SpectralSequences v1.2: clean up and trim

M2/Macaulay2/m2/matrix2.m2

@@ -396,6 +396,7 @@ Matrix \\ Matrix := Matrix => (g, f) -> quotient'(f, g)
 quotient(Matrix, Matrix) := Matrix => opts -> (f, g) -> (
     -- given f: A-->C and g: B-->C, then find (f//g): A-->B such that g o (f//g) + r = f
     if target f != target g then error "quotient: expected maps with the same target";
+    if f == 0 then return map(source g, source f, 0);
     c := runHooks((quotient, Matrix, Matrix), (opts, f, g), Strategy => opts.Strategy);
     if c =!= null then c else error "quotient: no method implemented for this type of input")
 
@@ -408,11 +409,19 @@ addHook((quotient, Matrix, Matrix), Strategy => Default,
 	    MinimalGenerators => opts.MinimalGenerators };
 	map(source g, source f, homomorphism(homomorphism'(f, opts) // Hom(source f, g, opts)))))
 
--- FIXME: this is still causing unreasonable slow downs, e.g. for (large m) // (scalar)
-addHook((quotient, Matrix, Matrix), Strategy => "Reflexive", (opts, f, g) -> if f == 0 or isFreeModule source f then (
-     L := source f;	     -- result may not be well-defined if L is not free
+addHook((quotient, Matrix, Matrix), Strategy => "Reflexive", (opts, f, g) -> (
+     L := source f;
      M := target f;
      N := source g;
+     -- TODO: should this be a separate strategy?
+     if not isFreeModule L then return (
+	 -- result may not be well-defined if L is not free,
+	 -- unless the composition h * syz p is zero
+	 p := coverMap L;
+	 h := quotient(f * p, g, Strategy => "Reflexive");
+	 -- TODO: does h * gens ker p != 0 suffice?
+	 if h * inducedMap(source p, kernel p) == 0 then map(N, L, h));
+     --
      if M.?generators then (
 	  M = cokernel presentation M;	    -- this doesn't change the cover
 	  );

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

@@ -152,8 +152,8 @@ Node
       reduction of @TT "f"@ modulo a Gröbner basis for the image of @TT "dual g"@.
       See @TO quotient@ for the dual notion.
 
-      If the remainder @TT "f - h*g"@ is zero, then the quotient @TT "g\\f"@
-      satisfies the equation @TT "f === (g\\f) * g"@. Otherwise, the equation
+      If the remainder @TT "f - h*g"@ is zero, then the quotient @TT "g\\\\f"@
+      satisfies the equation @TT "f === (g\\\\f) * g"@. Otherwise, the equation
       @TT "h * g + r === f"@ will hold, where @TT "r"@ is the map provided by
       @TO remainder'@.
     Example

M2/Macaulay2/packages/Macaulay2Doc/ov_system.m2

@@ -1870,7 +1870,12 @@ document { Key => "loadedFiles",
      PARA { "After each source file is successfully loaded, the full path to the file is stored in the hash table ", TO "loadedFiles", ".  It is stored as the
 	  value, with the corresponding key being a small integer, consecutively assigned, starting at 0."
 	  },
-     EXAMPLE "peek loadedFiles"}
+     EXAMPLE lines ///
+	loadedFiles#0
+        #loadedFiles
+     ///,
+     --SeeAlso => { "filesLoaded" },
+     }
 
 document { Key => "homeDirectory",
      Headline => "the home directory of the user",