CoCoAlib (Computations in Commutative Algebra library)
This thing is actually nice. My tired-brain can understand C/C++. It is well documented and has tests and debugging procedures. Is that a Hilbert Algebra? I can has type PolyRing?
http://cocoa.dima.unige.it/cocoalib/index.shtml
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https://cocoa.dima.unige.it/cocoa/cocoalib/
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Update link
https://cocoa.dima.unige.it/cocoa/cocoalib/