1 files changed, 83 insertions, 1 deletions
diff --git a/src/algebra/matcat.spad.pamphlet b/src/algebra/matcat.spad.pamphlet
index 0a74157c..c895e038 100644
--- a/src/algebra/matcat.spad.pamphlet
+++ b/src/algebra/matcat.spad.pamphlet
@@ -569,8 +569,90 @@ RectangularMatrixCategory(m,n,R,Row,Col): Category == Definition where
   Row : DirectProductCategory(n,R)
   Col : DirectProductCategory(m,R)
 
-  Definition == Join(MatrixCategory(R,Row,Col),BiModule(R,R)) with
+  Definition ==> Join(BiModule(R,R),HomogeneousAggregate(R)) with
+
+    finiteAggregate
+      ++ matrices are finite
+
     if R has CommutativeRing then Module(R)
+
+--% Matrix creation
+
+    matrix: List List R -> %
+      ++ \spad{matrix(l)} converts the list of lists l to a matrix, where the
+      ++ list of lists is viewed as a list of the rows of the matrix.
+
+--% Predicates
+
+    square?  : % -> Boolean
+      ++ \spad{square?(m)} returns true if m is a square matrix (i.e. if m
+      ++ has the same number of rows as columns) and false otherwise.
+    diagonal?: % -> Boolean
+      ++ \spad{diagonal?(m)} returns true if the matrix m is square and diagonal
+      ++ (i.e. all entries of m not on the diagonal are zero) and false
+      ++ otherwise.
+    symmetric?: % -> Boolean
+      ++ \spad{symmetric?(m)} returns true if the matrix m is square and
+      ++ symmetric (i.e. \spad{m[i,j] = m[j,i]} for all \spad{i} and j) and
+      ++ false otherwise.
+    antisymmetric?: % -> Boolean
+      ++ \spad{antisymmetric?(m)} returns true if the matrix m is square and
+      ++ antisymmetric (i.e. \spad{m[i,j] = -m[j,i]} for all \spad{i} and j)
+      ++ and false otherwise.
+
+--% Size inquiries
+
+    minRowIndex : % -> Integer
+      ++ \spad{minRowIndex(m)} returns the index of the 'first' row of the
+      ++ matrix m.
+    maxRowIndex : % -> Integer
+      ++ \spad{maxRowIndex(m)} returns the index of the 'last' row of the
+      ++ matrix m.
+    minColIndex : % -> Integer
+      ++ \spad{minColIndex(m)} returns the index of the 'first' column of the
+      ++ matrix m.
+    maxColIndex : % -> Integer
+      ++ \spad{maxColIndex(m)} returns the index of the 'last' column of the
+      ++ matrix m.
+    nrows : % -> NonNegativeInteger
+      ++ \spad{nrows(m)} returns the number of rows in the matrix m.
+    ncols : % -> NonNegativeInteger
+      ++ \spad{ncols(m)} returns the number of columns in the matrix m.
+
+--% Part extractions
+
+    listOfLists: % -> List List R
+      ++ \spad{listOfLists(m)} returns the rows of the matrix m as a list
+      ++ of lists.
+    elt: (%,Integer,Integer) -> R
+      ++ \spad{elt(m,i,j)} returns the element in the \spad{i}th row and
+      ++ \spad{j}th column of the matrix m.
+      ++ Error: if indices are outside the proper
+      ++ ranges.
+    qelt: (%,Integer,Integer) -> R
+      ++ \spad{qelt(m,i,j)} returns the element in the \spad{i}th row and
+      ++ \spad{j}th column of
+      ++ the matrix m. Note: there is NO error check to determine if indices are
+      ++ in the proper ranges.
+    elt: (%,Integer,Integer,R) -> R
+      ++ \spad{elt(m,i,j,r)} returns the element in the \spad{i}th row and
+      ++ \spad{j}th column of the matrix m, if m has an \spad{i}th row and a
+      ++ \spad{j}th column, and returns r otherwise.
+    row: (%,Integer) -> Row
+      ++ \spad{row(m,i)} returns the \spad{i}th row of the matrix m.
+      ++ Error: if the index is outside the proper range.
+    column: (%,Integer) -> Col
+      ++ \spad{column(m,j)} returns the \spad{j}th column of the matrix m.
+      ++ Error: if the index outside the proper range.
+
+--% Map and Zip
+
+    map: (R -> R,%) -> %
+      ++ \spad{map(f,a)} returns b, where \spad{b(i,j) = a(i,j)} for all i, j.
+    map:((R,R) -> R,%,%) -> %
+      ++ \spad{map(f,a,b)} returns c, where c is such that
+      ++ \spad{c(i,j) = f(a(i,j),b(i,j))} for all \spad{i}, j.
+
 --% Arithmetic
 
     if R has IntegralDomain then