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# homogeneous polynomial

A polynomial $P(x_{1},\cdots,x_{n})$ of degree $k$ is called homogeneous if $P(cx_{1},\cdots,cx_{n})=c^{{k}}P(x_{1},\cdots,x_{n})$ for all constants $c$.

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

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

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

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new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag