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The Bernstein–Kushnirenko theorem (or Bernstein–Khovanskii–Kushnirenko (BKK) theorem ), proven by and in 1975, is a theorem in algebra. It states that the number of non-zero complex solutions of a system of Laurent polynomial equations is equal to the mixed volume of the Newton polytopes of the polynomials , assuming that all non-zero coefficients of are generic. A more precise statement is as follows:

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  • Teorema de Bernstein-Kushnirenko (ca)
  • Bernstein–Kushnirenko theorem (en)
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  • El teorema de Bernstein-Kushnirenko o teorema de Bernstein-Khovanskii-Kushnirenko (BKK), provat per i Anatoli Kushnirenko el 1975, és un teorema en l'àlgebra. Afirma que el nombre de solucions complexes no nul·les d’un sistema d’equacions de polinomis de Laurent és igual al dels dels polinomis , suposant que tots els coeficients diferents de zero de siguin genèrics. El nom de Kushnirenko també s'escriu Kouchnirenko. David Bernstein és germà de . ha trobat unes 15 proves diferents d’aquest teorema. Una afirmació més precisa del teorema és la següent: (ca)
  • The Bernstein–Kushnirenko theorem (or Bernstein–Khovanskii–Kushnirenko (BKK) theorem ), proven by and in 1975, is a theorem in algebra. It states that the number of non-zero complex solutions of a system of Laurent polynomial equations is equal to the mixed volume of the Newton polytopes of the polynomials , assuming that all non-zero coefficients of are generic. A more precise statement is as follows: (en)
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  • El teorema de Bernstein-Kushnirenko o teorema de Bernstein-Khovanskii-Kushnirenko (BKK), provat per i Anatoli Kushnirenko el 1975, és un teorema en l'àlgebra. Afirma que el nombre de solucions complexes no nul·les d’un sistema d’equacions de polinomis de Laurent és igual al dels dels polinomis , suposant que tots els coeficients diferents de zero de siguin genèrics. El nom de Kushnirenko també s'escriu Kouchnirenko. David Bernstein és germà de . ha trobat unes 15 proves diferents d’aquest teorema. Una afirmació més precisa del teorema és la següent: (ca)
  • The Bernstein–Kushnirenko theorem (or Bernstein–Khovanskii–Kushnirenko (BKK) theorem ), proven by and in 1975, is a theorem in algebra. It states that the number of non-zero complex solutions of a system of Laurent polynomial equations is equal to the mixed volume of the Newton polytopes of the polynomials , assuming that all non-zero coefficients of are generic. A more precise statement is as follows: (en)
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