local backup copy of HilbertSchemes.m2

Author: aalmousa

Positroid.m2

@@ -27,7 +27,8 @@ export{
     "basicPositroidVariety",	    	 -- NOT DOCUMENTED
     "leadTermBasicPositroid",	     	 -- NOT DOCUMENTED
     "leadTermBasicPositroidWrapAround",	 -- NOT DOCUMENTED
-    "hodgeDegenerationBasicPositroid"	 -- NOT DOCUMENTED
+    "hodgeDegenerationBasicPositroid",	 -- NOT DOCUMENTED
+    "getMultidegree"	    	    	 -- NOT DOCUMENTED
 }
 
 ------------------------------------------------------------------------------
@@ -246,13 +247,14 @@ hodgeDegenerationBasicPositroid(ZZ,ZZ,List,ZZ) := o -> (k,n,L,r) -> (
     if any(L, i-> i==1) and any(L, i-> i==n) then (
 	tabs := leadTermBasicPositroidWrapAround(k,n,L,r);
 	)
-    else (tabs := leadTermBasicPositroid(k,n,L,r));
+    else (tabs = leadTermBasicPositroid(k,n,L,r));
     ideal apply(tabs, tab -> product(apply(entries tab, i -> varHash#i)))
     );
 
 getMultidegree = method();
 
 getMultidegree(MonomialIdeal) := I -> (
+    t := symbol t;
     R := ring I;
     varList := R_*;
     n := last last baseName varList#(#varList-1);
@@ -339,6 +341,7 @@ end---------------------------------------------------------------------------
 ------------------------------------------------------------------------------
 ------------------------------------------------------------------------------
 
+I = 
 
 ---------------------
 --Ayah's sandbox
@@ -347,6 +350,7 @@ end---------------------------------------------------------------------------
 I1 = hodgeDegenerationBasicPositroid(3,6,{5,6,1,2,3},2);
 I2 = sub(hodgeDegenerationBasicPositroid(3,6,{1,2},1),ring I1);
 I = I1+I2;
+getMultidegree monomialIdeal I
 codim I
 
 J2 = sub(hodgeDegenerationBasicPositroid(3,6,{6,1,2},1),ring I1);

symInvariant.m2

@@ -285,15 +285,18 @@ netList listFacetGens(L,2,2)
 ----------------------------
 -*
 1 1 0      
-1 0 1 
+1 0 1
+0 1 1 
 *-
 
-Q = ZZ/101[x_(1,1)..x_(2,3)];
-I = ideal(x_(1,1)*x_(1,2)*x_(2,1)*x_(2,3));
-L = (idealSym(I,2,3,5))/monomialIdeal;
+Q = ZZ/101[x_(1,1)..x_(3,3)];
+I = ideal(x_(1,1)*x_(1,2)*x_(2,1)*x_(2,3)*x_(3,2)*x_(3,3));
+L = (idealSym(I,3,3,6))/monomialIdeal;
 
-netList listDualGens(L,2,3)
-netList listFacetGens(L,2,3)
+netList listDualGens(L,3,3)
+
+apply(listDualGens(L,3,3), i-> #i)
+netList listFacetGens(L,3,3)
 
 ------------------------------------
 --Examples: 2-orbits, coprime
@@ -315,6 +318,8 @@ L1 = (idealSym(I1,2,2,5))/monomialIdeal
 L2 = (idealSym(I2,2,2,5))/monomialIdeal
 L = (idealSym(I,2,2,5))/monomialIdeal
 
+apply(listDualGens(L,2,2), i-> #i)
+
 --List the Alexander dual generators for L1, L2, and L
 netList {listDualGens(L1,2,2), listDualGens(L2,2,2), listDualGens(L,2,2)}
 -
@@ -451,6 +456,7 @@ L1 = (idealSym(I1,3,3,5))/monomialIdeal;
 L2 = (idealSym(I2,3,3,5))/monomialIdeal;
 L = (idealSym(I,3,3,5))/monomialIdeal;
 
+apply(listDualGens(L,3,3), i-> #i)
 
 netList {listDualGens(L1,3,3), listDualGens(L2,3,3), listDualGens(L,3,3)}