. The invariants are rather complicated when written as polynomials in the coefficients of the ternary cubic, and are given explicitly in The ring of covariants The ring of covariants is given as follows. The identity covariant ''U'' of a ternary cubic has degree 1 and order 3. The Hessian ''H'' is a covariant of ternary cubics of degree 3 and order 3. There is a covariant ''G'' of ternary cubics of degree 8 and order 6 that vanishes on points ''x'' lying on the Salmon conic of the polar of ''x'' with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cayleyan
In algebraic geometry, the Cayleyan is a variety associated to a hypersurface In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface. A hypersurface is a manifold or an algebraic variety of dimension , which is embedded in an ambient space of dimension , generally a Euclidean ... by , who named it the pippian in and also called it the Steiner–Hessian. See also * Quippian References * * * Algebraic geometry {{algebraic-geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quippian
In mathematics, a quippian is a degree 5 class 3 contravariant of a plane cubic introduced by and discussed by . In the same paper Cayley also introduced another similar invariant that he called the pippian, now called the Cayleyan. See also *Glossary of classical algebraic geometry References * *{{Citation , authorlink=Igor Dolgachev , last1=Dolgachev , first1=Igor V. , title=Classical Algebraic Geometry: a modern view , url=http://www.math.lsa.umich.edu/~idolga/CAG.pdf , publisher=Cambridge University Press Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing hou ... , isbn=978-1-107-01765-8 , year=2012 Algebraic geometry Invariant theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ternary Quartic
In mathematics, a ternary quartic form is a degree 4 homogeneous polynomial in three variables. Hilbert's theorem showed that a positive semi-definite ternary quartic form over the reals can be written as a sum of three squares of quadratic forms. Invariant theory The ring of invariants is generated by 7 algebraically independent invariants of degrees 3, 6, 9, 12, 15, 18, 27 (discriminant) , together with 6 more invariants of degrees 9, 12, 15, 18, 21, 21, as conjectured by . discussed the invariants of order up to about 15. The Salmon invariant is a degree 60 invariant vanishing on ternary quartics with an inflection bitangent. Catalecticant 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 *Ternary cubic *Invariants of a binary form References * * * * *. * * *{{Citation , last1=Thomsen , first1=H. Ivah , title=Some I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Invariants Of A Binary Form
In mathematical invariant theory, an invariant of a binary form is a polynomial in the coefficients of a binary form in two variables ''x'' and ''y'' that remains invariant under the special linear group acting on the variables ''x'' and ''y''. Terminology A binary form (of degree ''n'') is a homogeneous polynomial Σ ()''a''''n''−''i''''x''''n''−''i''''y''''i'' = ''a''''n''''x''''n'' + ()''a''''n''−1''x''''n''−1''y'' + ... + ''a''0''y''''n''. The group ''SL''2(C) acts on these forms by taking ''x'' to ''ax'' + ''by'' and ''y'' to ''cx'' + ''dy''. This induces an action on the space spanned by ''a''0, ..., ''a''''n'' and on the polynomials in these variables. An invariant is a polynomial in these ''n'' + 1 variables ''a''0, ..., ''a''''n'' that is invariant under this action. More generally a covariant is a polynomial in ''a''0, ..., ''a''''n'', ''x'', ''y'' that is invariant, so an invariant is a special case of a co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Journal Of Mathematics
The ''American Journal of Mathematics'' is a bimonthly mathematics journal published by the Johns Hopkins University Press. History The ''American Journal of Mathematics'' is the oldest continuously published mathematical journal in the United States, established in 1878 at the Johns Hopkins University by James Joseph Sylvester, an English-born mathematician who also served as the journal's editor-in-chief from its inception through early 1884. Initially W. E. Story was associate editor in charge; he was replaced by Thomas Craig in 1880. For volume 7 Simon Newcomb became chief editor with Craig managing until 1894. Then with volume 16 it was "Edited by Thomas Craig with the Co-operation of Simon Newcomb" until 1898. Other notable mathematicians who have served as editors or editorial associates of the journal include Frank Morley, Oscar Zariski, Lars Ahlfors, Hermann Weyl, Wei-Liang Chow, S. S. Chern, André Weil, Harish-Chandra, Jean Dieudonné, Henri Cartan, Stephen S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing house specializing in monographs and scholarly journals. Most are nonprofit organizations and an integral component of a large research university. They publish work that has been reviewed by schola ... in the world. It is also the King's Printer. Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. It became part of Cambridge University Press & Assessment, following a merger with Cambridge Assessment in 2021. With a global sales presence, publishing hubs, and offices in more than 40 Country, countries, it publishes over 50,000 titles by authors from over 100 countries. Its publishing includes more than 380 academic journals, monographs, reference works, school and uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematische Annalen
''Mathematische Annalen'' (abbreviated as ''Math. Ann.'' or, formerly, ''Math. Annal.'') is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann. Subsequent managing editors were Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück, and Nigel Hitchin. Currently, the managing editor of Mathematische Annalen is Thomas Schick. Volumes 1–80 (1869–1919) were published by Teubner. Since 1920 (vol. 81), the journal has been published by Springer. In the late 1920s, under the editorship of Hilbert, the journal became embroiled in controversy over the participation of L. E. J. Brouwer on its editorial board, a spillover from the foundational Brouwer–Hilbert controversy. Between 1945 and 1947 the journal briefly ceased publication. References External links''Mathematische Annalen''homepage at Springer''Mathematische Annalen''archive (1869†... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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