[Axiom-developer] Re: [fricas-devel] Re: RectangularMatrixCategory should have Finite

[Martin Rubey]

Dear Waldek, Gaby, Tim,

below a patch that makes RMATCAT Finite if it is.  A testcase is

R==>RectangularMatrix(2,4, PF 2)
every?(zero?, [lookup(index(i))$R - i for i in 1..2^8])

should give true.

I slightly extended the documentation of HOAGG, since, when I read the
original, I was first led to believe that *domains* that have finiteAggregate
would be finite.  Although the docstring doesn't say that, of course.

Martin



Index: aggcat.spad.pamphlet
===================================================================
--- aggcat.spad.pamphlet        (Revision 150)
+++ aggcat.spad.pamphlet        (Arbeitskopie)
@@ -82,9 +82,31 @@
 ++ In the current system, all aggregates are homogeneous.
 ++ Two attributes characterize classes of aggregates.
 ++ Aggregates from domains with attribute \spadatt{finiteAggregate}
-++ have a finite number of members.
-++ Those with attribute \spadatt{shallowlyMutable} allow an element
+++ have a finite number of members. Of course, such a domain may have an
+++ infinite number of elements, like, for example \spadtype{List}.
+++ Those domains with attribute \spadatt{shallowlyMutable} allow an element  
 ++ to be modified or updated without changing its overall value.
+@
+
+It would probably make sense to make [[HOAGG S]] export [[Finite]], when this
+is the case.  The following modifications would be necessary:
+\begin{itemize}
+\item we need another attribute, say, [[constantSizeAggregate]], that says that
+  each aggregate has the same number of members.
+\item we need a way to construct an aggregate given a list of its parts, i.e.,
+  an operation
+\begin{verbatim}
+    construct: List R -> %
+\end{verbatim}
+\end{itemize}
+Then, the exports of [[Finite]] could be implemented similar to
+[[RectangularMatrixCategory]].
+
+We should also consider making [[finiteAggregate]] and
+[[constantSizeAggregate]] categories, rather than attributes.  This would make
+a lot of things cleaner.
+
+<<category HOAGG HomogeneousAggregate>>=
 HomogeneousAggregate(S:Type): Category == Aggregate with
    if S has SetCategory then SetCategory
    if S has SetCategory then
Index: matcat.spad.pamphlet
===================================================================
--- matcat.spad.pamphlet        (Revision 150)
+++ matcat.spad.pamphlet        (Arbeitskopie)
@@ -570,6 +570,8 @@
     finiteAggregate
       ++ matrices are finite
 
+    if R has Finite then Finite
+
     if R has CommutativeRing then Module(R)
 
 --% Matrix creation
@@ -674,6 +676,38 @@
         ++ \spad{nullSpace(m)}+ returns a basis for the null space of
         ++ the matrix m.
    add
+
+     if R has Finite then
+         size() == (size()$R)**(m*n)
+
+         random() == matrix [[random()$R for i in 1..m] for j in 1..n]
+
+         lookup x ==
+             s := size()$R
+             pow: Integer := 1
+             l := listOfLists(x)
+             res: Integer := 1
+             for r in l repeat
+                 for c in r repeat
+                     res := res + (lookup(c)$R-1)*pow
+                     pow := pow*s
+             res::PositiveInteger
+
+         index i ==
+             s := size()$R
+             old := divide(i-1, s)
+             res: List List R := []
+            
+             for i in 1..m repeat
+                 row: List R := []
+                 for j in 1..n repeat
+                     el:R := index((old.remainder + 1)::PositiveInteger)$R
+                     row := cons(el, row)
+                     old := divide(old.quotient, s)
+                 res := cons(reverse! row, res)
+
+             matrix reverse! res
+
      nrows x == m
      ncols x == n
      square? x == m = n