Ideal ? Ideal is not defined, so a list of ideals cannot be sorted

[d-torrance]

---

This issue was triaged from one request inside bugs/dan/doc-changes, 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

? -- ? for ideals?

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

Where it stands today

Ideal ? Ideal is not defined, so a list of ideals cannot be sorted:

i1 : R = QQ[x,y];

i2 : sort {ideal x, ideal(x,y), ideal(x^2)}
stdio:2:1:(3): error: no method for binary operator ? applied to objects:
--            ideal x (of class Ideal)
--       ?    ideal (x, y) (of class Ideal)

i3 : sort {monomialIdeal x, monomialIdeal(x,y)}      -- same

whereas the corresponding modules sort fine:

i4 : sort {module ideal x, module ideal(x,y)}
o4 = {image | x |, image | x y |}

Why the module case works and this is the natural gap

The method that makes i4 work exists for exactly this purpose. m2/modules.m2:370:

-- used for sorting a list of modules
Module ? Module := (M, N) -> if rank M != rank N then rank M ? rank N else degrees M ? degrees N

So it is an arbitrary total order on rank then degrees — deliberately not containment — provided so that lists of
modules can be sorted into a canonical arrangement. CoherentSheaf ? CoherentSheaf exists too. Ideals are the more
commonly handled object of the three, and they are the one that cannot be sorted.

To be clear about what is and isn't missing: the unary ? works on ideals already, inheriting briefDocumentation from
(?, Thing), so ? I and ? Ideal both print brief documentation. This is only about the binary comparison.

lookup(symbol ?, Ideal, Ideal) returns a function rather than null, which is not evidence of a method — it is the
installed "no method" error at m2/robust.m2:88, the subject of #4572.

Not a duplicate of #660

#660 "comparison of ideals" is about == on ideals being slower than
necessary because it does two isSubset calls, and asks why some code there is commented out. That is mathematical
equality and its cost; this is an arbitrary ordering for sorting. They would be fixed in different places, though anyone
touching ideal comparison may want to look at both.

Provenance

One entry from bugs/dan/doc-changes, which reads simply:

?	? for ideals?

It sits between the == and != entries, among the comparison operators, which is what settles it as the binary reading
rather than the unary one. The remaining 32 entries of that file were triaged in the same pass and are recorded in the
catalogue.

Searched titles for compare ideal, sort ideal and codim, and comments for Ideal ? Ideal; nothing tracks this.

_{open · disposition issue · ask 7 of bugs/dan/doc-changes · source of truth: bug-triage/asks.tsv}