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单词 JacobianConjecture
释义

Jacobian conjecture


Let F:nn be a polynomial map, i.e.,

F(x1,,xn)=(f1(x1,,xn),,fn(x1,,xn))

for certain polynomialsPlanetmathPlanetmath fi[X1,,Xn].

If F is invertiblePlanetmathPlanetmathPlanetmathPlanetmath, then its Jacobi determinant det(fi/xj), which is a polynomial over ,vanishes nowhere and hence must be a non-zero constant.

The Jacobian conjecture asserts the converseMathworldPlanetmath: every polynomial mapnn whose Jacobi determinant is a non-zero constantis invertible.

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更新时间:2025/5/4 20:48:30