The GroupRevLex documentation says the feature is not implemented yet, but it works

[d-torrance]

---

This issue was triaged from one request inside bugs/dan/0-bugs-iswanson.m2, one of the 857 files removed from the pre-GitHub bugs/ tree by d2c8d27826 and catalogued in #36. That file is a wishlist holding several unrelated requests, so its asks were split apart and filed separately rather than as one issue nobody could close. The commentary below was written by Claude (Claude Opus 5, via Claude Code), not by @d-torrance, whose account posted it -- please weigh it accordingly.

The request, verbatim

GroupRevLex does not seem to be installed; then uncomment the lines in monomorderings.m2 in the manual for GroupRevLex

The rest of the file is unrelated to this request; it is linked in the footer below.

Where it stands today

The documentation for GroupRevLex ends with

     Caveat => { "This feature has not been implemented yet."}

at ov_monomial_orderings.m2:616,
but the feature works. Running that node's own example verbatim:

i1 : R = QQ[a..d, MonomialOrder=>GroupRevLex=>2, Global=>false];

i2 : (monoid R).Options.MonomialOrder
o2 = {MonomialSize => 32, GroupRevLex => 2, GRevLex => {1, 1}, Position => Up}

i3 : a^-1
      -1
o3 = a

i4 : a^-1 * a
o4 = 1

i5 : a^-2 * a^3
o5 = a

i6 : b^-1
      -1
o6 = b

i7 : try c^(-1) else "failed"
o7 = failed

That is exactly what the node's prose promises — "inverts the first n variables in the polynomial ring. In the
following example, a^-1 is in the ring, but c^-1 is not." The inverted variables behave as units, and the boundary
falls where documented.

Why this is worth a moment rather than a one-line deletion

A caveat saying a feature is unimplemented is self-fulfilling: a reader deciding whether GroupRevLex is usable reads it
and stops. So the order may well have gone unused for years while working.

But I would not simply delete the line, because these caveats are not boilerplate. The sibling GroupLex node, twelve
lines below, carries a substantive one:

The element a/b is in the fraction ring, while a*b^(-1) belongs to R.

— a real distinction a user needs. Whoever knows how complete GroupRevLex is should decide what belongs in its place.

One genuine limitation I did find: Gröbner bases fail over such a ring.

i8 : gens gb ideal(a*c-b)
     -- error

so a caveat scoped to Gröbner bases may be warranted where the blanket one is now. I have not probed further than ring
construction, arithmetic and gb, so there may be other gaps; that is precisely why this is filed as a question about
the documentation rather than as a patch.

Provenance

One request from bugs/dan/0-bugs-iswanson.m2, which reads:

GroupRevLex does not seem to be installed
Then uncomment the lines in monomorderings.m2 in the manual
for GroupRevLex.

The situation has inverted since. The manual lines are no longer commented out — monomorderings.m2 is now
ov_monomial_orderings.m2 and documents GroupRevLex at :608, with cross-references at :93, :114, :168 and
:684 — so that half of the request is done. What remains is the opposite of what was reported: the feature is
installed and the documentation says it isn't.

For the record, my own first attempt reproduced the 2005 report, because I wrote MonomialOrder=>{GroupRevLex=>4} over
all four variables without Global => false and read the resulting error as the feature being absent. The documented
form works.

The other seven requests in that file were triaged in the same pass and are recorded in the catalogue: six are met —
including the exponent limits, which now cap at exactly the 2^15-1 and 2^7-1 the file asked for, erroring instead of
wrapping silently — and one is a duplicate of #3449.

Searched titles for GroupRevLex, GroupLex, Laurent, invert, MonomialSize and "inverse of a variable", bodies for
GroupRevLex, and comments for GroupRevLex, GroupLex and "not been implemented yet". Nothing tracks this; the
Laurent and invert hits are unrelated (#598 Laurent series, #4357 denominators, #2718 matrices, #3973 tower rings
via toField).

_{open · disposition issue · ask 8 of bugs/dan/0-bugs-iswanson.m2 · source of truth: bug-triage/asks.tsv}