Square of a polynomial has non negative coefficients implies that the polynomial has non negative...
0
Let $f$ be a $n$ variate homogeneous polynomial with real coefficients. Suppose $f^2$ has non negative coefficients, does it imply that $f$ also has non negative coefficients?
polynomials
edited Dec 3 '18 at 7:27
астон вілла олоф мэллбэрг
37.3k33376
asked Dec 3 '18 at 7:24
user50123
1
add a comment |
0
Let $f$ be a $n$ variate homogeneous polynomial with real coefficients. Suppose $f^2$ has non negative coefficients, does it imply that $f$ also has non negative coefficients?
polynomials
edited Dec 3 '18 at 7:27
астон вілла олоф мэллбэрг
37.3k33376
asked Dec 3 '18 at 7:24
user50123
1
3
What about $(-x)$ or $(-x-y)$?
– Berci
Dec 3 '18 at 7:30
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Dec 3 '18 at 7:31
Or, more complicated but maybe what OP had in mind, $x^6+x^5+x^4-x^3+x^2+x+1$.
– Gerry Myerson
Dec 3 '18 at 7:31
add a comment |
0
0
0
Let $f$ be a $n$ variate homogeneous polynomial with real coefficients. Suppose $f^2$ has non negative coefficients, does it imply that $f$ also has non negative coefficients?
polynomials
edited Dec 3 '18 at 7:27
астон вілла олоф мэллбэрг
37.3k33376
asked Dec 3 '18 at 7:24
user50123
1
Let $f$ be a $n$ variate homogeneous polynomial with real coefficients. Suppose $f^2$ has non negative coefficients, does it imply that $f$ also has non negative coefficients?
polynomials
polynomials
edited Dec 3 '18 at 7:27
астон вілла олоф мэллбэрг
37.3k33376
asked Dec 3 '18 at 7:24
user50123
1
edited Dec 3 '18 at 7:27
астон вілла олоф мэллбэрг
37.3k33376
asked Dec 3 '18 at 7:24
user50123
1
edited Dec 3 '18 at 7:27
астон вілла олоф мэллбэрг
37.3k33376
edited Dec 3 '18 at 7:27
астон вілла олоф мэллбэрг
37.3k33376
edited Dec 3 '18 at 7:27
астон вілла олоф мэллбэрг
37.3k33376
37.3k33376
asked Dec 3 '18 at 7:24
user50123
1
asked Dec 3 '18 at 7:24
user50123
1
asked Dec 3 '18 at 7:24
user50123
1
1
3
What about $(-x)$ or $(-x-y)$?
– Berci
Dec 3 '18 at 7:30
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Dec 3 '18 at 7:31
Or, more complicated but maybe what OP had in mind, $x^6+x^5+x^4-x^3+x^2+x+1$.
– Gerry Myerson
Dec 3 '18 at 7:31
add a comment |
3
What about $(-x)$ or $(-x-y)$?
– Berci
Dec 3 '18 at 7:30
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Dec 3 '18 at 7:31
Or, more complicated but maybe what OP had in mind, $x^6+x^5+x^4-x^3+x^2+x+1$.
– Gerry Myerson
Dec 3 '18 at 7:31
3
3
What about $(-x)$ or $(-x-y)$?
– Berci
Dec 3 '18 at 7:30
What about $(-x)$ or $(-x-y)$?
– Berci
Dec 3 '18 at 7:30
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Dec 3 '18 at 7:31
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Dec 3 '18 at 7:31
Or, more complicated but maybe what OP had in mind, $x^6+x^5+x^4-x^3+x^2+x+1$.
– Gerry Myerson
Dec 3 '18 at 7:31
Or, more complicated but maybe what OP had in mind, $x^6+x^5+x^4-x^3+x^2+x+1$.
– Gerry Myerson
Dec 3 '18 at 7:31
add a comment |
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3
What about $(-x)$ or $(-x-y)$?
– Berci
Dec 3 '18 at 7:30
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Dec 3 '18 at 7:31
Or, more complicated but maybe what OP had in mind, $x^6+x^5+x^4-x^3+x^2+x+1$.
– Gerry Myerson
Dec 3 '18 at 7:31