Question: Hironaka standard basis algorithms?

Hi, everyone!

I'm trying to do some computations with (truncated) multivariable power series, which I'd like to put into Hironaka standard basis form.  This is almost the same as a Groebner basis, except that the "leading" terms have smallest degree instead of largest.  This requires slight changes to the algorithms in order to make sure they terminate.  Does anyone know if this has been implemented in Maple or have a good way to fake it?  Here's what I've thought of:

  • Using the Groebner package with grlex_min instead of grlex.  The documentation warns that this may not terminate, and sure enough, it doesn't.  (At least not before my computer runs out of memory.)
  • Replacing the truncated power series with their palindromes, using the Groebner package, and then switching back, making sure all the degrees are correctly accounted for.  This should work, but it's going to be a major pain.
  • Reimplementing the Groebner routines.  I'd really rather not, but I'd love to know if anyone else has.

Anybody have any other ideas or suggestions?



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