The RationalMaps package implements Rees algebra and Jacobian dual matrix criteria to invert rational maps and test birationality, with a hybrid strategy that is often faster than prior packages.
Boehm : Parametrization, Package for Macaulay2, see \\ http://www.math.uiuc.edu/Macaulay2/doc/Macaulay2-1.14/share/doc/Macaulay2/Parametrization/html/
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RationalMaps, a package for Macaulay2
The RationalMaps package implements Rees algebra and Jacobian dual matrix criteria to invert rational maps and test birationality, with a hybrid strategy that is often faster than prior packages.