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- Harmonic_polynomial abstract "In mathematics, in abstract algebra, a multivariate polynomial over a field whose Laplacian is zero is termed a harmonic polynomial.The harmonic polynomials form a vector subspace of the vector space of polynomials over the field. In fact, they form a graded subspace.The Laplacian is the sum of second partials with respect to all the variables, and is an invariant differential operator under the action of the orthogonal group viz the group of rotations.The standard separation of variables theorem states that every multivariate polynomial over a field can be decomposed as a finite sum of products of a radical polynomial and a harmonic polynomial. This is equivalent to the statement that the polynomial ring is a free module over the ring of radical polynomials.".
- Harmonic_polynomial wikiPageID "5755288".
- Harmonic_polynomial wikiPageLength "1147".
- Harmonic_polynomial wikiPageOutDegree "16".
- Harmonic_polynomial wikiPageRevisionID "544442341".
- Harmonic_polynomial wikiPageWikiLink Abstract_algebra.
- Harmonic_polynomial wikiPageWikiLink Bertram_Kostant.
- Harmonic_polynomial wikiPageWikiLink Category:Abstract_algebra.
- Harmonic_polynomial wikiPageWikiLink Category:Polynomials.
- Harmonic_polynomial wikiPageWikiLink Differential_operator.
- Harmonic_polynomial wikiPageWikiLink Free_module.
- Harmonic_polynomial wikiPageWikiLink Graded_algebra.
- Harmonic_polynomial wikiPageWikiLink Graded_ring.
- Harmonic_polynomial wikiPageWikiLink Group_(mathematics).
- Harmonic_polynomial wikiPageWikiLink Invariant_(mathematics).
- Harmonic_polynomial wikiPageWikiLink Laplace_operator.
- Harmonic_polynomial wikiPageWikiLink Laplacian.
- Harmonic_polynomial wikiPageWikiLink Mathematics.
- Harmonic_polynomial wikiPageWikiLink Orthogonal_group.
- Harmonic_polynomial wikiPageWikiLink Polynomial.
- Harmonic_polynomial wikiPageWikiLink Radical_polynomial.
- Harmonic_polynomial wikiPageWikiLink Separation_of_variables_theorem.
- Harmonic_polynomial wikiPageWikiLink Vector_space.
- Harmonic_polynomial wikiPageWikiLinkText "Harmonic polynomial".
- Harmonic_polynomial wikiPageWikiLinkText "harmonic polynomial".
- Harmonic_polynomial hasPhotoCollection Harmonic_polynomial.
- Harmonic_polynomial wikiPageUsesTemplate Template:Algebra-stub.
- Harmonic_polynomial subject Category:Abstract_algebra.
- Harmonic_polynomial subject Category:Polynomials.
- Harmonic_polynomial type Type.
- Harmonic_polynomial type Function.
- Harmonic_polynomial type Polynomial.
- Harmonic_polynomial type Type.
- Harmonic_polynomial comment "In mathematics, in abstract algebra, a multivariate polynomial over a field whose Laplacian is zero is termed a harmonic polynomial.The harmonic polynomials form a vector subspace of the vector space of polynomials over the field.".
- Harmonic_polynomial label "Harmonic polynomial".
- Harmonic_polynomial sameAs m.0f2y5q.
- Harmonic_polynomial sameAs Гармонический_многочлен.
- Harmonic_polynomial sameAs Гармонічний_многочлен.
- Harmonic_polynomial sameAs Q4133834.
- Harmonic_polynomial sameAs Q4133834.
- Harmonic_polynomial wasDerivedFrom Harmonic_polynomial?oldid=544442341.
- Harmonic_polynomial isPrimaryTopicOf Harmonic_polynomial.