Varieties v0.3 #3567

mahrud · 2024-11-01T08:10:33Z

This is a repeat of #3517, which is on top of #3522 and shares a exact few commits with #3526, but I don't believe there should be a conflict.

mahrud · 2024-11-06T23:25:09Z

@ggsmith @mikestillman is everyone happy with merging this?

Also changed g \\ f to call quotient'(f, g) instead.

homomorphism

...

mahrud · 2024-11-22T02:41:27Z

It would be good to have this merged soon so the branch is free to continue developing on.

mahrud · 2024-12-04T15:08:59Z

@mikestillman @ggsmith should I go ahead and merge this? We shouldn't wait until a week before the next release to merge big pull requests.

ggsmith · 2024-12-04T15:12:29Z

I haven't yet had time to look at the details

mahrud · 2024-12-04T16:06:28Z

You had reviewed the previous PR #3517, which I accidentally closed and had to reopen. I think I've addressed all of your comments there. No other changes have been added since.

Do you have an estimate of when you could look at the details? Varieties wasn't updated in version 1.24.05 and again didn't get updated in 1.24.11. There are new features and bug fixes that Devlin and I have worked on, but I'm afraid if we continue it won't make it to 1.25 either.

mikestillman · 2025-01-10T20:50:28Z

@mahrud I'm ready to look at your few open PR's. I'm a bit confused about which to do in what order. 3522 first, then 3550, then 3567, then 3582? Are there duplicate commits in these?

mahrud · 2025-01-10T20:54:06Z

You can start from the smallest ones if you prefer, but the order they're reviewed or merged doesn't matter.

Devlin-Mallory · 2025-02-03T20:45:54Z

@ggsmith @mikestillman Just wanted to check on this PR - it would be good to be able to continue developing the SheafMaps branch. If there's any changes that require explanation I'd be happy to discuss.

mikestillman · 2025-02-05T22:19:05Z

M2/Macaulay2/m2/modules2.m2

-pushout(Matrix, Matrix) := Module => (f, g) -> (
-    if source f =!= source g then error "expected maps with the same source";
-    h := f || -g;
+pushout List := Module => applyUniformMethod(symbol pushout, "pushout")


There is no documentation for new versions of pushout, pullback, pushoutMaps, pullbackMaps? It appears that there was no doc earlier too... But we should add it.

Yes, there are lots of things not documented. (To be clear, pushout/pullback didn't exist in the Core before we added them for Varieties in the last PR)

mikestillman · 2025-02-05T22:22:14Z

M2/Macaulay2/m2/shared.m2

@@ -28,6 +28,9 @@ isNormal = method()

 normalCone = method(Options => true)

+isMorphism = method(TypicalValue => Boolean)
+isAbelianCategory = method(TypicalValue => Boolean)


For Abelian categories, we need: coimageToImage map, and kernel and coker universal properties. I have code for that (at least for some categories, e.g. Modules, R-complexes), should we include it somewhere? Have you added it for sheaves, complexes of sheaves?

It would be interesting, especially if this worked for other types of modules (e.g. quiver representations), but I was trying to do the minimal absolute necessary changes to get complexes of sheaves.

mikestillman · 2025-02-08T02:55:23Z

M2/Macaulay2/packages/Varieties.m2

@@ -172,7 +190,7 @@ dim     AffineVariety := X -> dim ring X
 dim ProjectiveVariety := X -> dim ring X - 1 -- TODO: - Picard rank instead?

 char     AffineVariety := X -> char ring X
-char ProjectiveVariety := X -> char(ring X / saturate ideal X) -- TODO: saturate with respect to B?
+char ProjectiveVariety := X -> char quotient saturate ideal X -- TODO: saturate with respect to B?

 -- TODO: should these be defined, but return 0 for an AffineVariety?


Isn't there a well defined degree for an affine variety? The number of intersection points of a complementary dimensional affine linear space? This is computed as degree ideal leadTerm I, for the defining variety of I, as long as the monomial order is a degree order... It doesn't have as nice properties, but...

mikestillman · 2025-02-08T02:56:57Z

M2/Macaulay2/packages/Varieties.m2

@@ -186,26 +204,23 @@ ambient     AffineVariety :=     AffineVariety => X -> Spec ambient ring X
 ambient ProjectiveVariety := ProjectiveVariety => X -> Proj ambient ring X

 -- arithmetic ops
-- TODO: document
 AffineVariety     **     AffineVariety :=     AffineVariety => (X, Y) -> Spec(ring X ** ring Y)


Even though these are affine varieties, the tensor product will create multi-degrees? That might not be desired...

"Spec" will ignore the (multi)grading.

mikestillman · 2025-02-08T02:59:40Z

M2/Macaulay2/packages/Varieties.m2


 -- constructors
 sheaf = method()
 -- TODO: sheaf Ring and sheaf Module should return a sheaf over variety of the ring rather than Proj,
 -- and if a variety doesn't already exist then either Proj or Spec should be defined and cached.
-sheaf Ring := Ring ~ := SheafOfRings =>     R  -> sheaf(Proj R, R)
+sheaf Ring := Ring^~ := SheafOfRings =>     R  -> sheaf(variety R, R)


Is this a breaking change?

Not until we remove this in a future release:

-- TODO: remove by M2 1.25 tildeWarn = true Thing~ := x -> (if tildeWarn then (tildeWarn = false; printerr "Note: M~ is deprecated; use M^~ or sheaf instead."); x^~)

mikestillman · 2025-02-08T03:29:13Z

M2/Macaulay2/packages/Varieties/doc-varieties.m2

+
+--Comment about this code: isn't it sufficient to just check that the quotient by the
+--jacobian + the original ideal has finite length? Using the singularLocus command to do this
+--adds an additional saturation computation that seems unnecessary


mikestillman · 2025-02-08T03:31:00Z

M2/Macaulay2/packages/Varieties/genus-doc.m2

@@ -13,7 +13,7 @@ document {
     Inputs => {"F" => {ofClass{CoherentSheaf,Module,Ideal} }},
     Outputs => {ZZ },
     "Computes the arithmetic genus of the coherent sheaf ", TT "F", " that is (-1)^dim-support * (chi(F) - 1)).  If ", TT "F", " is a module
-     over a ring, then the genus of ", TT "F~", " is computed.  If ", TT "I", " is an ideal in a ring ", TT "R", " then the genus of ", TT "(R/I)~", " is


Maybe change to tex? Not for this PR maybe...

mikestillman · 2025-02-08T12:50:55Z

M2/Macaulay2/packages/Macaulay2Doc/functions/quotient-remainder-doc.m2

+    Description
+      Text
+        If either @TT "f"@ or @TT "g"@ is a ring element, then it is taken to be a
+        scalar matrix acting on @TT "H"@. If @TT "g"@ is a @TO "MonomialIdeal"@,


Good question. This is identically moved here from the documentation of Matrix // Matrix. In particular, the typo is present in the current version.

mikestillman · 2025-02-08T12:51:57Z

M2/Macaulay2/packages/Macaulay2Doc/functions/quotient-remainder-doc.m2

+      g:{Matrix,MonomialIdeal,GroebnerBasis}
+    Description
+      Text
+        If either @TT "f"@ or @TT "g"@ is a ring element, then it is taken to be a


Lately I have been preferring using $f$, $g$ instead of TT for these... Or use {\tt f} ?

mikestillman · 2025-02-08T13:01:06Z

M2/Macaulay2/m2/matrix1.m2

-     else error "expected a table of ring elements or matrices, or a list of elements of the same module")
+matrix List := Matrix => opts -> L -> (
+    if #L === 0 then return matrix(ZZ, {});
+    L = apply(splice L, splice); -- TODO: is this deepSplice?


I believe this is only "deepSplice" to 2 levels...

mahrud · 2025-02-12T16:25:50Z

@mikestillman could you clarify which of your comments are things you want changed before this is merged and which are suggestions for future? Unless others want to contribute, the documentation suggestions are not going to happen in this PR.

mahrud changed the base branch from master to development November 1, 2024 08:10

mahrud force-pushed the SheafMaps branch from f3a5d86 to e164086 Compare November 3, 2024 21:32

mahrud mentioned this pull request Nov 15, 2024

Improvements to Simplicial Toric Varieties #3582

Open

mahrud and others added 26 commits November 22, 2024 03:35

added hook for non-free maps in quotient & quotient'

165b363

Also changed g \\ f to call quotient'(f, g) instead.

commented a few methods of \\

2331a04

updated docs for quotient and quotient'

67e2a49

changed BettiCharacters to use left factorization via \\

cd6b0b9

fixed a test based on the augmented form of \\

c842e52

added tests for quotient' for non-free maps

a664af1

separated ZZ and InexactField strategies for (quotient, Matrix, Matrix)

fececd7

added slight optimization for quotient and quotient'

2d96ad6

added length limits for connectingExtMap

65b995d

added method for truncating source of map more than target

dbc0c9d

fixed bug in prune for coherent sheaves on toric varieties

2cabe60

cached the output of nefGenerators

51d1710

cached variety of a ring in R.variety

88df62f

cached minimal presentation of SheafMap

298966f

preserved components after sheafification

30cda95

added check that rings of projective varieties are standard graded

af50a3c

added extra constructors for SheafMap

95c08e4

added isIsomorphic for CoherentSheaf and SheafMap

58f4486

changed "isIsomorphic" to prune rather than truncate, as discussed today

8fa584c

added SheafMap == SheafMap

07e08b1

improved global Ext of sheaves

0544a67

avoided minimization of truncations for sheaf map algorithms

182494a

added Complexes to dependencies of Varieties

0f51b3a

added yonedaSheafExtension

8a73de9

changed sheaf map composition, SheafMap == ZZ, and started connecting

040acc0

homomorphism

added concatenation (| and ||) for sheaf maps

225f94f

mahrud and others added 17 commits November 22, 2024 03:37

added part for modules, matrices, ideals, and rings

67db95a

switched to using part instead of moveToField

3eb98c2

added part for ring maps

8fd4baa

changed ring of sheaves to return OO_X

c16a941

simplified commonRing so it can handle a SheafMap (temporary fix)

15ec629

changed SheafOfRings to inherit from Ring

484ae9a

added isWellDefined and isCommutative for SheafOfRings

cd761c7

changed a line in documentation of basis

53d7916

removed HH^ZZ Complex from Varieties

e6d514f

Small documentation addition

f17d11d

...

small fix to documentation

3cab22a

some changes to canonicalBundle

7f23f83

some changes; bug left to be fixed though

12ea63c

added HH^i(F(*)) to usage for cohomology

cc11f10

removed DegreeLimit in Hom, which causes issues in inverse

a6c7d28

temporarily disable SheafComplexes

8b3de82

bumped version of Varieties

82c516b

mahrud force-pushed the SheafMaps branch from e164086 to 82c516b Compare November 22, 2024 02:39

mahrud requested review from mikestillman and ggsmith December 4, 2024 15:09

mikestillman reviewed Feb 11, 2025

View reviewed changes

fixed bug in euler(Complex)

8aed321

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Varieties v0.3 #3567

Varieties v0.3 #3567

mahrud commented Nov 1, 2024

mahrud commented Nov 6, 2024

mahrud commented Nov 22, 2024

mahrud commented Dec 4, 2024

ggsmith commented Dec 4, 2024

mahrud commented Dec 4, 2024

mikestillman commented Jan 10, 2025

mahrud commented Jan 10, 2025

Devlin-Mallory commented Feb 3, 2025

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mahrud commented Feb 12, 2025

Varieties v0.3 #3567

Are you sure you want to change the base?

Varieties v0.3 #3567

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mahrud commented Nov 1, 2024

mahrud commented Nov 6, 2024

mahrud commented Nov 22, 2024

mahrud commented Dec 4, 2024

ggsmith commented Dec 4, 2024

mahrud commented Dec 4, 2024

mikestillman commented Jan 10, 2025

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mahrud commented Feb 12, 2025