PieriMaps: 2.0 overhaul

[kellerlv]

Adds projection-direction maps (dualPieri, dualPieriColumn, dualLR),
point evaluators (applyPieri, applyPieriColumn, applyLR, applyDualPieri,
applyDualLR, applyDualPieriColumn), three basis conventions
(Row / Filling / Weyl) with conversion utilities, GL_n equivariance
and well-definedness checkers (verifyEquivariant, verifyWellDefined),
and symbolic display of any constructed map (symbolicForm).

[kellerlv]

One comment about this: since version 1.0 was verified as a JSAG paper, the citation generator was automatically adding me as an author of the actual JSAG article, which isn't correct. So I manually removed the JSAG certification but kept a line in the documentation stating that 1.0 was certified. However, it seems like a small oversight that any authors added after JSAG certification are automatically added as authors of the actual JSAG article.

[d-torrance]

Yeah -- that's definitely a minor bug with the PackageCitations package. But on the other hand, keeping track of two separate sets of authors in the package metadata doesn't seem great, either. The solution is to use a Citation key in the main doc node of the package, e.g.,:

M2/M2/Macaulay2/packages/TerraciniLoci.m2

Lines 137 to 147 in 661767f

	Citation
	@article{Galuppi_2025,
	title={Geometry of First Nonempty Terracini Loci},
	ISSN={1793-6683},
	url={http://dx.doi.org/10.1142/S0219199725500531},
	DOI={10.1142/s0219199725500531},
	journal={Communications in Contemporary Mathematics},
	publisher={World Scientific Pub Co Pte Ltd},
	author={Galuppi, Francesco and Santarsiero, Pierpaola and Torrance, Douglas A. and Turatti, Ettore Teixeira},
	year={2025},
	month=apr }

[d-torrance]

Thanks for the contribution! I have a few comments

[d-torrance]

See append comment above

[d-torrance]

Thanks for the updates! Found one more append issue

[mahrud]

@d-torrance this is a good suggestion to support: accumulate-or-init H#k = (H#k ?? 0) + new. Maybe H#k += new should do this automatically even if H#k doesn't exist yet?

[d-torrance]

Thanks again! Tentatively approving pending the Ubuntu builds finally working. (We're still recovering from a cyberattack on Canonical the other day, and fetching information from their servers keeps timing out...)

[d-torrance]

this is a good suggestion to support: accumulate-or-init H#k = (H#k ?? 0) + new. Maybe H#k += new should do this automatically even if H#k doesn't exist yet?

This reminds me of Python's defaultdict class:

>>> import collections
>>> x = collections.defaultdict(lambda:0)
>>> x[0]
0
>>> x[1] += 1
>>> x[1]
1

We could do it all at top level if we use _ instead of #:

i1 : DefaultDict = new SelfInitializingType of MutableHashTable;

i2 : new DefaultDict from Function := (T, f) -> (
         d := new DefaultDict;
         d.DefaultFactory = f;
         d);

i3 : DefaultDict_Thing := (d, k) -> (
         if d#?k then d#k
         else d#k = d.DefaultFactory());

i4 : DefaultDict_Thing = (d, k, e) -> d#k = e;

i5 : x = DefaultDict(() -> 0)

o5 = DefaultDict{...1...}

o5 : DefaultDict

i6 : x_0

o6 = 0

i7 : x_1 += 1

o7 = 1

i8 : x_1

o8 = 1

[mahrud]

That's way too complicated. I would prefer something simple and intuitive, e.g. maybe H#k op= x initialize H#k with the unit of op (so 0 for += and -= but 1 for *= and /=). Anyway, let's continue elsewhere.