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In algebra, a multivariate polynomial
is quasi-homogeneous or weighted homogeneous, if there exist r integers w 1 , … , w r {\displaystyle w_{1},\ldots ,w_{r}} , called weights of the variables, such that the sum w = w 1 i 1 + ⋯ + w r i r {\displaystyle w=w_{1}i_{1}+\cdots +w_{r}i_{r}} is the same for all nonzero terms of f. This sum w is the weight or the degree of the polynomial.
The term quasi-homogeneous comes from the fact that a polynomial f is quasi-homogeneous if and only if
for every λ {\displaystyle \lambda } in any field containing the coefficients.