changes to documentation, including use of ofClass and Hom to \operat…

…orname{Hom}, imported a test from Core related to total Ext
Macaulay2 · Sep 9, 2024 · 6884cfb · 6884cfb
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diff --git a/M2/Macaulay2/packages/Complexes/ChainComplexDoc.m2 b/M2/Macaulay2/packages/Complexes/ChainComplexDoc.m2
@@ -173,6 +173,7 @@ doc ///
                 TO (Ext, ZZ, Module, Module),
                 TO (Ext, ZZ, Matrix, Module),
                 TO (Ext, ZZ, Module, Matrix),
+                TO (Ext, Module, Module),
                 TO (Hom, Complex, Complex),
                 TO (Hom, ComplexMap, ComplexMap),
                 TO (homomorphism, ComplexMap),
@@ -2350,10 +2351,8 @@ doc ///
    Usage
      D = C1 ** C2
    Inputs
-     C1:Complex
-       or @ofClass Module@
-     C2:Complex
-       or @ofClass Module@
+     C1:{Module}
+     C2:{Module}
    Outputs
      D:Complex
        tensor product of {\tt C1} and {\tt C2}
@@ -2410,19 +2409,17 @@ doc ///
    Usage
      D = Hom(C1,C2)
    Inputs
-     C1:Complex
-       or @ofClass Module@, or @ofClass Ring@
-     C2:Complex
-       or @ofClass Module@, or @ofClass Ring@
+     C1:{Module, Ring}
+     C2:{Module, Ring}
    Outputs
      D:Complex
        the complex of homomorphisms between {\tt C1} and {\tt C2}
    Description
     Text
       The complex of homomorphisms is a complex $D$ whose $i$th component is
-      the direct sum of $Hom(C1_j, C2_{j+i})$ over all $j$.
-      The differential on $Hom(C1_j, C2_{j+i})$ is the differential 
-      $Hom(id_{C1}, dd^{C2}) + (-1)^j Hom(dd^{C1}, id_{C2})$.
+      the direct sum of $\operatorname{Hom}(C1_j, C2_{j+i})$ over all $j$.
+      The differential on $\operatorname{Hom}(C1_j, C2_{j+i})$ is the differential 
+      $\operatorname{Hom}(id_{C1}, dd^{C2}) + (-1)^j \operatorname{Hom}(dd^{C1}, id_{C2})$.
       $dd^{C1} \otimes id_{C2} + (-1)^j id_{C1} \otimes dd^{C2}$.
 
       In particular, for this operation to be well-defined, both
@@ -2434,7 +2431,7 @@ doc ///
       dd^D
       assert isWellDefined D
     Text
-      The homology of this complex is $Hom(C, ZZ/101)$
+      The homology of this complex is $\operatorname{Hom}(C, ZZ/101)$
     Example
       prune HH D == Hom(C, coker vars S)
     Text
@@ -2481,17 +2478,17 @@ doc ///
         g = homomorphism f
     Inputs
         f:ComplexMap
-            a map of the form $f : R^1 \to Hom(C, D)$, where
+            a map of the form $f : R^1 \to \operatorname{Hom}(C, D)$, where
             $C$ and $D$ are complexes,
-            $Hom(C,D)$ has been previously computed, and $R$ is
+            $\operatorname{Hom}(C,D)$ has been previously computed, and $R$ is
             the underlying ring of these complexes
     Outputs
         g:ComplexMap
             the corresponding map of chain complexes from $C$ to $D$
     Description
         Text
             As a first example, consider two Koszul complexes $C$ and $D$.
-            From a random map $f : R^1 \to Hom(C, D)$, we construct 
+            From a random map $f : R^1 \to \operatorname{Hom}(C, D)$, we construct 
             the corresponding map of chain complexes $g : C \to D$.
         Example
             R = ZZ/101[a,b,c]
@@ -2504,9 +2501,9 @@ doc ///
             isWellDefined g
             assert not isCommutative g
         Text
-            The map $g : C \to D$ corresponding to a random map into $Hom(C,D)$
+            The map $g : C \to D$ corresponding to a random map into $\operatorname{Hom}(C,D)$
             does not generally commute with the differentials.  However, if the
-            element of $Hom(C,D)$ is a cycle, then the corresponding map does commute.
+            element of $\operatorname{Hom}(C,D)$ is a cycle, then the corresponding map does commute.
         Example
             f = randomComplexMap(H, complex R^{-2}, Cycle => true)
             isWellDefined f
@@ -2552,12 +2549,12 @@ doc ///
             from $C$ to $D$
     Outputs
         f:ComplexMap
-            a map of the form $f : R^1 \to Hom(C, D)$, where
+            a map of the form $f : R^1 \to \operatorname{Hom}(C, D)$, where
             $R$ is the underlying ring of these complexes
     Description
         Text
             As a first example, consider two Koszul complexes $C$ and $D$.
-            From a random map $f : R^1 \to Hom(C, D)$, we construct 
+            From a random map $f : R^1 \to \operatorname{Hom}(C, D)$, we construct 
             the corresponding map of chain complexes $g : C \to D$.
         Example
             R = ZZ/101[a,b,c]
@@ -2568,9 +2565,9 @@ doc ///
             f = homomorphism' g
             isWellDefined f
         Text
-            The map $g : C \to D$ corresponding to a random map into $Hom(C,D)$
+            The map $g : C \to D$ corresponding to a random map into $\operatorname{Hom}(C,D)$
             does not generally commute with the differentials.  However, if the
-            element of $Hom(C,D)$ is a cycle, then the corresponding map does commute.
+            element of $\operatorname{Hom}(C,D)$ is a cycle, then the corresponding map does commute.
         Example
             g = randomComplexMap(D, C, Cycle => true, InternalDegree => 3)
             isWellDefined g
@@ -2613,7 +2610,7 @@ doc ///
             method returns the corresponding map of complexes of degree $i$.
         Text
             As a first example, consider two Koszul complexes $C$ and $D$.
-            From a random map $f \colon R^1 \to Hom(C, D)$, we construct 
+            From a random map $f \colon R^1 \to \operatorname{Hom}(C, D)$, we construct 
             the corresponding map of chain complexes $g \colon C \to D$.
         Example
             R = ZZ/101[a,b,c];
@@ -2625,9 +2622,9 @@ doc ///
             assert isWellDefined g
             assert not isCommutative g
         Text
-            The map $g \colon C \to D$ corresponding to a random map into $Hom(C,D)$
+            The map $g \colon C \to D$ corresponding to a random map into $\operatorname{Hom}(C,D)$
             does not generally commute with the differentials.  However, if the
-            element of $Hom(C,D)$ is a cycle, then the corresponding map does commute.
+            element of $\operatorname{Hom}(C,D)$ is a cycle, then the corresponding map does commute.
         Example
             h = randomComplexMap(E, complex R^{-2}, Cycle => true, Degree => -1)
             f = h_0
@@ -2751,7 +2748,7 @@ doc ///
      :Complex
    Description
     Text
-      The dual of a complex $C$ is by definition $Hom(C, R)$, where $R$ is the ring of $C$.
+      The dual of a complex $C$ is by definition $\operatorname{Hom}(C, R)$, where $R$ is the ring of $C$.
     Example
       S = ZZ/101[a..d];
       B = intersect(ideal(a,c),ideal(b,d))
@@ -4385,10 +4382,10 @@ doc ///
     Usage
         Ext(M, N)
     Inputs
-        M:Module
-            or ofClass{Ideal,Ring}, that is homogeneous
-        N:Module
-            or ofClass{Ideal,Ring} over the same ring as $M$, that is also homogeneous
+        M:{Ideal, Ring}
+            that is homogeneous
+        N:{Ideal, Ring}
+            over the same ring as $M$, that is also homogeneous
     Outputs
         :Module
             the $\operatorname{Ext}$ module of $M$ and $N$, as a

diff --git a/M2/Macaulay2/packages/Complexes/Ext.m2 b/M2/Macaulay2/packages/Complexes/Ext.m2
@@ -60,7 +60,7 @@ Ext(Module, Module) := Module => opts -> (M, N) -> (
     blks := new MutableHashTable;
     blks#(exponents 1_Rmon) = C.dd;
     scan(0 .. c-1, i -> 
-       blks#(exponents Rmon_i) = nullHomotopy (- f_i*id_C));
+       blks#(exponents Rmon_i) = nullHomotopy(- f_i*id_C, FreeToExact => true));
     -- a helper function to list the factorizations of a monomial
     factorizations := (gamma) -> (
         -- Input: gamma is the list of exponents for a monomial
@@ -81,7 +81,7 @@ Ext(Module, Module) := Module => opts -> (M, N) -> (
                         then blks#alpha * blks#beta
                         else 0));
                 -- compute and save the nonzero nullhomotopies
-                if s != 0 then blks#gamma = nullhomotopy s))));
+                if s != 0 then blks#gamma = nullHomotopy(s, FreeToExact => true)))));
     -- make a free module whose basis elements have the right degrees
     (loC, hiC) := concentration C;
     Cstar := S^(apply(toList(loC..hiC),

diff --git a/M2/Macaulay2/packages/Complexes/FreeResolutionTests.m2 b/M2/Macaulay2/packages/Complexes/FreeResolutionTests.m2
@@ -897,3 +897,19 @@ TEST ///
   assert(M === (target epsilon)_0)
 ///
 
+TEST ///
+  -- errorDepth = 0
+  A = ZZ/103[x,y,z];
+  J = ideal(x^3,y^4,z^5);
+  B = A/J;
+  f = matrix {{27*x^2-19*z^2, 38*x^2*y+47*z^3},
+      { -5*x^2+z^2, -37*x^2*y+51*x*y^2-36*y^3+11*y*z^2+8*z^3},
+      {x^2-x*y, z^3}};
+  M = cokernel f;
+  N = B^1/(x^2 + z^2,y^3 - 2*z^3);
+  time E = Ext(M,N); -- used 3.32 seconds in version 0.9.92
+  t = tally degrees target presentation E
+  u = new Tally from {{-3, -7} => 7, {-3, -6} => 7, {0, 1} => 3, {0, 2} => 4, {-4, -9} => 4, {-4, -8} => 1, {-4, -7} => 1, {-1, -2} => 4, {-2, -5} => 3,
+        {-2, -4} => 8}
+  assert ( t === u )
+///
diff --git a/M2/Macaulay2/tests/normal/ext-total.m2 b/M2/Macaulay2/tests/normal/ext-total.m2
@@ -16,7 +16,32 @@ assert ( degs == apply( newdegs, repair ))
 
 heft0 = {-3, 1}
 degs1 = {{0, 0}, {0, 0}, {0, 0}, {1, 2}, {1, 3}, {1, 3}, {1, 3}, {1, 3}, {1, 4}, {1, 4}, {1, 4}, {1, 5}, {1, 5}, {1, 5}, {2, 5}, {2, 6}, {2, 6}, {2, 7}, {2, 7}, {2, 7}, {2, 7}, {2, 7}, {2, 7}, {2, 7}, {2, 7}, {2, 7}, {2, 8}, {2, 8}, {2, 8}, {3, 9}, {3, 9}, {3, 9}, {3, 9}, {3, 9}, {3, 9}, {3, 9}};
-degs2 = {{0, -2}, {0, -3}, {0, -3}, {0, -4}, {0, -5}, {0, -2}, {0, -3}, {0, -3}, {0, -4}, {0, -5}, {0, -2}, {0, -3}, {0, -3}, {0, -4}, {0, -5}, {1, 0}, {1, -1}, {1, -1}, {1, -2}, {1, -3}, {1, 1}, {1, 0}, {1, 0}, {1, -1}, {1, -2}, {1, 1}, {1, 0}, {1, 0}, {1, -1}, {1, -2}, {1, 1}, {1, 0}, {1, 0}, {1, -1}, {1, -2}, {1, 1}, {1, 0}, {1, 0}, {1, -1}, {1, -2}, {1, 2}, {1, 1}, {1, 1}, {1, 0}, {1, -1}, {1, 2}, {1, 1}, {1, 1}, {1, 0}, {1, -1}, {1, 2}, {1, 1}, {1, 1}, {1, 0}, {1, -1}, {1, 3}, {1, 2}, {1, 2}, {1, 1}, {1, 0}, {1, 3}, {1, 2}, {1, 2}, {1, 1}, {1, 0}, {1, 3}, {1, 2}, {1, 2}, {1, 1}, {1, 0}, {2, 3}, {2, 2}, {2, 2}, {2, 1}, {2, 0}, {2, 4}, {2, 3}, {2, 3}, {2, 2}, {2, 1}, {2, 4}, {2, 3}, {2, 3}, {2, 2}, {2, 1}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 6}, {2, 5}, {2, 5}, {2, 4}, {2, 3}, {2, 6}, {2, 5}, {2, 5}, {2, 4}, {2, 3}, {2, 6}, {2, 5}, {2, 5}, {2, 4}, {2, 3}, {3, 7}, {3, 6}, {3, 6}, {3, 5}, {3, 4}, {3, 7}, {3, 6}, {3, 6}, {3, 5}, {3, 4}, {3, 7}, {3, 6}, {3, 6}, {3, 5}, {3, 4}, {3, 7}, {3, 6}, {3, 6}, {3, 5}, {3, 4}, {3, 7}, {3, 6}, {3, 6}, {3, 5}, {3, 4}, {3, 7}, {3, 6}, {3, 6}, {3, 5}, {3, 4}, {3, 7}, {3, 6}, {3, 6}, {3, 5}, {3, 4}};
+degs2 = {{0, -2}, {0, -3}, {0, -3}, {0, -4}, {0, -5}, {0, -2},
+    {0, -3}, {0, -3}, {0, -4}, {0, -5}, {0, -2}, {0, -3},
+    {0, -3}, {0, -4}, {0, -5}, {1, 0}, {1, -1}, {1, -1},
+    {1, -2}, {1, -3}, {1, 1}, {1, 0}, {1, 0}, {1, -1},
+    {1, -2}, {1, 1}, {1, 0}, {1, 0}, {1, -1}, {1, -2},
+    {1, 1}, {1, 0}, {1, 0}, {1, -1}, {1, -2}, {1, 1},
+    {1, 0}, {1, 0}, {1, -1}, {1, -2}, {1, 2}, {1, 1},
+    {1, 1}, {1, 0}, {1, -1}, {1, 2}, {1, 1}, {1, 1},
+    {1, 0}, {1, -1}, {1, 2}, {1, 1}, {1, 1}, {1, 0}, {1, -1},
+    {1, 3}, {1, 2}, {1, 2}, {1, 1}, {1, 0}, {1, 3}, {1, 2},
+    {1, 2}, {1, 1}, {1, 0}, {1, 3}, {1, 2}, {1, 2}, {1, 1},
+    {1, 0}, {2, 3}, {2, 2}, {2, 2}, {2, 1}, {2, 0}, {2, 4},
+    {2, 3}, {2, 3}, {2, 2}, {2, 1}, {2, 4}, {2, 3}, {2, 3},
+    {2, 2}, {2, 1}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2},
+    {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 5}, {2, 4},
+    {2, 4}, {2, 3}, {2, 2}, {2, 5}, {2, 4}, {2, 4}, {2, 3},
+    {2, 2}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 5},
+    {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 5}, {2, 4}, {2, 4},
+    {2, 3}, {2, 2}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2},
+    {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 6}, {2, 5},
+    {2, 5}, {2, 4}, {2, 3}, {2, 6}, {2, 5}, {2, 5}, {2, 4},
+    {2, 3}, {2, 6}, {2, 5}, {2, 5}, {2, 4}, {2, 3}, {3, 7},
+    {3, 6}, {3, 6}, {3, 5}, {3, 4}, {3, 7}, {3, 6}, {3, 6},
+    {3, 5}, {3, 4}, {3, 7}, {3, 6}, {3, 6}, {3, 5}, {3, 4},
+    {3, 7}, {3, 6}, {3, 6}, {3, 5}, {3, 4}, {3, 7}, {3, 6},
+    {3, 6}, {3, 5}, {3, 4}, {3, 7}, {3, 6}, {3, 6}, {3, 5}, {3, 4}, {3, 7}, {3, 6}, {3, 6}, {3, 5}, {3, 4}};
 degDB = {-1, 0}
 
 degs' = apply(degs, adjust)
@@ -57,39 +82,8 @@ assert ( t' === u )
 << "then we do the computation with unadjusted degrees" << endl
 comp (degs,heft0,degs1,degs2,degDB)
 t = tally degrees target presentation E
-
 assert ( t === u )
 
--*
-
-the answer changed between these two versions:
-
-u123$ ls -l ~/local.Linux/encap/Macaulay2-0.9.95/bin/M2
--rwxr-xr-x 1 dan academic 5036156 2006-11-06 11:50 /home/25/dan/local.Linux/encap/Macaulay2-0.9.95/bin/M2
-
-u123$ ls -l ~/local.Linux/encap/Macaulay2-0.9.94/bin/M2
--rwxr-xr-x 1 dan academic 5028988 2006-10-24 10:33 /home/25/dan/local.Linux/encap/Macaulay2-0.9.94/bin/M2
-
-*-
-
-
--- errorDepth = 0
-A = ZZ/103[x,y,z];
-J = ideal(x^3,y^4,z^5);
-B = A/J;
-f = matrix {{27*x^2-19*z^2, 38*x^2*y+47*z^3},
-      { -5*x^2+z^2, -37*x^2*y+51*x*y^2-36*y^3+11*y*z^2+8*z^3},
-      {x^2-x*y, z^3}};
-M = cokernel f;
-N = B^1/(x^2 + z^2,y^3 - 2*z^3);
--- gbTrace = 3
-debugLevel = 99
-time E = Ext(M,N);
-     -- used 3.32 seconds in version 0.9.92
-t = tally degrees target presentation E
-u = new Tally from {{-3, -7} => 7, {-3, -6} => 7, {0, 1} => 3, {0, 2} => 4, {-4, -9} => 4, {-4, -8} => 1, {-4, -7} => 1, {-1, -2} => 4, {-2, -5} => 3,
-        {-2, -4} => 8}
-assert ( t === u )
 -- Local Variables:
 -- compile-command: "make -C $M2BUILDDIR/Macaulay2/packages/Macaulay2Doc/test ext-total.out"
 -- End: