| 1. | Let in be a homogeneous polynomial of degree " d ".
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| 2. | Homogeneous polynomials are ubiquitous in mathematics and physics.
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| 3. | For more details, see homogeneous polynomial.
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| 4. | The zero polynomial is homogeneous, and, as homogeneous polynomial, its degree is undefined.
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| 5. | This corresponds to a symmetric homogeneous polynomial
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| 6. | It is then defined by a single equation, a homogeneous polynomial in the homogeneous coordinates.
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| 7. | Additionally, one can look at curves in the projective plane, given by homogeneous polynomials.
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| 8. | Note that quadratic forms and cubic forms are precisely homogeneous polynomials of degrees 2 and 3.
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| 9. | For her thesis, Noether extended Gordan's computational proof to homogeneous polynomials in three variables.
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| 10. | Therefore if " S " is any set of homogeneous polynomials we may reasonably speak of
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