Polinômio homogêneo

Em matemática, um polinômio homogêneo é um polinômio onde os monômios com coeficientes não-nulos têm o mesmo grau total.^[1] Por exemplo, $x^{5}+2x^{3}y^{2}+9xy^{4}$ é um polinômio de grau 5, em duas variáveis; a soma dos expoentes nos têrmos é sempre 5. O polinômio $x^{3}+3x^{2}y+z^{7}$ não é homogêneo, pois a soma de cada um dos expoentes termo a termo não é a mesma. Uma forma algébrica, ou simplesmente forma, é outro nome para um polinômio homogêneo. A teoria das formas algébricas é muito extensa, e há numerosas aplicações por toda a matemática e física teóricas.

Ligações externas

Weisstein, Eric W. «Homogeneous Polynomial». MathWorld (em inglês)

Referências

↑ D. Cox, J. Little, D. O'Shea: Using Algebraic Geometry, 2nd ed., page 2. Springer-Verlag, 2005.

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