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homogeneous polynomial

(Definition)

A polynomial $P(x_1, \cdots, x_n)$ of degree is called homogeneous if $P(cx_1, \cdots, cx_n) = c^{k}P(x_1, \cdots, x_n)$ for all constants .

An equivalent definition is that all terms of the polynomial have the same degree (i.e. ).

Observe that a polynomial is homogeneous iff $\deg P = {\mathrm{ord}}P$ .

As an important example of homogeneous polynomials one can mention the symmetric polynomials.

"homogeneous polynomial" is owned by jgade.

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Cross-references: symmetric polynomials, iff, terms, equivalent, homogeneous, degree, polynomial
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This is version 8 of homogeneous polynomial, born on 2003-01-04, modified 2005-02-26.
Object id is 3872, canonical name is HomogenousPolynomial.
Accessed 3578 times total.

Classification:

12-00 (Field theory and polynomials :: General reference works )

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