homogeneous polynomial
- noun
- /ˌhoʊməˈdʒiːnəs pəˈlɪnəʊmiəl/
- Specialized
:
polinomio homogéneo
- The equation x² + y² is a homogeneous polynomial of degree 2.
Examples
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A homogeneous polynomial has terms of equal degree.
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The expression is a homogeneous polynomial in two variables.
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Every term in a homogeneous polynomial must have the same total degree.
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In advanced algebra, homogeneous polynomials are often used to simplify problems involving symmetry.
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Every term in a homogeneous polynomial must have the same total degree.
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The equation x² + y² is a homogeneous polynomial of degree 2.
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In advanced algebra, homogeneous polynomials are often used to simplify problems involving symmetry.
Synonyms
A math expression with two or more variables whose terms all have the same total degree
Surface Forms
Morphology
The phrase is compositionally related: 'homogeneous' (of the same kind or uniform) combined with 'polynomial' suggests a polynomial whose terms share some common property. However, the precise technical meaning — that every term has the same total degree — is a specialised mathematical detail that an average B1 learner, even knowing the constituent words, is unlikely to infer without subject‑specific knowledge.
Etymology
Homogeneous polynomial gets its name because homogeneous means 'the same' and a polynomial is a math expression made of terms, so imagine each term as a tower all the same height. So, if every tower has the same height, the polynomial is 'homogeneous' — that is, all terms have the 'same degree'.
