A polynomial map 
, with ![f=(f_1,...,f_n) in (K[X_1,...,X_n])^m](/images/equations/InvertiblePolynomialMap/Inline2.svg)
in a field 
is called invertible if there exist ![g_1,...,g_m in K[X_1,...,x_n]](/images/equations/InvertiblePolynomialMap/Inline4.svg)
such that 
for 
so that 
(Becker and Weispfenning 1993,
p. 330). Gröbner bases provide a means
to decide for given 
whether or not 
is invertible.
Invertible Polynomial Map
See also
Gröbner Basis, Invertible Polynomial, Jacobian Conjecture, Polynomial MapExplore with Wolfram|Alpha
References
Becker, T. and Weispfenning, V. Gröbner Bases: A Computational Approach to Commutative Algebra. New York: Springer-Verlag, p. 330, 1993.Referenced on Wolfram|Alpha
Invertible Polynomial MapCite this as:
Weisstein, Eric W. "Invertible Polynomial Map." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/InvertiblePolynomialMap.html