fixed a couple of issues in SpectralSequences

Author: mahrud

M2/Macaulay2/packages/SpectralSequences.m2

@@ -68,7 +68,7 @@ export {
     "targetPruningMap",
     "Page",
     "PageMap",
-    "page" ,
+    "page",
     "pruningMaps",
     "edgeComplex",
     "filteredHomologyObject",
@@ -608,6 +608,7 @@ page SpectralSequencePage := Page => opts -> E -> (
 	    );
 	);
     H)
+page Page := Page => opts -> identity
 
 -- the following two methods are used to view the modules
 -- on the r th page in grid form.
@@ -745,9 +746,9 @@ connectingMorphism(ComplexMap, ZZ) := (a, n) -> (
     e := spectralSequence K;
     e^1 .dd_{1, n})
 
-hilbertPolynomial SpectralSequencePage := Page => o -> E -> (
+hilbertPolynomial Page := Page => o -> E -> (
     P := new Page;
-    apply(spots E .dd, i -> P#i = hilbertPolynomial(E_i));
+    apply(spots page E, i -> P#i = hilbertPolynomial(E_i));
     P)
 
 pruningMaps = method()
@@ -759,7 +760,7 @@ pruningMaps SpectralSequencePage := E -> (
     P)
 
 basis(ZZ,   SpectralSequencePage) :=
-basis(List, SpectralSequencePage) := opts -> (deg, E) -> (
+basis(List, SpectralSequencePage) := Page => opts -> (deg, E) -> (
     P := new Page;
     apply(spots E.dd, i -> P#i = basis(deg,E_i));
     P)

M2/Macaulay2/packages/SpectralSequences/docs.m2

@@ -10,6 +10,7 @@ undocumented {
     (net, PageMap),
     (net, SpectralSequence),
     (net, SpectralSequencePage),
+    (page, Page),
     (page, SpectralSequencePage),
     (ring, Page),
     (spots, PageMap),
@@ -925,7 +926,7 @@ doc ///
 	> "minimalPresentation(SpectralSequencePage)"
 	> "pruningMaps(SpectralSequencePage)"
 	> "basis(List,SpectralSequencePage)"
-	> "hilbertPolynomial(SpectralSequencePage)"
+	> "hilbertPolynomial(Page)"
 	> "SpectralSequencePage ^ List"
   Caveat
       The isomorphisms $4$ and $4$' are not explicitly
@@ -1108,18 +1109,18 @@ doc ///
 
 doc ///
   Key
-    (hilbertPolynomial, SpectralSequencePage)
+    (hilbertPolynomial, Page)
   Headline
-    the Hilbert polynomial of a spectral sequence page
+    the Hilbert polynomial of a page
   Usage
     H = hilbertPolynomial(E)
   Inputs
-    E:SpectralSequencePage
+    E:Page
   Outputs
       H:Page
   Description
     Text
-      Returns the Hilbert polynomials of all modules of the spectral sequence page
+      Returns the Hilbert polynomials of all modules in a page.
 
       As a specific example consider the filtered complex $K$ below, obtained by multiplying the minimal free resolution of
       the rational quartic space curve by successive powers of the irrelevant ideal.