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Re:Computational algebraic geometry for high school students by madars on Tuesday August 03, 2021 @02:18PM (#28052322)
Magma should do it (http://magma.maths.usyd.edu.au/magma/handbook/text/970 claims a Alan Steel's non-commutative generalization of Faugère F4 and noncommutative Buchberger algorithm) and US institutions can get it via the Simmons agreement. Not sure what's good for home users, though.

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