merging

MatrixSchubert/MatrixSchubertConstructionsDOC.m2

@@ -324,7 +324,7 @@ doc ///
 	    # pipeDreams w == # (decompose inI)
 	Text
 	    To read off an associated prime of the antidiagonal initial ideal from a pipe dream,
-	    one reads off the + tiles from the grid. When there is a + in location (i,j), then $z_{i,j}$ 
+	    one reads off the + tiles from the grid. When there is a + in location $(i,j)$, then $z_{i,j}$ 
 	    is a generator of the associated prime in question.
 	Example
 	    netList ((pipeDreams w)_0)
@@ -718,7 +718,7 @@ doc ///
     	:Ideal
     Description
         Text
-            Given a permutation in 1-line notation or, more generally, a partial alternating sign matrix, outputs the associated alternating sign matrix ideal (which is called a Schubert determinantal ideal in the case of a permutation).  (The convention throughout this package is that the permutation matrix of a pemutation w has 1's in positions (i,w(i)).)
+            Given a permutation in 1-line notation or, more generally, a partial alternating sign matrix, outputs the associated alternating sign matrix ideal (which is called a Schubert determinantal ideal in the case of a permutation).  (The convention throughout this package is that the permutation matrix of a pemutation $w$ has 1's in positions $(i,w(i))$.)
 
 	    This function computes over the coefficient field of rational numbers unless an alternative is specified.
         Example

MatrixSchubert/MatrixSchubertInvariantsDOC.m2

@@ -99,7 +99,7 @@ doc ///
         -- :PolynomialRing --Not sure what to put here, PolynomialRing makes the compiler angry
     Description
         Text
-            Given a partial ASM $A$, compute the K Polynomial of its corresponding Ideal, defined as the numerator of its Hilbert series. The multi-degree variables are indexed along rows.
+            Given a partial ASM $A$, compute the K-polynomial of its corresponding Ideal, defined as the numerator of its Hilbert series. The multidegree variables are indexed along rows.
         Example
             A = matrix{{0,0,0,1},{0,1,0,0},{1,-1,1,0},{0,1,0,0}};
             KPolynomialASM A

MatrixSchubert/permutationMethodsDOC.m2

@@ -542,7 +542,7 @@ doc ///
         w:List
     Description
         Text
-            Given a permutation in one line notation, finds the set of reduced pipe dreams. Each element of the output is a square array containing "+" and "/" symbols. The "+" symbols are interpreted as crossing tiles and the "/" are interpreted as bump tiles. Starting on the left edge, the path starting at row i will end at column w(i). This function only returns reduced pipe dreams (i.e. pipe dreams for which each pair of pipes crosses at most once).
+            Given a permutation in one line notation, finds the set of reduced pipe dreams. Each element of the output is a square array containing "+" and "/" symbols. The "+" symbols are interpreted as crossing tiles and the "/" are interpreted as bump tiles. Starting on the left edge, the path starting at row $i$ will end at column $w_i$. This function only returns reduced pipe dreams (i.e. pipe dreams for which each pair of pipes crosses at most once).
         Example
             w = {2,1,4,3,6,5};
             netList (pipeDreams w)_0
@@ -562,7 +562,7 @@ doc ///
         w:List
     Description
         Text
-            Given a permutation in one line notation, finds the set of  pipe dreams. Each element of the output is a square array containing "+" and "/" symbols. The "+" symbols are interpreted as crossing tiles and the "/" are interpreted as bump tiles. Starting on the left edge, the path starting at row i will end at column w(i). This function returns all pipe dreams of w, including those containing pairs of pipes that cross more than once.
+            Given a permutation in one line notation, finds the set of  pipe dreams. Each element of the output is a square array containing "+" and "/" symbols. The "+" symbols are interpreted as crossing tiles and the "/" are interpreted as bump tiles. Starting on the left edge, the path starting at row $i$ will end at column $w_i$. This function returns all pipe dreams of w, including those containing pairs of pipes that cross more than once.
         Example
             w = {2,1,4,3,6,5};
             netList (pipeDreamsNonReduced w)_1