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  • preferably areas of algebra of value and interest to computing practitioners.
  • any level from introductory to (say) Grobner bases.
  • preferably using open source computer algebra software.
  • no preference as to Windows, Mac, Linux, etc.
  • in English or French.

Thanks for your input.

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There's Abstract Algebra: Theory and Applications by Judson and Beezer. It doesn't get to Grobner bases but does cover the standard material (and some non-standard stuff, too). It has Sage code and exercises throughout. I will also add that it includes chapters on coding theory, cryptography and lattices and boolean algebras, all of interest to people in computer science.

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