And mathML(Complex) and related updates #3726

d-torrance · 2025-04-09T12:10:16Z

We introduce a new type, ComplexExpression, to unify the printing of both the legacy ChainComplex and the newer Complex types. In particular, the latter didn't have a mathML method, and so they previously weren't supported in TeXmacs or Jupyter when using TeXmacs mode:

Now, net, texMath, and mathML just call expression first, and so we only need to implement each once and they'll work for both types:

A couple other related changes:

We add short(Module) for use in complex expressions. It uses moduleAbbrv (which has been slightly rewritten to just return null instead of having a backup representation) to use the module's variable name when possible, unless the module is free over a ring that's been assigned to a variable, in which case we use that respresentation.
We try to use substitute when building a legacy complex using chainComplex if the differential maps are given over different rings. This is to fix some issues with value(ComplexExpression), where the differential maps are MatrixExpression objects that may have forgotten some important info like what rings they were over. value(ComplexExpression) isn't perfect -- it still fails in other situtations like when we've lost degree information.

pzinn · 2025-04-09T13:12:27Z

Looking good. I tried your code on M2web and I get:

I wonder how it will look after your PR?

d-torrance · 2025-04-09T13:47:55Z

It should look the same. texMath(ComplexExpression) is essentially identical to the old texMath(ChainComplex). There were some subtle differences between that and texMath(Complex) in how to "shorten" the differential maps. The ChainComplex version used short(Matrix) and the Complex version rolled its own texMatrixShort, but they were pretty similar, so I just went with short(Matrix) for everything.

pzinn · 2025-04-09T14:05:29Z

great. yeah texMatrixShort was supposed to be gone but it somehow resurfaced in Complex...

d-torrance · 2025-04-09T14:05:49Z

Yikes! Apparently constructing these expressions isn't very efficient:

i9 : elapsedTime T = tateExtension W;
 -- .420421s elapsed

i10 : elapsedTime expression T;
 -- 12.5284s elapsed

I'll see if I can improve things.

pzinn · 2025-04-09T14:11:01Z

one potential issue (I'm not sure if that's the one you're facing in your example) is that you probably don't want to take the expression (MatrixExpression) of a huge matrix since it literally spits out the list of entries (even if eventually it shortens it as in the current display in WebApp mode).

d-torrance · 2025-04-09T14:16:26Z

Lol yeah -- that's exactly what's happening:

i12 : profileSummary

o12 = #run     %time   position                                                       
      1        93.71   src/macaulay2/M2/M2/Macaulay2/m2/chaincomplexes.m2:135:4-137:51
      16       93.7    src/macaulay2/M2/M2/Macaulay2/m2/matrix.m2:217:4-217:42        
      4586444  44.17   src/macaulay2/M2/M2/Macaulay2/m2/polyrings.m2:205:61-205:73

4.5 million calls to expression 0...

pzinn · 2025-04-09T20:54:05Z

on vanilla, I resolved this by having short act at the level of Matrix directly -- but I think you've reached the same conclusion. the only problem being, value won't work any more -- but I think that's an acceptable price to pay.

mahrud · 2025-04-09T23:16:36Z

What's the point of an intermediary type ComplexExpression? I want to remove SheafExpression already.

d-torrance · 2025-04-10T01:07:14Z

What's the point of an intermediary type ComplexExpression? I want to remove SheafExpression already.

For the time being, while we have two distinct complex types with Complex and ChainComplex, it gives us a way to write the various printing methods just once.

Also, based on the Expression docs, it seems like having expression classes for mathematical objects is part of the design of the language:

they are an intermediate phase in the conversion of a mathematical object to a net that can be printed

What's the problem with SheafExpression?

pzinn · 2025-04-11T10:22:27Z

I think the only problem with your short(Matrix) is that it doesn't correctly treat zero matrices? (comparing quickly with the code on vanilla which I never got around to PRing)

d-torrance · 2025-04-11T11:02:25Z

Oh ok -- I didn't think about zero matrices. I just used your commit instead.

d-torrance · 2025-04-11T12:08:05Z

Hmm, there's something wrong with toString(MatrixExpression) after cherry-picking your commits, even live on the webapp:

i2 : toString short map(ZZ^2, ZZ^2, 0)

stdio:2:8:(3)]: error: expected a list, sequence, string, net, hash table, database, or dictionary

pzinn · 2025-04-11T12:13:49Z

interesting. this is a good opportunity to clean up/debug this code...

mahrud · 2025-04-12T08:14:03Z

M2/Macaulay2/m2/modules.m2

+    else if hasAttribute(M, ReverseDictionary)
+    then getAttribute(M, ReverseDictionary))
+
+short Module := M -> moduleAbbrv M ?? expression M


I don't understand why you removed the second input of moduleAbbrv, when this could have been implemented as:

Suggested change

short Module := M -> moduleAbbrv M ?? expression M

short Module := M -> moduleAbbrv(M, expression M)

I've always thought that moduleAbbrv's two inputs were kind of clunky. For example, in Matrix.AfterPrint, we don't need the second input at all -- if we can't abbreviate the module, then we just don't print anything. I figured this was an opportunity to update it.

d-torrance · 2025-04-12T12:35:46Z

I've updated the behavior of MatrixExpression for zero matrices that are either 0x0 or produced by short. The MatrixExpression object now has a zero option, whose value is a two-element sequence containing the target and source. This way, we have enough information to regenerate the matrix when using value.

d-torrance · 2025-04-15T11:21:45Z

@sashahbc: Sorry to keep bugging you with these ToricHigherDirectImages issues!

Test 7 is failing on the builds for this PR:

i9 : assert(presentation RD2 == matrix {{y_1,0},{0,y_1^2},{0,0}})
stdio:10:6:(3): error: assertion failed

The rows were permuted a bit from the expected matrix:

i55 : presentation RD2

o55 = | 0   0     |
      | y_1 0     |
      | 0   y_1^2 |

              3      2
o55 : Matrix Q  <-- Q

From what I can tell, RD2 is the first homology of a complex generated by the unexported HDIComplex method. And its main loop is:

    directSum for mu in keys eigenchars list (

Since eigenchars is a hash table, we're not sure what order its keys will appears in the list returned by keys. Could that be the issue?

sashahbc · 2025-04-15T19:53:42Z

Yeah that's definitely the problem. Not sure what the best solution would be. I was hoping components would detect the different summands but once we've taken homology I guess it loses track of that.

sashahbc · 2025-04-15T19:59:14Z

It seems like a bad idea because it's a probabilistic test but could we do
assert( isIsomorphic( RD2, coker matrix {{y_1,0},{0,y_1^2},{0,0}} )_0 )?

d-torrance · 2025-04-15T20:29:51Z

I suppose that would work. Is it okay that the order of the rows isn't deterministic, though?

sashahbc · 2025-04-15T21:05:24Z

Yeah I am a bit uncomfortable with the order changing. Mahrud had a suggestion which I'll make a PR for in a sec.

pzinn · 2025-05-02T21:02:11Z

M2/Macaulay2/m2/expressions.m2

+    Blocks => null,
+    Degrees => null,
+    MutableMatrix => false,
+    zero => null};


any reason zero is the only lowercase option? and incidentally which type is this zero?

I went with zero since it's already exported. When it's non-null, it will be a sequence of two modules (the target and source).

I meant, what is the class of zero itself, not the option labelled zero.
usually it's nice if all options have the same type; which one is a matter of taste, it seems (all symbols seems the most common choice, though there's serious overhead in doing that; I would think all strings would actually make more sense, but it's rarely used. I digress)

This is an excellent question! I thought I'd put symbol zero here, but I didn't. And zero is a function closure, which should have raised an error...

i1 : new OptionTable from {zero => null} stdio:1:0:(3): error: expected option key to be a symbol, a string, or a type

Ohhh I figured it out -- zero is still a symbol at this point since it's not defined as a function until integers.m2, which is later in the load sequence. (Same with MutableMatrix -- it's a type defined in mutablemat.m2, but it's a symbol here).

I'll change this so they're both explicitly symbols, just in case any code gets moved around

pzinn · 2025-05-02T21:10:45Z

M2/Macaulay2/m2/matrix.m2

@@ -215,6 +215,7 @@ protect Blocks
 blockMatrixForm=false;  -- governs expression Matrix inclusion of blocks
 expression Matrix := m -> (
    x := applyTable(entries m, expression);
+    if #x == 0 then x = {symbol zero => (target m, source m)};


I don't understand why this line is not above the previous one (why go through all the entries if the matrix is zero anyway?)

err, I mean, and why the test isn't simply x==0

Great point!

Ok, I've updated this so expression of a zero matrix always just uses the short form and never deals with the individual entries.

mahrud

This PR conflicts heavily with the chain complex changes.

d-torrance · 2025-05-10T02:14:59Z

Yeah, with both complex types moving to their own packages, I don't know if having a shared expression type in Core makes sense any more...

I think I'll trim this down to just the MatrixExpression changes and adding mathML(Complex).

mahrud · 2025-05-10T03:27:13Z

M2/Macaulay2/m2/chaincomplexes.m2

@@ -137,15 +137,15 @@ net ChainComplex := C -> (
 	  a := s#0;
 	  b := s#-1;
 	  horizontalJoin between(" <-- ", apply(a .. b,i ->
-		  stack (net moduleAbbrv(C_i, C_i)," ",net i)))))


This file is moved in the Complexes PR, so you might as well rebase on top of that PR I think.

For nonfree modules, use the variable name if one exists. This will replace moduleAbbrv when printing complexes. We rewrite moduleAbbrv to return null when we can't abbreviate it and leave it up to the caller (now only AfterPrint for Matrix/Vector) to handle what to do with it.

mikestillman · 2025-05-14T21:17:03Z

This is probably not relevant to what you are doing here, but it is something that is a problem.

 M = random(ZZ^2000, ZZ^2000);
13 M

or even

try(13 M; false) else true

This last one takes about 30 seconds on my laptop...

mikestillman

This looks good to me. Thanks! It appears that much of the discussion in the PR is related to pre-chain complex movement to OldChainComplexes, Complexes. Sorry about that!

@pzinn Is there a regression in the web printing of Complexes? Are we using something that you got rid of, without our noticing?

d-torrance requested a review from pzinn April 9, 2025 12:10

d-torrance force-pushed the complex-expression branch from 772d9ef to 90dfa5a Compare April 10, 2025 02:34

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d-torrance force-pushed the complex-expression branch from ba139fa to 3639dee Compare April 11, 2025 12:01

d-torrance added waiting for review Core Issues involving the Core scripts. labels Apr 12, 2025

d-torrance force-pushed the complex-expression branch from 11b9d1f to 44d25f9 Compare April 12, 2025 04:05

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d-torrance mentioned this pull request Apr 12, 2025

Update ToricHigherDirectImages test so that order doesn't matter #3729

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d-torrance force-pushed the complex-expression branch from 44d25f9 to ed5bf36 Compare April 15, 2025 01:01

sashahbc mentioned this pull request Apr 15, 2025

Added sorting to eigencharacter keys #3732

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d-torrance force-pushed the complex-expression branch 3 times, most recently from ec0f2ee to e41348b Compare April 18, 2025 13:33

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d-torrance force-pushed the complex-expression branch from 95a577e to d46e46e Compare May 10, 2025 02:50

d-torrance changed the title ~~Add ComplexExpression for expression-ifying ChainComplex and Complex objects~~ And mathML(Complex) and related updates May 10, 2025

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d-torrance force-pushed the complex-expression branch from d46e46e to de3a185 Compare May 10, 2025 03:58

d-torrance and others added 8 commits May 12, 2025 21:33

fix short Matrix

b9d81e3

fix toString zero matrix

5e143cd

Add mutableMatrix(Ring, List) for specifying ring

d15361e

Add target and source for mutable matrices

ac5b5dd

Keep track of target/source for zero matrix expressions

0d91377

Add mathML(Complex)

8a337a6

Add mathML(ComplexMap) (+ mathML(RowExpression), which is a prereq)

025a54c

d-torrance force-pushed the complex-expression branch from de3a185 to 025a54c Compare May 13, 2025 01:35

mikestillman approved these changes May 14, 2025

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d-torrance merged commit ac7b8b9 into Macaulay2:development May 15, 2025
5 checks passed

	short Module := M -> moduleAbbrv M ?? expression M
	short Module := M -> moduleAbbrv(M, expression M)

And mathML(Complex) and related updates #3726

And mathML(Complex) and related updates #3726

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