From 9b29e3df4df0eecae5c34e91b1460df934d79eda Mon Sep 17 00:00:00 2001
From: Mahrud Sayrafi <mahrud@berkeley.edu>
Date: Mon, 15 Jul 2024 13:40:17 +0200
Subject: [PATCH] used ??= to cache image, coker, coimage

---
 M2/Macaulay2/m2/matrix1.m2 | 16 +++++++---------
 M2/Macaulay2/m2/modules.m2 |  1 +
 2 files changed, 8 insertions(+), 9 deletions(-)

diff --git a/M2/Macaulay2/m2/matrix1.m2 b/M2/Macaulay2/m2/matrix1.m2
index bfd968fab9..26fe033633 100644
--- a/M2/Macaulay2/m2/matrix1.m2
+++ b/M2/Macaulay2/m2/matrix1.m2
@@ -416,15 +416,13 @@ Matrix#AfterPrint = Matrix#AfterNoPrint = f -> (
 
 -- precedence Matrix := x -> precedence symbol x
 
-image Matrix := Module => f -> (
-     if f.cache.?image then f.cache.image else f.cache.image = subquotient(f,)
-     )
-coimage Matrix := Module => f -> (
-     if f.cache.?coimage then f.cache.coimage else f.cache.coimage = cokernel inducedMap(source f, kernel f)
-     )
-cokernel Matrix := Module => m -> (
-     if m.cache.?cokernel then m.cache.cokernel else m.cache.cokernel = subquotient(,m)
-     )
+-- source and target are defined in modules.m2
+-- image caches f in M.cache.Monomials
+image    Matrix := Module => f -> f.cache.image    ??= subquotient(f, null)
+cokernel Matrix := Module => f -> f.cache.cokernel ??= subquotient(null, f)
+-- kernel is defined in pushforward.m2
+coimage  Matrix := Module => f -> f.cache.coimage  ??= cokernel inducedMap(source f, kernel f)
+-- homology is defined further down
 
 cokernel RingElement := Module => f -> cokernel matrix {{f}}
 image RingElement := Module => f -> image matrix {{f}}
diff --git a/M2/Macaulay2/m2/modules.m2 b/M2/Macaulay2/m2/modules.m2
index 6c98e9b6d0..61545e352b 100644
--- a/M2/Macaulay2/m2/modules.m2
+++ b/M2/Macaulay2/m2/modules.m2
@@ -15,6 +15,7 @@ ring Matrix := f -> (
      if R =!= S then error "expected module map with source and target over the same ring";
      if f.?RingMap then error "expected module map with no ring map";
      R)
+-- FIXME: can't set the typical output type because Module isn't defined yet!
 source Matrix := f -> f.source
 target Matrix := f -> f.target