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Check if it is in Sage's source code:

search_doc('buchberger')

This reveals that there is a file

$SAGE_ROOT/devel/sage/sage/rings/polynomial/toy_buchberger.py

(where $SAGE_ROOT is your Sage root directory).

In this file there is a function buchberger and a function buchberger_improved.

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Added "??" instructions; added links to online doc and online source code.

Check if it is in Sage's source code:

search_doc('buchberger')

This reveals that there is a file

$SAGE_ROOT/devel/sage/sage/rings/polynomial/toy_buchberger.py

(where $SAGE_ROOT is your Sage root directory).

In this file there is a function buchberger and a function buchberger_improved.

To get the code for Buchberger's algorithm, type

sage: from sage.rings.polynomial.toy_buchberger import buchberger
sage: buchberger??

It uses a function to compute the S-polynomial of two polynomials, whose source code you can see by typing

sage: from sage.rings.polynomial.toy_buchberger import spol
sage: spol??

See also the online documentation for toy_buchberger.

You can also browse the source code online at github. See toy_buchberger there.