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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?

MarcoB
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Bob Jones
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    "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 [tag:undocumented] tag, you will see SE users making use of these. – J. M.'s missing motivation Apr 22 '20 at 01:56
  • "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 – Nasser Apr 22 '20 at 01:57
  • @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? – Bob Jones Apr 22 '20 at 02:00
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    see what-are-some-useful-undocumented-mathematica-functions There is no official document to document the undocumented functions. – Nasser Apr 22 '20 at 02:02
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    If you do look around SE, you'll find this highly-voted post in the [tag:undocumented] tag. :) – J. M.'s missing motivation Apr 22 '20 at 02:02

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