From: piet-l@vanoostrum.org   
      
   asetofsymbols@gmail.com writes:   
      
   > a:=matrix[[i+j for i in 1..4] for j in 1..4]   
   >   
   > One can access the element i,j with   
   >   
   > a(i,j)   
   >   
   > But if i want a matrix of lists as   
   > a:=matrix[[[i,j] for i in 1..4] for j in 1..4]   
   >   
   > a(i,j) result to me can not return [i,j]   
   >   
   > Where is the error? What does it mean "SUB"?   
      
   Elements of a matrix must belong to a domain that is an Abelian monoid   
   (AbelianMonoid), and lists are not that. Therefore you cannot make a   
   matrix out of [[[i,j] for i in 1..4] for j in 1..4]   
      
   The consequence is that there is no function called 'matrix' that   
   applies. Then 'matrix' will be interpreted as a symbol, and the [...] as   
   a subscript, like in   
      
   (47) -> m[1]   
      
      (47)  m   
             1   
                                                                    Type: Symbol   
   (48) -> matrix[1]   
      
      (48)  matrix   
                  1   
                                                                   Type: Symbol   
   And the same when the expression between [...] is more complicated.   
      
   The reason that SUB is added is that the subscript is so long that it is   
   broken across lines and you probably would not recognize that it is a   
   subscript. So the SUB is there to remind you that it really is a   
   subscript operation that you see. If you make it smaller, it disappears:   
      
   (50) -> a := matrix [[[i,j] for i in 1..2] for j in 1..2]   
      
      (50)  matrix   
                  [[1, 1], [2, 1]], [[1, 2], [2, 2]]   
                                                                    Type: Symbol   
      
   You can also check that is a subscript expression with 'scripts':   
      
   (51) -> a := matrix [[[i,j] for i in 1..4] for j in 1..4]   
      
      (51)   
      SUB   
         matrix   
     ,   
           [[1, 1], [2, 1], [3, 1], [4, 1]], [[1, 2], [2, 2], [3, 2], [4, 2]]   
        ,   
           [[1, 3], [2, 3], [3, 3], [4, 3]], [[1, 4], [2, 4], [3, 4], [4, 4]]   
                                                                    Type: Symbol   
   (52) -> scripts a   
      
      (52)   
      [   
          sub   
        =   
          [[[1, 1], [2, 1], [3, 1], [4, 1]], [[1, 2], [2, 2], [3, 2], [4, 2]],   
           [[1, 3], [2, 3], [3, 3], [4, 3]], [[1, 4], [2, 4], [3, 4], [4, 4]]]   
        ,   
       sup = [], presup = [], presub = [], args = []]   
   Type: Record(sub: List(OutputForm),sup: List(OutputForm),presup:   
   List(OutputForm),presub: List(OutputForm),args: List(OutputForm))   
      
   > What about use as nxn matrix, list of list?   
   >   
   > Here   
   > b:=[[[i,j] for i in 1..4] for j in 1..4]   
   >   
   > here b.i.j return [i,j]   
   >   
   > But if with list of list one can have matrix types, why define a new type   
   Matrix?   
      
   Because Matrix does have additional operations, like matrix addition,   
   multiplication (if the elements come from a Ring) and inverse (if the   
   elements come from a Field).   
   --   
   Piet van Oostrum    
   WWW: http://piet.vanoostrum.org/   
   PGP key: [8DAE142BE17999C4]   
      
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