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Invertible Polynomial Map


A polynomial map phi_(f), with f=(f_1,...,f_n) in (K[X_1,...,X_n])^m in a field K is called invertible if there exist g_1,...,g_m in K[X_1,...,x_n] such that g_i(f_1,...,f_n)=X_i for 1<=n<=n so that phi_(g) degreesphi_(f)=id_(k^n) (Becker and Weispfenning 1993, p. 330). Gröbner bases provide a means to decide for given f whether or not phi_(f) is invertible.


See also

Gröbner Basis, Invertible Polynomial, Jacobian Conjecture, Polynomial Map

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References

Becker, T. and Weispfenning, V. Gröbner Bases: A Computational Approach to Commutative Algebra. New York: Springer-Verlag, p. 330, 1993.

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Invertible Polynomial Map

Cite this as:

Weisstein, Eric W. "Invertible Polynomial Map." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/InvertiblePolynomialMap.html

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