Thanks Xavier for bringing this up.

Piecewise-defined functions do need work in Sage.

Related tickets and discussions:

  https://trac.sagemath.org/query?order=id&desc=1&summary=~piecewise
  https://trac.sagemath.org/wiki/symbolics#limitationsofPiecewisefunctions
  
https://groups.google.com/forum/#!searchin/sage-devel/piecewise%7Csort:date
  
https://groups.google.com/forum/#!searchin/sage-support/piecewise%7Csort:date
  
https://ask.sagemath.org/questions/scope:all/sort:activity-desc/page:1/query:piecewise/

This might be a good topic for a supervised student project.

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