Talk:Homogeneous polynomial

It appears that that the first paragraph uses a nonstandard definition of "monomial." It claims that x3+2x+y3 is a homogenous polynomial because the middle term has no exponent, and is therefore not a monomial. First of all, it does have an exponent (1), which is customarily left out. Second, the middle term certainly fits the second definition of a monomial as given on the wikipedia page for it. It does not fit the first definition from the Monomial page, but that seems irrelevant, as the prior examples of homogenous polynomials contains terms that also do not fit the first definition of a monomial. I will admit to a lack of expertise in this area, but it appears that there is definitely an error here somewhere. 74.76.122.74 (talk) 01:08, 29 May 2009 (UTC)


 * Weird. You're completely correct I'll fix this. RobHar (talk) 04:51, 29 May 2009 (UTC)

Symmetric tensors
This section has multiple issues: For all these reasons, I will suppress this section.
 * The notion of symmetric tensor being more advanced that the one of homogeneous polynomial, the relationship between these two notions should not appear here but in symmetric tensor.
 * The section is not sourced: the reference given in the article contains nothing about this section but contains all the remainder material of the page.
 * The section is so poorly written that understand is difficult, even for a senior mathematician (me), author of several papers on homogeneous polynomials.
 * It appears that the section is full of mathematical non senses. For example the homogeneous polynomials are described as parameterized by two vector spaces. Two lines before, a formula implies that homogeneous polynomials are univariate.

D.Lazard (talk) 10:16, 25 March 2012 (UTC)

Homogeneous?
The article claims that a polynomial is homogeneous of degree d if and only if $$P(tX_1,tX_2,...,tX_n)=t^d P(X_1,X_2,...,X_n)$$. But the second condition is satisfied for all $$t$$ in $$F_3$$ and $$P(X_1,X_2)=X_1X_2+ X_1^2 X_2^2$$, $$d=2$$,$$P$$ not being homogeneous. Isn't the claimed property thus wrong? 87.240.242.155 (talk) 17:20, 3 May 2016 (UTC)