Update PositivityToricBundles to v1.8

M2/Macaulay2/packages/PositivityToricBundles.m2

@@ -7,8 +7,8 @@
 
 newPackage("PositivityToricBundles",
            Headline => "check positivity of toric vector bundles",
-           Version => "1.7",
-           Date => "April, 2024",
+           Version => "1.8",
+           Date => "July, 2024",
            Authors => { 
             {Name => "Andreas Hochenegger",
              Email => "[email protected]"}},
@@ -100,9 +100,11 @@ flags = method()
 flags (ToricVectorBundleKlyachko) := (cacheValue symbol filtrationFlags) ( tvb -> (
   hashTable for rho in rays tvb list (
    filtSteps := flatten entries (filtration tvb)#rho;
-   rho => for i in unique filtSteps list (
+   rayFlag := for i in unique filtSteps list (
     ((base tvb)#rho)_(positions(filtSteps, j->j<=i))
-   )
+   );
+   rayFlag = sort(rayFlag, mat -> numgens source mat);
+   rho => rayFlag
  )
 ))
 
@@ -1125,8 +1127,6 @@ document {
 --         If this changes at some point in the future, all tests will fail.
 
 -- Test 0
--- [RJS, Example 3.7]
-
 TEST ///
 -- This is [RJS, Example 3.7]
 -- auxiliary methods
@@ -1164,7 +1164,7 @@ assert(
         set {{0,2},{-1,0},{1,1}} } );
 ///
 
-
+-- Test 1
 TEST ///
 -- This is [RJS, Example 3.8] for d=2
 V = tangentBundle(projectiveSpaceFan 2);
@@ -1190,10 +1190,9 @@ assert(isVeryAmple V);
 
 assert(isNef V);
 assert(isAmple V);
-
 ///
 
-
+-- Test 2
 TEST ///
 -- This is [RJS, Example 3.8] for d=3
 V = tangentBundle(projectiveSpaceFan 3);
@@ -1221,9 +1220,9 @@ assert(isVeryAmple V);
 
 assert(isNef V);
 assert(isAmple V);
-
 ///
 
+-- Test 3
 TEST ///
 -- This is [RJS, Example 4.2] 
 -- auxiliary methods
@@ -1267,10 +1266,9 @@ assert(not isVeryAmple V);
 
 assert(isNef V);
 assert(isAmple V);
-
-
 ///
 
+-- Test 4
 TEST ///
 -- This is [RJS, Example 4.4] 
 -- auxiliary methods
@@ -1313,9 +1311,9 @@ assert(isVeryAmple V);
 
 assert(isNef V);
 assert(isAmple V);
-
 ///
 
+-- Test 5
 TEST ///
 -- This is [RJS, Example 6.4] 
 -- auxiliary methods
@@ -1358,10 +1356,9 @@ assert(not isVeryAmple V);
 
 assert(isNef V);
 assert(isAmple V);
-
 ///
 
-
+-- Test 6
 TEST ///
 -- Test with a randomized vector bundle on 3-dim variety
 
@@ -1420,11 +1417,9 @@ foundList = for i in 0 ..< #cList list (
 )
 
 assert(all(foundList, i->i>=0))
-
-
 ///
 
-
+-- Test 7
 TEST ///
 -- Test with a randomized vector bundle of rank 3 on hirzebruch
 
@@ -1480,11 +1475,9 @@ foundList = for i in 0 ..< #cList list (
 )
 
 assert(all(foundList, i->i>=0))
-
-
 ///
 
-
+-- Test 8
 TEST ///
 -- Test with a randomized vector bundle of rank 4 on hirzebruch
 
@@ -1540,7 +1533,35 @@ foundList = for i in 0 ..< #cList list (
 )
 
 assert(all(foundList, i->i>=0))
+///
 
+-- Test 9
+TEST ///
+-- Test whether the filtration steps obtained from the toric Chern character are correct
+-- Such a test would have failed before version 1.8, 
+-- because of a bug in the internal method flags:
+-- the method made an assumption on the form how the filtration steps are ordered 
+-- in the bundles generated by the package ToricVectorBundles. 
+-- Usually true, this assumption does not apply, if the bundle arises 
+-- by using the method dual of ToricVectorBundles (e.g. cotangent bundles).
+
+E = dual tangentBundle projectiveSpaceFan 2
+
+getCols = mat -> toList apply( 0..<numgens source mat, i->mat_i )
+
+filtE = applyValues(filtration E, filt -> flatten entries filt);
+raysE = keys filtE;
+filtFromTCC := applyPairs( toricChernCharacter E, (cone,us) -> 
+ cone => (
+  filtRay := for ray in getCols cone list sort apply(us, u -> ( (transpose matrix ray)*u)_(0,0))
+ )
+);
+
+applyPairs(filtFromTCC, (cone, filts) -> (
+  cone => for ray in getCols cone do
+           assert isMember( sort filtE#(matrix ray), filts)
+ )
+)
 ///
 
 end