I was trying to calculate a Groebner basis for a given set of polynomials, and I did it successfully. But I wanted to calculate the conversion matrix between the original basis and the Groebner basis. Apparently Mathematica is able to do that with GroebnerBasis`BasisAndConversionMatrix in place of GroebnerBasis.

First, what does the ` mean? Searching in the documentation only gives me things about precision. Is BasisAndConversionMatrix a sub-function of GroebnerBasis?

Second, why is there a symbol that is unrecognized by Mathematica (it's blue when you type it), appears nowhere in the documentation, and yet appears to correctly do an important job? Where am I supposed to have officially learned about this symbol? Is it an official part of Mathematica, or is it a part of some unofficial package I've downloaded?

  • 3
    $\begingroup$ "Is BasisAndConversionMatrix a sub-function of GroebnerBasis?" - pretty much. A lot of explicitly available functions in Mathematica are implemented using undocumented low-level or utility functions, that are usually not intended for users. That being said, if you look at the undocumented tag, you will see SE users making use of these. $\endgroup$ Apr 22, 2020 at 1:56
  • $\begingroup$ "what does the ` mean" this is used to tell the context of the symbol. For global symbol, it is "Global` x" but Global is the default so no one adds it explicitly. so GroebnerBasis`BasisAndConversionMatrix means BasisAndConversionMatrix in context GroebnerBasis $\endgroup$
    – Nasser
    Apr 22, 2020 at 1:57
  • $\begingroup$ @J.M. If there are undocumented functions, is there an unofficial list of them collected somewhere, or do you just have to look around StackExchange for what you want? $\endgroup$
    – Bob Jones
    Apr 22, 2020 at 2:00
  • 5
    $\begingroup$ see what-are-some-useful-undocumented-mathematica-functions There is no official document to document the undocumented functions. $\endgroup$
    – Nasser
    Apr 22, 2020 at 2:02
  • 3
    $\begingroup$ If you do look around SE, you'll find this highly-voted post in the undocumented tag. :) $\endgroup$ Apr 22, 2020 at 2:02


Browse other questions tagged or ask your own question.